Showing papers in "International Journal for Numerical Methods in Fluids in 2005"
TL;DR: Numerical calculations of the 2-D steady incompressible driven cavity flow are presented and comparisons are made with benchmark solutions found in the literature.
Abstract: SUMMARY Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The NavierStokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601 × 601. The steady driven cavity solutions are computed for Re ≤ 21,000 with a maximum absolute residuals of the governing equations that were less than 10 −10 . A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.
531 citations
TL;DR: This paper extends the methodology to the parametrized steady incompressible Navier–Stokes equations and exploits affine parametric structure and offline–online computational decompositions to provide real‐time deployed response.
Abstract: We present a technique for the evaluation of linear-functional outputs of parametrized elliptic partial differential equations in the context of deployed (in service) systems. Deployed systems require real-time and certified output prediction in support of immediate and safe (feasible) action. The two essential components of our approach are (i) rapidly, uniformly convergent reduced-basis approximations, and (ii) associated rigorous and sharp a posteriori error bounds; in both components we exploit affine parametric structure and oflline-online computational decompositions to provide real-time deployed response. In this paper we extend our methodology to the parametrized steady incompressible Navier-Stokes equations. We invoke the Brezzi-Rappaz-Raviart theory for analysis of variational approximations of non-linear partial differential equations to construct rigorous, quantitative, sharp, inexpensive a posteriori error estimators
387 citations
TL;DR: The Tangent of Hyperbola for Interface Capture (THINC) as mentioned in this paper is a simple and practical scheme for capturing moving interfaces or free boundaries in multi-fluid simulations.
Abstract: This paper presents a simple and practical scheme for capturing moving interfaces or free boundaries in multi-fluid simulations. The scheme, which is called THINC (tangent of hyperbola for interface capturing), makes use of the hyperbolic tangent function to compute the numerical flux for the fluid fraction function, and gives a conservative, oscillation-less and smearing-less solution to the fluid fraction function even for the extremely distorted interfaces of arbitrary complexity. The numerical results from the THINC scheme possess adequate quality for practical applications, which make the extra geometric reconstruction, such as those in most of the volume of fluid (VOF) methods unnecessary. Thus the scheme is quite simple. The numerical tests show that the THINC scheme has competitive accuracy compared to most exiting methods. Copyright © 2005 John Wiley & Sons, Ltd.
378 citations
TL;DR: In this article, a mass-conserving Level-Set method to model bubbly flows is presented, which can handle high density-ratio flows with complex interface topologies, such as flows with simultaneous occurrence of bubbles and droplets.
Abstract: A mass-conserving Level-Set method to model bubbly flows is presented. The method can handle high density-ratio flows with complex interface topologies, such as flows with simultaneous occurrence of bubbles and droplets. Aspects taken into account are: a sharp front (density changes abruptly), arbitrarily shaped interfaces, surface tension, buoyancy and coalescence of droplets/bubbles. Attention is paid to mass-conservation and integrity of the interface. The proposed computational method is a Level-Set method, where a Volume-of-Fluid function is used to conserve mass when the interface is advected. The aim of the method is to combine the advantages of the Level-Set and Volume-of-Fluid methods without the disadvantages. The flow is computed with a pressure correction method with the Marker-and-Cell scheme. Interface conditions are satisfied by means of the continuous surface force methodology and the jump in the density field is maintained similar to the ghost fluid method for incompressible flows
224 citations
TL;DR: In this paper, a collocated unstructured computational fluid dynamics (CUCFD) code was used to analyze the flow of two tandem cylinders in a lid-friven cavity.
Abstract: Flows over two tandem cylinders were analysed using the newly developed collocated unstructured computational fluid dynamics (CUCFD) code, which is capable of handling complex geometries. A Reynolds number of 100, based on cylinder diameter, was used to ensure that the flow remained laminar. The validity of the code was tested through comparisons with benchmark solutions for flow in a lid-friven cavity and flow around a single cylinder. For the tandem cylinder flow, also mesh convergence was demonstrated, to within a couple of percent for the RMS lift coefficient. The mean and fluctuating lift and drag coefficients were recorded for centre-to-centre cylinder spacings between 2 and 10 diameters. A critical cylinder spacing was found between 3.75 and 4 diameters. The fluctuating forces jumped appreciably at the critical spacing. It was found that there exists only one reattachment and one separation point on the downstream cylinder for spacings greater than the critical spacing. The mean and the fluctuating surface pressure distributions were compared as a function of the cylinder spacing. The mean and the fluctuating pressures were significantly different between the upstream and the downstream cylinders. These pressures also differed with the cylinder spacing.
213 citations
TL;DR: In this article, a single-phase level set method for unsteady viscous free surface flows is presented, where the location of the interface is determined using a signed distance function and appropriate interpolations at the fluid/fluid interface are used to enforce the jump conditions.
Abstract: : The single-phase level set method for unsteady viscous free surface flows is presented. In contrast to the standard level set method for incompressible flows, the single-phase level set method is concerned with the solution of the flow field in the water (or the denser) phase only. Some of the advantages of such an approach are that the interface remains sharp, the computation is performed within a fluid with uniform properties and that only minor computations are needed in the air. The location of the interface is determined using a signed distance function, and appropriate interpolations at the fluid/fluid interface are used to enforce the jump conditions. A reinitialization procedure has been developed for non-orthogonal grids with large aspect ratios. A convective extension is used to obtain the velocities at previous time-steps for the grid points in air, which allows a good estimation of the total derivatives. In this report we discuss the details of such implementations. The method was applied to three unsteady tests: a plane progressive wave, sloshing in a two-dimensional tank, and the wave diffraction problem in a surface ship, and the results compared against analytical solutions or experimental data. The method can in principle be applied to any problem in which the standard level-set method works, as long as the stress on the second phase can be specified (or neglected) and no bubbles appear in the flow during the computation.
178 citations
TL;DR: In this article, a semi-implicit, staggered finite volume technique for non-hydrostatic, free-surface flow governed by the incompressible Euler equations is presented that has a proper balance between accuracy, robustness and computing time.
Abstract: A semi-implicit, staggered finite volume technique for non-hydrostatic, free-surface flow governed by the incompressible Euler equations is presented that has a proper balance between accuracy, robustness and computing time. The procedure is intended to be used for predicting wave propagation in coastal areas. The splitting of the pressure into hydrostatic and non-hydrostatic components is utilized. To ease the task of discretization and to enhance the accuracy of the scheme, a vertical boundary-fitted co-ordinate system is employed, permitting more resolution near the bottom as well as near the free surface. The issue of the implementation of boundary conditions is addressed. As recently proposed by the present authors, the Keller-box scheme for accurate approximation of frequency wave dispersion requiring a limited vertical resolution is incorporated. The both locally and globally mass conserved solution is achieved with the aid of a projection method in the discrete sense. An efficient preconditioned Krylov subspace technique to solve the discretized Poisson equation for pressure correction with an unsymmetric matrix is treated. Some numerical experiments to show the accuracy, robustness and efficiency of the proposed method are presented. Copyright © 2004 John Wiley & Sons, Ltd.
166 citations
TL;DR: In this paper, the authors investigated a possible relationship between the drag crisis (sudden loss of drag at Re ∼ 2 × 105) and the instability of the separated shear layer and found that the delay in flow separation is associated with narrowing of wake, increase in Reynolds shear stress near the shoulder of the cylinder and a significant reduction in the drag and base suction coefficients.
Abstract: Flow past a circular cylinder for Re=100 to 107 is studied numerically by solving the unsteady incompressible two-dimensional Navier–Stokes equations via a stabilized finite element formulation. It is well known that beyond Re ∼ 200 the flow develops significant three-dimensional features. Therefore, two-dimensional computations are expected to fall well short of predicting the flow accurately at high Re. It is fairly well accepted that the shear layer instability is primarily a two-dimensional phenomenon. The frequency of the shear layer vortices, from the present computations, agree quite well with the Re0.67 variation observed by other researchers from experimental measurements. The main objective of this paper is to investigate a possible relationship between the drag crisis (sudden loss of drag at Re ∼ 2 × 105) and the instability of the separated shear layer. As Re is increased the transition point of shear layer, beyond which it is unstable, moves upstream. At the critical Reynolds number the transition point is located very close to the point of flow separation. As a result, the shear layer eddies cause mixing of the flow in the boundary layer. This energizes the boundary layer and leads to its reattachment. The delay in flow separation is associated with narrowing of wake, increase in Reynolds shear stress near the shoulder of the cylinder and a significant reduction in the drag and base suction coefficients. The spatial and temporal power spectra for the kinetic energy of the Re=106 flow are computed. As in two-dimensional isotropic turbulence, E(k) varies as k−5/3 for wavenumbers higher than energy injection scale and as k−3 for lower wavenumbers. The present computations suggest that the shear layer vortices play a major role in the transition of boundary layer from laminar to turbulent state. Copyright © 2004 John Wiley & Sons, Ltd.
147 citations
TL;DR: In this paper, the interfacial dynamics-based cavitation model (IDCM) and filter-based k-e turbulence model are adopted to simulate 2D cavitating flows over the Clark-Y airfoil.
Abstract: Turbulent cavitating flow computations need to address both cavitation and turbulence modelling issues. A recently developed interfacial dynamics-based cavitation model (IDCM) incorporates the interfacial transport into the computational modelling of cavitation dynamics. For time-dependent flows, it is known that the engineering turbulence closure such as the original k–e model often over-predicts the eddy viscosity values reducing the unsteadiness. A recently proposed filter-based modification has shown that it can effectively modulate the eddy viscosity, rendering better simulation capabilities for time-dependent flow computations in term of the unsteady characteristics. In the present study, the IDCM along with the filter-based k–e turbulence model is adopted to simulate 2-D cavitating flows over the Clark-Y airfoil. The chord Reynolds number is Re=7.0 × 105. Two angles-of-attack of 5 and 8° associated with several cavitation numbers covering different flow regimes are conducted. The simulation results are assessed with the experimental data including lift, drag and velocity profiles. The interplay between cavitation and turbulence models reveals substantial differences in time-dependent flow results even though the time-averaged characteristics are similar. Copyright © 2005 John Wiley & Sons, Ltd.
116 citations
TL;DR: In this paper, a hybrid scheme composed of finite-volume and finite-difference methods is introduced for the solution of the Boussinesq equations, and four limiters have been tested, of which van-Leer limiter is found to be the most suitable.
Abstract: A hybrid scheme composed of finite-volume and finite-difference methods is introduced for the solution of the Boussinesq equations. While the finite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the finite-difference scheme. Fourth-order accuracy in space for the finite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams-Basforth third-order predictor and Adams-Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model HYWAVE, based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results. Copyright © 2005 John Wiley & Sons, Ltd.
114 citations
TL;DR: A novel solution method based on the conjugation of subiteration with a Newton–Krylov method is proposed, and its superiority and beneficial characteristics are demonstrated.
Abstract: The numerical solution of fluid-structure interactions with the customary subiteration method incurs numerous deficiencies. We propose a novel solution method based on the conjugation of subiteration with a Newton-Krylov method, and demonstrate its superiority and beneficial characteristics
TL;DR: In this paper, the smoothed particle hydrodynamics (SPH) method is applied to the solution of shallow water equations and a variational formulation using SPH interpolation is discussed.
Abstract: The smoothed particle hydrodynamics (SPH) method is applied to the solution of shallow water equations. A brief review of the method in its standard form is first described then a variational formulation using SPH interpolation is discussed. A new technique based on the Riemann solver is introduced to improve the stability of the method
TL;DR: An alternative method of controlling Lagrangian distortion is proposed, based on ideas of radial basis function (RBF) interpolation (briefly reviewed here), which is formulated grid-free, and is shown to be more accurate than standard remeshing.
Abstract: Vortex methods have a history as old as finite differences. They have since faced difficulties stemming from the numerical complexity of the Biot–Savart law, the inconvenience of adding viscous effects in a Lagrangian formulation, and the loss of accuracy due to Lagrangian distortion of the computational elements. The first two issues have been successfully addressed, respectively, by the application of the fast multipole method, and by a variety of viscous schemes which will be briefly reviewed in this article. The standard method to deal with the third problem is the use of remeshing schemes consisting of tensor product interpolation with high-order kernels. In this work, a numerical study of the errors due to remeshing has been performed, as well as of the errors implied in the discretization itself using vortex blobs. In addition, an alternative method of controlling Lagrangian distortion is proposed, based on ideas of radial basis function (RBF) interpolation (briefly reviewed here). This alternative is formulated grid-free, and is shown to be more accurate than standard remeshing. In addition to high-accuracy, RBF interpolation allows core size control, either for correcting the core spreading viscous scheme or for providing a variable resolution in the physical domain. This formulation will allow in theory the application of error estimates to produce a truly adaptive spatial refinement technique. Proof-of-concept is provided by calculations of the relaxation of a perturbed monopole to a tripole attractor.
TL;DR: In this paper, the authors present a well-posed Navier-Stokes (NS) solver for the unsteady augmented NS problem, based on a splitting of the computation of velocity and pressure on one side and the Lagrangian multiplier on the other.
Abstract: In the numerical simulation of blood flow problems it might happen that the only available physical boundary conditions prescribe the flow rate incoming/outgoing the vascular district at hand. In order to have a well-posed Navier–Stokes (NS) problem, these conditions need to be completed. In the bioengineering community, this problem is usually faced by choosing a priori a velocity profile on the inflow/outflow sections, that should fit the assigned flow rates. This approach strongly influences the accuracy of the numerical solutions. A less perturbative strategy is based on the so-called ‘do-nothing’ approach, advocated in Heywood et al. (Int. J. Num. Meth. Fluids 1996; 22:325–352). An equivalent approach, however, easier from the numerical discretization viewpoint, has been proposed in Formaggia et al. (SIAM J. Numer. Anal. 2002; 40(1):376–401). It is based on an augmented formulation of the problem, in which the conditions on the flow rates are prescribed in a weak sense by means of Lagrangian multipliers. In this paper we extend this analysis to the unsteady augmented NS problem, proving a well-posedness result. Moreover, we present some numerical methods for solving the augmented problem, based on a splitting of the computation of velocity and pressure on one side and the Lagrangian multiplier on the other one. In this way, we show how it is possible to solve the augmented problem resorting to available NS solvers. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, a semi-implicit time integration is proposed for the simulation of incompressible and compressible unsteady flows, where the stability is guaranteed independently of the speed of sound and the resulting method is independent of the Mach number.
Abstract: In this paper we present a method for the simulation of incompressible as well as compressible unsteady flows. At first we discuss three different forms, i.e. a primitive-, conservative- and a semi-conservative form of the governing equations. We use a semi-implicit time integration in such a fashion that the stability is guaranteed independently of the speed of sound and the resulting method is independent of the Mach number range. Moreover, with the application of the so-called multiple pressure variables (MPV) approach the difficulties with the pressure term can be circumvented as in the incompressible limit the hydrodynamic pressure decouples from the equation of state. Increasing approximation errors in the low Mach number regime are avoided. As a result, the proposed algorithm can also simulate incompressible flows as limit for zero Mach number. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: This paper presents a numerical method for free surface flows that couples the incompressible Navier–Stokes equations with the level set method in the finite element framework and indicates that the characteristic Galerkin approximation of thelevel set equations yields more accurate solutions.
Abstract: We present a numerical method for free surface flows that couples the incompressible Navier-Stokes equations with the level set method in the finite element framework. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are verified with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular fluid element. The results are compared with those calculated from the level set finite volume method of Yue et al. , which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system
TL;DR: In this article, a framework for adaptively inserting and removing particles with smoothed particle hydrodynamics (SPH) has been developed, and a number of SPH variants were examined for use in an adaptive method.
Abstract: A framework for adaptively inserting and removing particles with smoothed particle hydrodynamics (SPH) has been developed. A number of SPH variants were examined for use in an adaptive method. A minimum of linear consistency in the method has proven critical. Algorithms for particle placement and reassignment are discussed and results for a shock tube problem are shown
TL;DR: In this paper, the authors developed a model that will adequately simulate the dynamics of tsunami propagating across the continental shelf by using the three-dimensional Reynolds averaged Navier-Stokes equations to yield a set of equations that are similar to the shallow water equations but retain the non-hydrostatic pressure terms.
Abstract: The objective of this research is to develop a model that will adequately simulate the dynamics of tsunami propagating across the continental shelf. In practical terms, a large spatial domain with high resolution is required so that source areas and runup areas are adequately resolved. Hence efficiency of the model is a major issue. The three-dimensional Reynolds averaged Navier–Stokes equations are depth-averaged to yield a set of equations that are similar to the shallow water equations but retain the non-hydrostatic pressure terms. This approach differs from the development of the Boussinesq equations where pressure is eliminated in favour of high-order velocity and geometry terms. The model gives good results for several test problems including an oscillating basin, propagation of a solitary wave, and a wave transformation over a bar. The hydrostatic and non-hydrostatic versions of the model are compared for a large-scale problem where a fault rupture generates a tsunami on the New Zealand continental shelf. The model efficiency is also very good and execution times are about a factor of 1.8 to 5 slower than the standard shallow water model, depending on problem size. Moreover, there are at least two methods to increase model accuracy when warranted: choosing a more optimal vertical interpolation function, and dividing the problem into layers. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: This paper reviews the implementation of AD on Fortran CFD codes and gives details of how small rearrangements can be used to produce competitive tangent and adjoint code using source transformation AD.
Abstract: Adjoint methods are a computationally inexpensive way of deriving sensitivity information where there are fewer dependent (cost) variables than there are independent (input) variables. Automatic differentiation (AD) software makes it possible to create discrete adjoint codes with minimal human effort, an issue that had previously restricted acceptance of adjoint CFD codes. In terms of computational performance, automatic code is often assumed to be inferior to hand code. The structure of the underlying code is critical to the performance of the transformed code. We review the implementation of AD on Fortran CFD codes and give details of how small rearrangements can be used to produce competitive tangent and adjoint code using source transformation AD
TL;DR: In this paper, an arbitrary Lagrangian Eulerian (ALE) method for non-breaking free surface flow problems is presented, where the characteristic-based split (CBS) scheme has been employed to solve the ALE equations.
Abstract: An arbitrary Lagrangian Eulerian (ALE) method for non-breaking free surface flow problems is presented. The characteristic-based split (CBS) scheme has been employed to solve the ALE equations. A simple mesh smoothing procedure based on coordinate averaging (Laplacian smoothing) is employed in the calculations. The mesh velocity is calculated at each time step and incorporated as part of the scheme. Results presented show an excellent agreement with the available experimental data. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors present a solution based on enriching the pressure shape functions on the elements cut by the interface to enable the pressure gradient to be discontinuous at the interface, thus improving the ability to simulate the behavior of fluids with different density under a gravitational force.
Abstract: In this paper we present a problem we have encountered using a stabilized finite element method on fixed grids for flows with interfaces modelled with the level set approach. We propose a solution based on enriching the pressure shape functions on the elements cut by the interface. The enrichment is used to enable the pressure gradient to be discontinuous at the interface, thus improving the ability to simulate the behaviour of fluids with different density under a gravitational force. The additional shape function used is local to each element and the corresponding degree of freedom can therefore be condensed prior to assembly, making the implementation quite simple on any existing finite element code. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this article, a matrix-based stability analysis as well as Euler finite volume computations are compared to illustrate the importance of the internal shock structure to trigger the carbuncle phenomenon.
Abstract: Since the development of shock-capturing methods, the carbuncle phenomenon has been reported to be a spurious solution produced by almost all currently available contact-preserving methods. The present analysis indicates that the onset of carbuncle phenomenon is actually strongly related to the shock wave numerical structure. A matrix-based stability analysis as well as Euler finite volume computations are compared to illustrate the importance of the internal shock structure to trigger the carbuncle phenomenon
AVL1
TL;DR: In this paper, numerical calculations were carried out at the apex cone and various axial positions of a gas cyclone separator for industrial applications using two different NS-solvers (a commercial one (CFX 4.4 ANSYS GmbH, Munich, Germany, CFX Solver Documentation, 1998), and a research code (Post-doctoral Thesis, Technical University of Chemnitz, German, September, 2002)) based on a pressure correction algorithm of the SIMPLE method have been applied to predict the flow behaviour.
Abstract: Numerical calculations were carried out at the apex cone and various axial positions of a gas cyclone separator for industrial applications. Two different NS-solvers (a commercial one (CFX 4.4 ANSYS GmbH, Munich, Germany, CFX Solver Documentation, 1998), and a research code (Post-doctoral Thesis, Technical University of Chemnitz, Germany, September, 2002)) based on a pressure correction algorithm of the SIMPLE method have been applied to predict the flow behaviour. The flow was assumed as unsteady, incompressible and isothermal. A κ-e turbulence model has been applied first using the commercial code to investigate the gas flow. Due to the nature of cyclone flows, which exhibit highly curved streamlines and anisotropic turbulence, advanced turbulence models such as Reynolds stress model (RSM) and large eddy simulation (LES) have been used as well. The RSM simulation was performed using the commercial package activating the Launder et al.'s approach, while for the LES calculations the research code has been applied utilizing the Smagorinsky model. It was found that the κ-e model cannot predict flow phenomena inside the cyclone properly due to the strong curvature of the streamlines. The RSM results are comparable with LES results in the area of the apex cone plane. However, the application of the LES reveals qualitative agreement with the experimental data, but requires higher computer capacity and longer running times than RSM. This paper is organized into five sections. The first section consists of an introduction and a summary of previous work. Section 2 deals with turbulence modelling including the governing equations and the three turbulence models used. In Section 3, computational parameters are discussed such as computational grids, boundary conditions and the solution algorithm with respect to the use of MISTRAL/PartFlow-3D. In Section 4, prediction profiles of the gas flow at axial and apex cone positions are presented and discussed. Section 5 summarizes and concludes the paper.
TL;DR: In this article, a unified strategy for numerical modeling of two-fluid interfacial flows is proposed, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem.
Abstract: The present work is devoted to the study on unsteady flows of two immiscible viscous fluids separated by free moving interface. Our goal is to elaborate a unified strategy for numerical modelling of two-fluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh–Taylor instability are presented to validate the computational method. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this article, the authors compare existing and new pressure relaxation procedures in terms of both accuracy and computational efficiency for multiphase compressible flow models, and also present some generalizations of these procedures in the context of multi-phase flows with an arbitrary number of fluids.
Abstract: This paper deals with pressure relaxation procedures for multiphase compressible flow models. Such models have nice mathematical properties (hyperbolicity) and are able to solve a wide range of applications: interface problems, detonation physics, shock waves in mixtures, cavitating flows, etc. The numerical solution of such models involves several ingredients. One of those ingredients is the instantaneous pressure relaxation process and is of particular importance.
In this article, we present and compare existing and new pressure relaxation procedures in terms of both accuracy and computational efficiency. Among these procedures we enhance an exact one in the particular case of fluids governed by the stiffened gas equation of state, and approximate procedures for general equations of state, which are particularly well suited for problems with large pressure variations. We also present some generalizations of these procedures in the context of multiphase flows with an arbitrary number of fluids. Some tests are provided to illustrate these comparisons. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this article, a finite difference pseudo-spectral (FD-PS) algorithm was developed to simulate the viscous fingering instability in high mobility-ratio (MR) miscible displacements.
Abstract: A finite difference-pseudo-spectral (FD-PS) algorithm is developed to simulate the viscous fingering instability in high mobility-ratio (MR) miscible displacements. This novel algorithm uses the fully implicit alternating-direction implicit (ADI) method combined with a Hartley based pseudo-spectral method to solve the Poisson equation involving the streamfunction and the vorticity. In addition, under-relaxation in the iterative evaluation of the streamfunction is adopted. The new code allowed to model successfully the viscous fingering instability for mobility-ratios as high as 1800, and new non-linear viscous fingering mechanisms are discovered. A systematic analysis of the effects of the MR, the Peclet number and the aspect ratio on the finger growth is conducted
TL;DR: In this article, a variational multiscale method for large eddy simulation of turbulent flows is proposed, in which residual-free bubbles are used for the numerical approximation of the small-scale momentum equation.
Abstract: The variational multiscale method provides a methodical framework for large eddy simulation of turbulent flows. In this work, a particular implementation in the form of a three-level finite element method separating large resolved, small resolved, and unresolved scales is proposed. Residual-free bubbles are used for the numerical approximation of the small-scale momentum equation. A stabilizing term is added, in order to take into account the effect of the small-scale continuity equation. This implementation guarantees the stability of the method without further provisions and offers substantial computational savings on the small-scale level. Furthermore, it is accounted for the unresolved scales by a specific dynamic modelling procedure. The method is tested for two different turbulent flow situations.
TL;DR: In this paper, the authors investigate how to accurately numerically approximate the equations governing 2D sediment transport by considering two approaches: a steady and unsteady approach and a high-resolution scheme based on Roe's scheme.
Abstract: We investigate how to accurately numerically approximate the equations governing 2D sediment transport by considering two approaches: a steady and unsteady approach. A high-resolution scheme based on Roe's scheme is used to approximate both approaches with the results compared for a 2D test case
TL;DR: A large eddy simulation (LES) methodology for turbulent flows in complex rigid geometries is developed using the immersed boundary method (IBM) in this article, where body force terms are added to the momentum equations to represent a complex rigid geometry on a fixed Cartesian mesh.
Abstract: A large eddy simulation (LES) methodology for turbulent flows in complex rigid geometries is developed using the immersed boundary method (IBM). In the IBM body force terms are added to the momentum equations to represent a complex rigid geometry on a fixed Cartesian mesh. IBM combines the efficiency inherent in using a fixed Cartesian grid and the ease of tracking the immersed boundary at a set of moving Lagrangian points. Specific implementation strategies for the IBM are described in this paper. A two-sided forcing scheme is presented and shown to work well for moving rigid boundary problems. Turbulence and flow unsteadiness are addressed by LES using higher order numerical schemes with an accurate and robust subgrid scale (SGS) stress model. The combined LES–IBM methodology is computationally cost-effective for turbulent flows in moving geometries with prescribed surface trajectories.
Several example problems are solved to illustrate the capability of the IBM and LES methodologies. The IBM is validated for the laminar flow past a heated cylinder in a channel and the combined LES–IBM methodology is validated for turbulent film-cooling flows involving heat transfer. In both cases predictions are in good agreement with measurements. LES–IBM is then used to study turbulent fluid mixing inside the complex geometry of a trapped vortex combustor. Finally, to demonstrate the full potential of LES–IBM, a complex moving geometry problem of stator–rotor interaction is solved. Copyright © 2005 John Wiley & Sons, Ltd.
TL;DR: In this paper, the mean properties and turbulence statistics up to fourth order, the budget and the wavenumber spectra of the temperature fluctuations, for three different wall boundary conditions are investigated.
Abstract: Direct numerical simulations (DNS) are carried out to study fully developed turbulent pipe flow and heat transfer at Reynolds number Rem≈5300 based on bulk velocity and pipe diameter. This paper provides detailed information on the mean properties and turbulence statistics up to fourth order, the budget and the wavenumber spectra of the temperature fluctuations, for three different wall boundary conditions. To investigate the differences between fully developed turbulent heat transfer in axisymmetric pipe and plane channel geometry, the present DNS results are compared to those obtained from channel flow simulations. The differences between channel and pipe flow statistics are modest and reveal that the temperature fluctuations in the pipe are slightly more intense. The present results show that the mean temperature profile does not conform to the accepted law of the wall. The boundary conditions affect the turbulence statistics both in the near-wall and core regions; this observation complements previous studies concerning different flow and heat transfer configurations. Copyright © 2005 John Wiley & Sons, Ltd.