Showing papers in "International Journal for Numerical Methods in Fluids in 1995"
TL;DR: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed and is called the reproducingkernel particle method (RKPM).
Abstract: A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element-free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods; however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducing kernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C∞, the solution and its derivatives are also C∞ in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two-dimensional examples of advection-diffusion equations and compressible Euler equations are also presented together with 2D multiple-scale decompositions.
2,682 citations
TL;DR: A novel algorithm is outlined which can be used for the solution of both compressible and incompressible Navier-Stokes or Euler equations and introduces a rational form of balancing dissipation.
Abstract: We outline the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier-Stokes or Euler equations. Full incompressibility can be dealt with if the algorithm is used in its semi-explicit corm and its structure permits arbitrary interpolation cunctions to be used avoiding the Babuska-Brezzi restriction. In a fully explicit version it introduces a rational form of balancing dissipation avoiding the use of arbitrary parameters and forms for this
395 citations
TL;DR: A three-field arbitrary Lagrangian-Eulerian (ALE) finite element/volume formulation for coupled transient aeroelastic problems is presented and a rigorous derivation of a geometric conservation law for flow problems with moving boundaries and unstructured deformable meshes is included.
Abstract: A three-field arbitrary Lagrangian-Eulerian (ALE) finite element/volume formulation for coupled transient aeroelastic problems is presented The description includes a rigorous derivation of a geometric conservation law for flow problems with moving boundaries and unstructured deformable meshes The solution of the coupled governing equations with a mixed explicit (fluid)/implicit (structure) staggered procedure is discussed with particular reference to accuracy, stability, distributed computing, I/O transfers, subcycling and parallel processing A general and flexible framework for implementing partitioned solution procedures for coupled aeroelastic problems on heterogeneous and/or parallel computational platforms is described This framework and the explicit/implicit partitioned procedures are demonstrated with the numerical investigation on an iPSC-860 massively parallel processor of the instability of flat panels with infinite aspect ratio in supersonic airstreams
368 citations
TL;DR: In this article, the Navier-Stokes equations were approximated to fourth-order accuracy with stencils extending only over a 3 x 3 square of points, and the key advantage of the new compact 4-order scheme is that it allows direct iteration for low-to-mediwn Reynolds numbers.
Abstract: SUMMARY We note in this study that the Navier-Stokes equations, when expressed in streamfunction-vorticity fonn, can be approximated to fourth--order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth-order scheme is that it allows direct iteration for low~to-mediwn Reynolds numbers. Numerical solutions are obtained for the model problem of the driven cavity and compared with solutions available in the literature. For Re $1500 point-SOR iteration is used and the convergence is fast.
238 citations
TL;DR: In this paper, multiple scale methods based on reproducing kernel and wavelet analysis are developed, which permit the response of a system to be separated into different scales, which can be either the wave numbers corresponding to spatial variables or the frequencies corresponding to temporal variables.
Abstract: Multiple scale methods based on reproducing kernel and wavelet analysis are developed. These permit the response of a system to be separated into different scales. These scales can be either the wave numbers corresponding to spatial variables or the frequencies corresponding to temporal variables, and each scale response can be examined separately. This complete characterization of the unknown response is performed through the integral window transform, and a space-scale and time-frequency localization process is achieved by dilating the flexible multiple scale window function. An error estimation technique based on this decomposition algorithm is developed which is especially useful for local mesh refinement and convergence studies. This flexible space-scale window function can be constructed to resemble the well-known unstructured multigrid and hp-adaptive finite element methods. However, the multiple scale adaptive refinements are performed simply by inserting nodes into the highest wavelet scale solution region and at the same time narrowing the window function. Hence hp-like adaptive refinements can be performed without a mesh.
222 citations
TL;DR: In this article, a fully coupled numerical model to simulate the slow transient phenomena involving heat and mass transfer in deforming porous media is developed, which makes use of the modified effective stress concept together with the capillary pressure relationship.
Abstract: A fully coupled numerical model to simulate the slow transient phenomena involving heat and mass transfer in deforming porous media is developed. It makes use of the modified effective stress concept together with the capillary pressure relationship. The heat transfer through conduction and convection as well as the latent heat transfer (evaporation and/or condensation) is taken into account.
The governing equations in terms of displacements, temperature, capillary pressure and gas pressure are coupled non-linear differential equatiosn and are solved by the finite element method.
The model is validated with respect to a documented experiment on semisaturated soil behaviour. Two other examples involving subsidence due to pumping from a phreatic aquifer and thermoelastic consolidation of saturated and semisaturated media are also presented.
162 citations
TL;DR: In this paper, the authors proposed a robust deferred-correction solution method and simple flux-limiter techniques for steady, quasi-one-dimensional flow, where the grid is aligned with the main flow direction.
Abstract: In many areas of computational fluid dynamics, especially numerical convective heat and mass transfer, the «Hybrid» and «Power-Law» schemes have been widely used for many years. The popularity of these methods for steady-state computations is based on a combination of algorithmic simplicity, fast convergence, and plausible looking results. By contrast, classical (second-order central) methods often involve convergence problems and may lead to obviously unphysical solutions exhibiting spurious numerical oscillations. Hybrid, Power-Law, and the exponential-difference scheme on which they are based give reasonably accurate solutions for steady, quasi-one-dimensional flow (when the grid is aligned with the main flow direction). However, they are often also used, out of context, for flows oblique or skew to the grid, in which case, inherent artificial viscosity (or diffusivity) seriously degrades the solution. This is particularly troublesome in the case of recirculating flows, sometimes leading to qualitatively incorrect results-since the effective artificial numerical Reynolds (or Peclet) number may then be orders of magnitude less than the correct physical value. This is demonstrated in the case of thermally driven flow in tall cavities, where experimentally observed recirculation cells are not predicted by the exponential-based schemes. Higher-order methods correctly predict the onset of recirculation cells. In the past, higher-order methods have not been popular because of convergence difficulties and a tendency to generate unphysical overshoots near (what should be) sharp, monotonic transitions. However, recent developments using robust deferred-correction solution methods and simple flux-limiter techniques have eliminated all of these difficulties. Highly accurate, physically correct solutions can now be obtained at optimum computational efficiency
155 citations
TL;DR: In this paper, a large-scale finite element formulation of 3D, unsteady incompressible flows, including those involving fluid-structure interactions, is presented, with time-varying spatial domains based on the deforming spatial domaidstabilized spacetime (DSD/SST) formulation.
Abstract: SUMMARY Massively parallel finite element computations of 3D, unsteady incompressible flows, including those involving fluid-structure interactions, are presented. The computations with time-varying spatial domains are based on the deforming spatial domaidstabilized spacetime (DSD/SST) finite element formulation. The capability to solve 3D problems involving fluid-structure interactions is demonstrated by investigating the dynamics of a flexible cantilevered pipe conveying fluid. Computations of flow past a stationary rectangular wing at Reynolds number 1000, 2500 and lo7 reveal interesting flow patterns. In these computations, at each time step approximately 3 x lo6 non-linear equations are solved to update the flow field. Also, preliminary results are presented for flow past a wing in flapping motion. In this case a specially designed mesh moving scheme is employed to eliminate the need for remeshing. All these computations are canied out on the Amy High Performance Computing Research Center supercomputers CM-200 and CM-5, with major speed-ups compared with traditional supercomputers. The coupled equation systems arising from the finite element discretizations of these large-scale problems are solved iteratively with diagonal preconditioners. In some cases, to reduce the memory requirements even further, these iterations are carried out with a matrix-fiee strategy. The finite element formulations and their parallel implementations assume unstructured meshes.
146 citations
TL;DR: In this paper, an algorithm is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent performance, such as nearly incompressible, viscous, flows through transonic applications to high speed flows with shocks.
Abstract: An algorithm is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent performance. Examples range from nearly incompressible, viscous, flows through transonic applications to high speed flows with shocks. In most examples linear triangular elements are used in the finite element approximation, but some use of quadratic approximation, again in triangles, indicates satisfactory performance even in the case of severe shocks
137 citations
TL;DR: In this paper, a staggered spectral element model for the solution of the oceanic shallow water equations is presented, and both an implicit and an explicit time integration scheme are compared, showing the performance of the implicit scheme to lag that of the explicit scheme because of the unpreconditioned implementation of GMRES.
Abstract: A staggered spectral element model for the solution of the oceanic shallow water equations is presented. We introduce and compare both an implicit and an explicit time integration scheme. The former splits the equations with the operator-integration factor method and solves the resulting algebraic system with generalized minimum residual (GMRES) iterations. Comparison of the two schemes shows the performance of the implicit scheme to lag that of the explicit scheme because of the unpreconditioned implementation of GMRES. The explicit code is successfully applied to various geophysical flows in idealized and realistic basins, notably to the wind-driven circulation in the North Atlantic Ocean. The last experiment reveals the geometric versatility of the spectral element method and the effectiveness of the staggering in eliminating sprious pressure modes when the flow is nearly non-divergent.
123 citations
TL;DR: An efficient 2D non-linear numerical wave tank called LONGTANK has been developed based on a multi-subdomain (MSD) approach combined with the conventional boundary element method (BEM) to minimize the computing time and reserved storage.
Abstract: An efficient 2D non-linear numerical wave tank called LONGTANK has been developed based on a multi-subdomain (MSD) approach combined with the conventional boundary element method (BEM). The multi-subdomain approach aims at optimized matrix diagonalization, thus minimizing the computing time and reserved storage. The CPU per time step in LONGTANK simulation is found to increase only linearly with the number of surface nodes, which makes LONGTANK highly efficient especially when simulating long-time wave evolutions in space.
Appropriate treatment of special points on the boundary ensures high resolution in LONGTANK simulation beyond initial deformation and breaking, which allows detailed study of breaking criterion, breaker morphology, breaking dissipation, vorticity generation, etc.
Detailed numerical implementation has been given with demonstration of LONGTANK simulations.
TL;DR: A unified formulation of non-oscillatory discretization schemes for the calculation of compressible flows on both structured and unstructured meshes is presented.
Abstract: SUMMARY A unified theory of non-oscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated on either structured or unstructured meshes. The second part examines the application of similar ideas to the treatment of systems of conservation laws. An analysis of discrete shock structure leads to conditions on the numerical flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a convective upwind and split pressure (CUSP) scheme, in which the coefficient of the pressure differences is fully determined by the coefficient of convective diffusion. Numerical results are presmted which confirm the properties of these schemes. This paper presents a unified formulation of non-oscillatory discretization schemes for the calculation of compressible flows on both structured and unstructured meshes. Over the past decade the principles underlying the design of non-oscillatory discretization schemes have been quite well established, and numerous variations of artificial diffusion, upwind biasing and flux splitting have been proposed and tested.' - * The non-oscillatory properties of the schemes analysed here are secured through the introduction of artificial viscosity which produces an upwind bias. This exactly reproduces an upwind scheme when the minimum sufficient amount of viscosity is used. Higher-order accuracy is obtained by the use of higher-order diffusive terms, with limiters to preserve monotonicity constraints. Schemes which blend low and high-order diffusion,' and both symmetric and upstream constructions using anti-diffusive terms controlled by limiters,' are readily included within the framework of this paper. Two main issues arise in the design of non-oscillatory discrete schemes. First there is the issue of how to construct an approximation to a scalar convection or convection-diffusion equation which is non-oscillatory, captures discontinuities with high resolution, and is sufficiently accurate. Second there is the issue of how to construct a numerical flux for a system of equations with waves travelling at different speeds, and sometimes in opposite directions. These two issues can be treated essentially independently, and by combining alternative non-oscillatory formulations with different constructions of the numerical flux one arrives at a matrix of candidate high
TL;DR: The flow problems the authors consider typically come from aerospace applications, including those in 3D and those involving moving boundaries interacting with boundary layers and shocks, and are solved using the deformable-spatial-domain/stabilized-space-time (DSD/SST) formulation.
Abstract: Massively parallel finite element computations of the compressible Euler and Navier-Stokes equations using parallel supercomputers are presented. The finite element formulations are based on the conservation variables and the streamline-upwind/Petrov-Galerkin (SUPG) stabilization method is used to prevent potential numerial oscillations due to dominant advection terms. These computations are based on both implicit and explicit methods and their parallel implementation assumes that the mesh is unstructured. The implicit computations are based on iterative strategies. Large-scale 3D problems are solved using a matrix-free iteration technique which reduces the memory requirements significantly. The flow problems we consider typically come from aerospace applications, including those in 3D and those involving moving boundaries interacting with boundary layers and shocks. Problems with fixed boundaries are solved using a semidiscrete formulation and the ones involving moving boundaries are solved using the deformable-spatial-domain/stabilized-space-time (DSD/SST) formulation.
TL;DR: An agglomeration multigrid strategy is developed and implemented for the solution of three-dimensional steady viscous flows that enables convergence acceleration with minimal additional memory overheads, and is completely automated, in that it can deal with grids of arbitrary construction.
Abstract: An agglomeration multigrid strategy is developed and implemented for the solution of three-dimensional steady viscous flows. The method enables convergence acceleration with minimal additional memory overheads, and is completely automated, in that it can deal with grids of arbitrary construction. The multigrid technique is validated by comparing the delivered convergence rates with those obtained by a previously developed overset-mesh multigrid approach, and by demonstrating grid independent convergence rates for aerodynamic problems on very large grids. Prospects for further increases in multigrid efficiency for high-Reynolds number viscous flows on highly stretched meshes are discussed.
TL;DR: In this paper, a new algorithm for the solution of the shallow water equations is introduced, based on a suitable operator-splitting procedure for which a characteristic-based rational form of including balancing dissipation terms is achieved.
Abstract: A new algorithm for the solution of the shallow water equations is introduced. The formulation is founded on a suitable operator-splitting procedure for which a characteristic-based rational form of including balancing dissipation terms is achieved. In the semi-explicit form the method circumvents the requirement of a critical time step given in terms of the wave celerity, which is restrictive for the analysis of long-wave propagation in shallow waters. In this work the robustness of the algorithm is illustrated for transient shallow water problems and for some supercritical flows, where the choice of an algorithm with optimal diffusion properties is manifest
TL;DR: In this article, boundary value problems for Stokes and Navier-Stokes equations with non-standard boundary conditions are studied, where the pressure or its normal derivative is given on some part of the boundary or the pressure is given up to a constant but given velocity flux.
Abstract: Boundary value problems for Stokes and Navier-Stokes equations with non-standard boundary conditions are studied. Included is the case where the pressure or its normal derivative is given on some part of the boundary or the pressure is given up to a constant but given velocity flux. First, a variational formulation is introduced which is shown to be equivalent to the Stokes equations with the non-standard boundary conditions under consideration. The existence and uniqueness of the solution of the variational problem are studied. Secondly, most of the results obtained for the Stokes equations are extended to the case of the Navier-Stokes equations. The final section is devoted to numerical experiments, flows in pipes and physiological flows.
TL;DR: In this article, the authors used a fractional step procedure with high-order spatial discretization to solve the pressure Poisson equation of a flow past a normal flat plate at low Reynolds numbers.
Abstract: Well-resolved two-dimensional numerical simulations of the unsteady separated flow past a normal flat plate at low Reynolds numbers have been performed using a fractional step procedure with high-order spatial discretization. A fifth-order upwind-biased scheme is used for the convective terms and the diffusive terms are represented by a fourth-order central difference scheme. The pressure Poisson equation is solved using a direct method based on eigenvalue decomposition of the coefficient matrix. A systematic study of the flow has been conducted with high temporal and spatial resolutions for a series of Reynolds numbers. The interactions of the vortices shed form the shear layers in the near-and far-wake regions are studied. For Reynolds numbers less than 250 the vortices are observed to convect parallel to the freestream. However, at higher Reynolds numbers (500 and 1000), complex interactions including vortex pairing, tearing and deformations are seen to occur in the far-wake region. Values of the drag coefficient and the wake closure length are presented and compared with previous experimental and numerical studies.
TL;DR: A time-accurate, finite volume method for solving the three-dimensional, incompressible Navier-Stokes equations on a composite grid with arbitrary subgrid overlapping is presented.
Abstract: A time-accurate, finite volume method for solving the three-dimensional, incompressible Navier-Stokes equations on a composite grid with arbitrary subgrid overlapping is presented. The governing equations are written in a non-orthogonal curvilinear co-ordinate system and are discretized on a non-staggered grid. A semi-implicit, fractional step method with approximate factorization is employed for time advancement. Multigrid combined with intergrid iteration is used to solve the pressure Poisson equation. Inter-grid communication is facilitated by an iterative boundary velocity scheme which ensures that the governing equations are well-posed on each subdomain. Mass conservation on each subdomain is preserved by using a mass imbalance correction scheme which is second-order-accurate. Three test cases are used to demonstrate the method's consistency, accuracy and efficiency
TL;DR: In this article, a model for simulating the process of mold filling in castings is presented, which involves an explicit finite element solution of a pure advection equation, and the free metal surface is predicted by advecting a pseudo-concentration function via the computed flow field.
Abstract: A model for simulating the process of mould filling in castings is presented. Many defects in a casting have their origins at the filling stage. Numerical simulation of this process can be of immense practical benefit to the foundry industry, however a rigorous analysis of this process must model a wide range of complex physical phenomena. In order to contain the costs and complexity that would be necessary for such a model, certain simplifying assumptions have been made. These assumptions limit the scope of this model to only predicting realistic thermal fields during the filling process. A laminar regime has been assumed for the flow field, which is obtained by solving the incompressible Wavier-Stokes equations using a velocity-pressure segregated semi-implicit finite element method. The free metal surface is predicted by advecting a pseudo-concentration function via the computed flow field. This involves an explicit finite element solution of a pure advection equation. The thermal field is calculated by solving the convective-diffusive energy equation by an explicit finite element method using the computed flow field and the location of the free surface. All the advection terms are discretized using a Taylor-Galerkin method. The interface between the metal and mould is modelled using special interface elements. The model is demonstrated by solving practical example problems. The results show that a sharp thermal front is maintained during the course of filling without excessive diffusion. The heat diffusion in the mould can be controlled by varying the metal mould heat transfer coefficient
TL;DR: A TVD version of the Lax-Wendroff scheme is used and its performance is shown in ID and 2D computations and the capability of this class of schemes to handle geometric source terms that arise to model the bottom variation is investigated.
Abstract: SUMMARY The inviscid shallow water equations provide a genuinely hyperbolic system and all the numerical tools that have been developed for a system of conservation laws can be applied to them. However, this system of equations presents some peculiarities that can be exploited when developing a numerical method based on Roe’s Riemann solver and enhanced by a slope limiting of MUSCL type. In the present paper a TVD version of the Lax-Wendroff scheme is used and its performance is shown in ID and 2D computations. Then two specific difficulties that arise in this context are investigated. The former is the capability of this class of schemes to handle geometric source terms that arise to model the bottom variation. The latter analysis pertains to situations in which strict hyperbolicity is lost, i.e. when two eigenvalues collapse into one.
TL;DR: In this paper, the Lagrange multiplier approach is applied to the solution of flow problems including external incompressible viscous flow modelled by the Navier-Stokes equations and then to an optimal shape problem for Stokes and Navier Stokes flow.
Abstract: In this article we discuss the fictitious domain solution of the Navier-Stokes equations modelling unsteady incompressible viscous flow. The method is based on a Lagrange multiplier treatment of the boundary conditions to be satisfied and is particularly well suited to the treatment of no-slip boundary conditions. This approach allows the use of structured meshes and fast specialized solvers for problems on complicated geometries. Another interesting feature of the fictitious domain approach is that it allows the solution of optimal shape problems without regriding. The resulting methodology is applied to the solution of flow problems including external incompressible viscous flow modelled by the Navier-Stokes equations and then to an optimal shape problem for Stokes and Navier-Stokes flow
TL;DR: In this article, a simplified marker and cell (SMAC) time-advancing method for solving the Navier-Stokes equations on non-staggered grids is developed in generalized co-ordinate systems.
Abstract: The SMAC (simplified marker and cell) time-advancing method for solving the unsteady incompressible Navier-Stokes equations on non-staggered grids is developed in generalized co-ordinate systems. The primitive variable formulation uses Cartesian velocities and pressure, all defined at the centre of the control volume, as the dependent variables. A special elliptic flux correction at the faces of the finite volume is utilized in discretizing the continuity equation to suppress pressure oscillations. The test flows considered are a polar cavity flow starting from rest and the flow around a circular cylinder. The numerical results are compared with experimental results and results obtained by the well-known SIMPLEC and PISO methods. The comparisons show that the elliptic flux correction technique works well in suppressing pressure oscillations and that the SMAC method is more efficient than the SIMPLEC and PISO methods for both steady and unsteady flows.
TL;DR: In this article, a combination of formal analysis and numerical experimentation is used to characterize the stability and accuracy that results from alternative treatments of the concentrations at the feet of the characteristic lines.
Abstract: Selected finite element Eulerian-Lagrangian methods for the solution of the transport equation are compared systematically in the relatively simple context of 1D, constant coefficient, conservative problems. A combination of formal analysis and numerical experimentation is used to characterize the stability and accuracy that results from alternative treatments of the concentrations at the feet of the characteristic lines. Within the methods analyzed, those that approach such treatment with the perspective of ‘integration’ rather than ‘interpolation’ tend to have superior accuracy. Exact integration leads to unconditional stability and excellent accuracy. Quadrature integration leads only to conditional stability, but newly derived criteria show that stability restrictions are relatively mild and should not preclude the usefulness of quadrature integration methods in a range of practical applications. While conclusions cannot be extended directly to multiple dimensions and complex flows and geometries, results should provide useful insight to the development and behaviour of specific Eulerian-Lagrangian transport models.
TL;DR: In this paper, a second order artificial viscosity scheme, explicit second order balancing terms, parallelization strategies, and grid adapting based on a spring analogy are discussed. But the authors focus on the second order Artificial Viscosity Scheme.
Abstract: Includes chapters on: A second order artificial viscosity scheme; explicit second order balancing terms; parallelization strategies; and, grid adapting based on a spring analogy.
TL;DR: In this article, a low-Reynolds number form of the k-ϵ tubulence model is used to model turbulence and a diagonally dominant alternating direction implicit (DDADI) factorized implicit time integration method was used to accelerate the convergence.
Abstract: In this paper Roe's flux-difference splitting is applied for the solution of Reynolds-averaged Navier-Stokes equations. Turbulence is modelled using a low-Reynolds number form of the k-ϵ tubulence model. The coupling between the turbulence kinetic energy equation and the inviscid part of the flow equations is taken into account. The equations are solved with a diagonally dominant alternating direction implicit (DDADI) factorized implicit time integration method. A multigrid algorithm is used to accelerate the convergence. To improve the stability some modifications are needed in comparison with the application of an algebraic turbulence model. The developed method is applied to three different test cases. These cases show the efficiency of the algorithm, but the results are only marginally better than those obtained with algebraic models.
TL;DR: In this paper, the authors compared the scalar upwind SUPG with the linear triangular element SUPG for scalar advection in hyperbolic systems such as the compressible Euler equations.
Abstract: Vertex-based multidimensional upwind schemes for scalar advection are compared with shock-capturing SUPG finite element methods based on linear triangular elements. Both methods share the same compact stencil and are formulated as cell-wise residual distribution methods. The distribution for the finite element method is 1/3, supplemented with a Lax-Wendrov-type dissipation term, while the distribution for the upwind schemes is limited to the downstream nodes of the element. The multidimensional upwind schemes use positivity as the monotonicity criterion, while the finite element method includes a residual-based non-linear dissipation.
For hyperbolic systems such as the compressible Euler equations the upwind method relies on a multidimensional wave model to decompose the residual into scalar contributions. From this observation a new SUPG formulation for systems is proposed in which the scalar SUPG method is applied to each of the decomposed residuals obtained from the wave model, thereby providing a better-founded definition of the τ dissipation matrix and shock-capturing term in the SUPG methods.
TL;DR: In this article, the computational analysis of thermohygrometric and mechanical behavior of concrete structures is carried out by means of the finite element method, using two FEM computer codes in sequence to apply the proposed approach to structures of any shape.
Abstract: The computational analysis of thermohygrometric and mechanical behaviour of concrete structures is carried out by means of the finite element method To evaluate the thermal and hygral performance of this material together with the damage and creep effects, the knowledge of the heat and moisture transfer processes taking place inside the medium is first required and then the consequent mechanical behaviour can be analysed The theoretical approach used to obtain the governing differential equations for heat and moisture tansfer is based on the procedure of averaging continuum equations applied to heat and mass transfer and drying processes According to that model the same set of equations is used to represent both the saturated zone (if present), the unsaturated one and the water-vapour phase changes The mechanical formulation is based on the virtual work principle and incorporates Prony–Dirichlet series expansion to represent the relaxation or creep functions, avoiding the memorization of the whole strain or stress history Damage effects are taken into account within a coupled formulation, following a procedure presented in a previous paper At this preliminary stage the analysis is performed in two stages (first the heat and mass transfer and then the mechanical analysis) using two FEM computer codes in sequence to apply the proposed approach to structures of any shape
TL;DR: This technique combines the strength of the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume-of-fluid (VOF) technique in advection of the fluid interfaces to produce a technique which can handle large surface deformations with accurate treatment of the boundary conditions.
Abstract: SUMMARY A numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength of the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume-of-fluid (VOF) technique in advection of the fluid interfaces. The advantage of the VOF technique is that it allows the simulation of interfaces with large deformations, including surface merging and breaking. However, its disadvantage is that in solving the flow equations, it cannot resolve interfaces smaller than the cell size, since information on the subgrid scale is lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surface tension forces) become grid-size-dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of the boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the two methods into a hybrid FEM-VOF method eliminates the major shortcomings of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For illustration, two computational examples are presented, namely the instability and break-up of a capillary jet and the coalescence collision of two liquid drops. Free surface flows and interfaces between two immiscible fluids or materials with different phases are observed in many natural and industrial processes. Various numerical techniques have been developed to simulate these flows. However, owing to the complexity of the problem, each technique is tailored to a particular category of flows. For instance, boundary integral techniques'" are mainly used for simulating inviscid irrotational flows and the limiting case of zero Reynolds number. Finite element methods (FEMs) and finite difference methods (FDMs) are potentially applicable to generalized Navier-Stokes equations; however, they have to be coupled with a technique to track the advecting fluid boundaries and interfaces. The difficulty in the interface tracking is inherently related to the complexity of its topology. Therefore techniques which can handle small surface deformations fail when applied to large interface distortions. For simulation of the former category of flows (small surface deformations) the FEM is more popular. Here the fluid boundary is described by a set of fixed4 or def~nning~-'~ meshes, the location of which is obtained by either an iterative procedure or the Lagrangian movement of the interface nodes. This results in the simultaneous calculation of the position of the free surface and the field variables at the new nodal positions. Boundary-fitted orthogonal c~-ordinates*~-'~ and Lagrangian technique^'^>'^ are also used to follow the advecting liquid interfaces. These techniques are confronted with difficulties when applied to large surface deformations, surface breaking and merging. CCC 0271-2091/95/121363-18 0 1995 by John Wiley & Sons, Ltd.
TL;DR: In this paper, the Van Leer method was extended to two-phase flow and a scheme was constructed to guarantee that the sum of the volume fractions is always unity and that the volume fiactions are always greater than or equal to zero.
Abstract: SUMMARY The Van Leer method for the computation of convective fluxes is extended to two-phase flow. By preventing spurious undershoots and overshoots, the scheme preserves physical realism while maintaining high-order accuracy. This is particularly important for two-phase flows, since phase exchange terms are typically a function of volume fraction products and numerical diffusion can incorrectly mix the two phases. The scheme described here is constructed to guarantee that the sum of the volume fractions is always unity and that the volume fiactions are always greater than or equal to zero. Various test problems are computed to demonstrate the accuracy of the method and to show how the scheme might be incorporated in existing computational methods. In addition to multiphase flow applications, setting equal phase velocities results in a volume marker scheme that is well suited to single-phase interface tracking problems. There are few known exact solutions of the governing equations of two-phase flow and those that are known represent simple physical systems that have limited practical application. Consequently, investigators of two-phase flow fall back on experimentally determined correlations and more recently solutions of the governing equations obtained by computer. This paper addresses the problem of minimizing numerical diffusion associated with numerical representation of the convective terms in the two-phase governing equations. It is well known that numerical schemes that discretize the convective terms with an upwind procedure suffer from excessive numerical diffusion; the use of a higher-order scheme can substantially reduce this problem but can also lead to oscillations causing non-physical undershoots or overshoots. The implication of these results for two-phase flow calculations is particularly significant for the computation of the convection of phase volume fraction (mass). If an upwind procedure is used for volume fraction advection, then numerical diffusion tends to smear gradients of volume fraction. Typical two-phase exchange terms involve the product of volume fractions, so smearing produces finite values in those exchange terms, leading to numerically induced source terms and consequent inaccuracies throughout the calculation. If a naive higher-order scheme is used for volume fraction advection, then non-physical oscillations might appear in the volume fraction profiles, as well as overshoots or undershoots, so that volume fractions may be less than zero or greater than unity, which again would produce unphysical phase exchange source terms. This paper describes the use of the Van Leer method' for the computation of convective fluxes as applied to the convective transport of phase volume fraction (mass) and phase momentum in two-phase flow. The Van Leer scheme prevents spurious oscillations while maintaining a high order of numerical
TL;DR: In this paper, an application of multidomain decomposition to the computation of the steady free surface flow past a ship hull is presented, where viscous effects are taken into account in the neighbourhood of solid walls and in the wake by the Reynolds averaged Navier-Stokes equations.
Abstract: An application of multidomain decomposition to the computation of the steady free surface flow past a ship hull is presented. Viscous effects are taken into account in the neighbourhood of solid walls and in the wake by the Reynolds averaged Navier-Stokes equations, whereas the assumption of irrotationality in the external flow allows a description by a potential model. Free surface boundary conditions have been implemented in a linearized form at the undisturbed waterplane. Suitable matching conditions are enforced at the interface between the viscous and the potential regions. The numerical results obtained for two merchant ship forms (the HSVA tanker and the Series 60 hull) are compared with experimental data available in the literature.