Showing papers on "Incompressible flow published in 1998"
TL;DR: In this paper, the conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations, and finite difference schemes for regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out.
978 citations
01 Nov 1998
TL;DR: In this article, a new lattice Boltzmann scheme was proposed for simulation of multiphase flow in the nearly incompressible limit. But this scheme is based on distribution functions.
Abstract: In this paper, we propose a new lattice Boltzmann scheme for simulation of multiphase flow in the nearly incompressible limit. The new scheme simulates fluid flows based on distribution functions. The interfacial dynamics, such as phase segregation and surface tension, are modeled by incorporating molecular interactions. The lattice Boltzmann equations are derived from the continuous Boltzmann equation with appropriate approximations suitable for incompressible flow. The numerical stability is improved by reducing the effect of numerical errors in calculation of molecular interactions. An index function is used to track interfaces between different phases. Simulations of the two-dimensional Rayleigh?Taylor instability yield satisfactory results. The interface thickness is maintained at 3?4 grid spacings throughout simulations without artificial reconstruction steps.
779 citations
TL;DR: In this paper, a moving particle semi-implicit (MPS) algorithm is used for two-dimensional incompressible non-viscous flow analysis and two types of breaking waves, plunging and spilling breakers, are observed in the calculation results.
Abstract: SUMMARY The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave. © 1998 John Wiley & Sons, Ltd.
767 citations
Book•
10 Dec 1998
TL;DR: In this article, the authors present the equations of the wave front and the product and present the case of a smooth initial data and the case when the vorticity is bounded.
Abstract: Introduction 1. Presentation of the equations 2. Littlewood-Paley theory 3. Around Biot-Savart's law 4. The case of a smooth initial data 5. When the vorticity is bounded 6. Vortex sheets 7. The wave front and the product 8. Analyticity and Gevrey regularity 9. Singular vortex patches References
629 citations
01 Jan 1998
TL;DR: A method for solving the equations governing time-dependent, variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids based on a projection formulation in which the first step is to solve advection?diffusion equations to predict intermediate velocities, and then project these Velocities onto a space of approximately divergence-free vector fields.
Abstract: In this paper we present a method for solving the equations governing timedependent, variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids. The method is based on a projection formulation in which we first solve advection‐diffusion equations to predict intermediate velocities, and then project these velocities onto a space of approximately divergence-free vector fields. Our treatment of the first step uses a specialized second-order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high Reynolds number flow. Density and other scalars are advected in such a way as to maintain conservation, if appropriate, and free-stream preservation. Our approach to adaptive refinement uses a nested hierarchy of logically-rectangular girds with simultaneous refinement of the girds in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithms’s accuracy and convergence properties, and illustrate the behavior of the method. An additional example demonstrates the performance of the method on a more realistic problem, namely, a three-dimensional variable density shear layer. c ∞ 1998 Academic Press
483 citations
TL;DR: In this article, the authors present a method for solving the equations governing time-dependent, variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids.
477 citations
TL;DR: In this paper, the amplitude of the rapid fluctuations introduces a length scale, α, below which wave activity is filtered by both linear and nonlinear dispersion, which enhances the stability and regularity of the new fluid models without compromising either their large scale behavior, or their conservation laws.
Abstract: We propose a new class of models for the mean motion of ideal incompressible fluids in three dimensions, including stratification and rotation. In these models, the amplitude of the rapid fluctuations introduces a length scale, α, below which wave activity is filtered by both linear and nonlinear dispersion. This filtering enhances the stability and regularity of the new fluid models without compromising either their large scale behavior, or their conservation laws. These models also describe geodesic motion on the volume-preserving diffeomorphism group for a metric containing the H1 norm of the fluid velocity.
334 citations
Book•
11 May 1998
TL;DR: The Navier-Stokes equation is derived from the advection-diffusion equation as discussed by the authors, and the Navier Stokes equation derived quantities are derived from weak operators some element matrices and projection methods.
Abstract: The advection-diffusion equation the Navier-Stokes equation derived quantities. Appendices: weak operators some element matrices and projection methods.
324 citations
TL;DR: In this article, a discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids, where the governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model.
Abstract: A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplyfying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.
279 citations
TL;DR: In this paper, the authors studied the transport of particles in a general, two-dimensional, incompressible flow in the presence of a transient eddy, i.e., a bounded set of closed streamlines with a finite time of existence.
220 citations
TL;DR: In this paper, the generalized momentum equation was used to simulate the temporal energy transport for incompressible flows through a packed bed and the governing equations were formulated according to the volume averaging method.
TL;DR: In this article, a 2D laminar free convection flow of an incompressible, viscous, electrically conducting (Newtonian or polar) fluid through a porous medium bounded by an infinite vertical plane surface of constant temperature is considered.
Abstract: The present work is concerned with unsteady 2-dimensional laminar free convection flow of an incompressible, viscous, electrically conducting (Newtonian or polar) fluid through a porous medium bounded by an infinite vertical plane surface of constant temperature. A uniform magnetic field acts perpendicular to the surface which absorbs the fluid with a suction velocity varying periodically with time about a non-zero constant mean value. The equations of conservation of mass, momentum, angular velocity, and energy, which govern the flow and heat transfer problem, are solved analytically using regular perturbation techniques. The effects of material parameters such as Grashof number, Prandtl number, permeability parameter, suction parameter, and magnetic parameter on the velocity, angular velocity, and temperature are discussed. Numerical results are presented graphically and discussed.
TL;DR: In this paper, a numerical simulation of forced convective, incompressible flow in a channel with an array of heated obstacles attached to one wall is presented, and three levels of Nusselt numbers are emphasized in this systematic analysis: local distributions along the obstacle exposed faces, mean values for individual faces, and overall obstacle mean values.
TL;DR: In this paper, a generalization of earlier preconditioning methods that enables efficient computation of arbitrary equation of state fluids, perfect gases, and incompressible fluids by a single procedure is presented.
Abstract: The extension of time-marching computations to fluids with arbitrary equations of state is demonstrated by means of stability analyses, simplified problems, and practical applications. Most of the examples use the properties of supercritical hydrogen for which the density varies by more than an order of magnitude for small changes in pressure and temperature, but representative computations for incompressible fluids and perfect gases are also given to demonstrate the generality of the procedure. Because representative flow velocities in typical supercritical fluids applications are much lower than the speed of sound, convergence enhancement through eigenvalue control is often necessary. This is accomplished through a generalization of earlier preconditioning methods that enables efficient computation of arbitrary equation of state fluids, perfect gases, and incompressible fluids by a single procedure. The present approach thus provides a single method that is uniformly applicable to all equations of state
TL;DR: The objective of the present work is to show the performance of this algorithm when it is used to solve thermal flow problems, both natural and forced convection and transient problems are considered.
Abstract: In our earlier papers we have presented a general algorithm for the solution of both compressible and incompressible Navier‐Stokes equations. The objective of the present work is to show the performance of this algorithm when it is used to solve thermal flow problems. Both natural and forced convection and transient problems are considered in this study. The semi‐implicit form of the algorithm has been used to deal with a variety of these problems.
TL;DR: In this paper, a multiple-time scale, single-space scale asymptotic analysis of the compressible Navier-Stokes equations reveals how the heat-release rate and heat conduction affect the zeroth-order global thermodynamic pressure, the divergence of velocity and the material change of density at low-Mach-numbers.
Abstract: A multiple-time scale, single-space scale asymptotic analysis of the compressible Navier-Stokes equations reveals how the heat-release rate and heat conduction affect the zeroth-order global thermodynamic pressure, the divergence of velocity and the material change of density at low-Mach-numbers The asymptotic analysis identifies the acoustic time change of the heat-release rate as the dominant source of sound in low-Mach-number flow The viscous and buoyancy forces enter the computation of the second-order ‘incompressible’ pressure in low-Mach-number flow in a similar way as they enter the pressure computation in incompressible flow, except for a nonzero velocity-divergence constraint If the flow equations are averaged over an acoustic wave period, the averaged velocity tensor describes the net acoustic effect on the averaged flow field Removing acoustics from the equations altogether leads to the low-Mach-number equations, which allow for large temperature and density changes as opposed to the Boussinesq equations
TL;DR: In this article, a semi-analytical method was developed to solve for the inviscid incompressible flow induced by a heavily loaded actuator disk with non-uniform loading.
Abstract: A semi-analytical method has been developed to solve for the inviscid incompressible flow induced by a heavily loaded actuator disk with non-uniform loading. The solution takes the contraction of the slipstream fully into account. The method is an extension of the analytical theory of Conway (1995) for the linearized actuator disk and is exact for an incompressible perfect fluid. The solutions for the velocities and stream function are given as one-dimensional integrals of expressions containing complete elliptic integrals. Any load distribution with bounded radial gradient can be treated. Results are presented here for both contra-rotating and normal propellers. For the special case of a contra-rotating propeller with a parabolic velocity profile in the ultimate wake, the vorticity in the slipstream is shown to be the same as in the analytically tractable spherical vortex of Hill (1894) and the related family of steady vortices explored by Fraenkel (1970, 1972) and Norbury (1973).
TL;DR: In this article, it was shown that compressible Navier-Stokes flows in two and three dimensions converge to incompressible flows in the limit as the Mach number tends to zero, and the essential mechanism in this process is a hyperbolic effect which becomes stronger with smaller Mach number and which ultimately drives the density to a constant.
Abstract: We prove that compressible Navier-Stokes flows in two and three space dimensions converge to incompressible Navier-Stokes flows in the limit as the Mach number tends to zero. No smallness restrictions are imposed on the external force, the initial velocity, or the time interval. We assume instead that the incompressible flow exists and is reasonably smooth on a given time interval, and prove that compressible flows with compatible initial data converge uniformly on that time interval. Our analysis shows that the essential mechanism in this process is a hyperbolic effect which becomes stronger with smaller Mach number and which ultimately drives the density to a constant.
TL;DR: In this paper, a tool for numerical shape optimization of axisymmetric bodies submerged in incompressible flow at zero incidence has been developed, where a source distribution on the body axis was chosen to model the body contour and the corresponding inviscid flowfield, with the source strengths being used as design variables for the optimization process.
Abstract: A tool for the numerical shape optimization of axisymmetric bodies submerged in incompressible flow at zero incidence has been developed. Contrary to the usual approach, the geometry of the body is not optimized in a direct way with this method. Instead, a source distribution on the body axis was chosen to model the body contour and the corresponding inviscid flowfield, with the source strengths being used as design variables for the optimization process. Boundary-layer calculation is performed by means of a proved integral method. To determine the transition location, a semiempirical method based on linear stability theory (e n method) was implemented. A commercially available hybrid optimizer as well as an evolution strategy with covariance matrix adaption of the mutation distribution are applied as optimization algorithms. Shape optimizations of airship hulls were performed for different Reynolds number regimes. The objective was to minimize the drag for a given volume of the envelope and a prescribed airspeed range
01 Jan 1998
TL;DR: In this article, the authors focus on finite volume methods of discretization for the partial differential equations manifesting the physical model of incompressible interfacial flows, i.e., flows possessing multiple distinct, immiscible fluids separated by interfaces of arbitrarily complex topology.
Abstract: Incompressible interfacial flows here refer to those incompressible flows possessing multiple distinct, immiscible fluids separated by interfaces of arbitrarily complex topology. A prototypical example is free surface flows, where fluid properties across the interface vary by orders of magnitude. Interfaces present in these flows possess topologies that are not only irregular but also dynamic, undergoing gross changes such as merging, tearing, and filamenting as a result of the flow and interface physics such as surface tension and phase change. The interface topology requirements facing an algorithm tasked to model these flows inevitably leads to an underlying Eulerian methodology. The discussion herein is confined therefore to Eulerian schemes, with further emphasis on finite volume methods of discretization for the partial differential equations manifesting the physical model.
TL;DR: The development of unstructured grid-based, finite-element methods for the simulation of fluid flows is reviewed, employing methods based upon a Galerkin discretization in space together with an appropriate finite-difference representation in time.
Abstract: The development of unstructured grid-based, finite-element methods for the simulation of fluid flows is reviewed. The review concentrates on solution techniques for the compressible Euler and Navier-Stokes equations, employing methods which are based upon a Galerkin discretization in space together with an appropriate finite-difference representation in time. It is assumed that unstructured assemblies of triangles are used to achieve the spatial discretization in two dimensions, with unstructured assemblies of tetrahedra employed in the three-dimensional case. Adaptive grid procedures are discussed and methods for accelerating the iterative solution convergence are considered. The areas of incompressible flow modelling and optimization are also included.
TL;DR: In this paper, a higher-order finite difference method (FDM) has been developed for the body-fitted coordinate system and the consistency and the conservatior property of FDMs are discussed for the collocated grid.
Abstract: To apply the direct numerical simulation (DNS) and the large-eddy simulation (LES) of turbulence to flow fields of complicated geometry, a higher-order finite difference method (FDM) has been developed for the body-fitted coordinate system The consistency and the conservat ior property of FDMs are discussed for the collocated grid As numerical examples, DNS results of decaying isotropic turbulence and DNS/LES results for plane channel flow are shown and the influence of variable arrangement is examined The results by the consistent 'interpolation' method for gradient form on the collocated grid agree well with those by other proper FDMs and the spectral method
TL;DR: In this paper, a complete system of dynamical equations for the invariants of the velocity gradient, the strain rate, and the rate-of-rotation tensors is deduced for an incompressible flow.
Abstract: A complete system of dynamical equations for the invariants of the velocity gradient, the strain rate, and the rate-of-rotation tensors is deduced for an incompressible flow. The equations for the velocity gradient invariants R and Q were first deduced by Cantwell [Phys. Fluids A 4, 782 (1992)] in terms of Hij, the tensor containing the anisotropic part of the pressure Hessian and the viscous diffusion term in the velocity gradient equation. These equations are extended here for the strain rate tensor invariants, RS and QS, and for the rate-of-rotation tensor invariant, QW, using HijS and HijW, the symmetric and the skew-symmetric parts of Hij, respectively. In order to obtain a complete system, an equation for the square of the vortex stretching vector, Vi≡Sijωj, is required. The resulting dynamical system of invariants is closed using a simple model for the velocity gradient evolution: an isotropic approximation for the pressure term and a linear model for the viscous diffusion term. The local topology ...
01 Feb 1998
TL;DR: In this paper, a higher order numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretisation.
Abstract: A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems
TL;DR: In this article, the homogenization of convection-diffusion in a time-dependent, ergodic, incompressible random flow with a bounded stream matrix and a constant mean drift was shown.
Abstract: We prove the homogenization of convection-diffusion in a time-dependent, ergodic, incompressible random flow which has a bounded stream matrix and a constant mean drift. We also prove two variational formulas for the effective diffusivity. As a consequence, we obtain both upper and lower bounds on the effective diffusivity.
TL;DR: In this article, the authors consider one-dimensional capillary redistribution of two immiscible and incompressible fluids in a porous medium with a single discontinuity and study a special time-dependent solution, a similarity solution, which is found when the initial saturation is discontinuous at the same point as the permeability and porosity, and is constant elsewhere.
TL;DR: In this paper, the dynamics of a passive particle in a two-dimensional incompressible flow generated by three point vortices advected by their mutual interaction is considered as a periodically forced Hamiltonian system.
Abstract: The dynamics of a passive particle in a two-dimensional incompressible flow generated by three point vortices advected by their mutual interaction is considered as a periodically forced Hamiltonian system. The geometry of the background vortex flow determines the degree of chaotization of the tracer motion. Two extreme regimes, of strong and weak chaos, are specified and investigated analytically. Mappings are derived for both cases, and the border between the chaotic and regular advection is found by applying the stochasticity criterion. In the case of strong chaos, there exist coherent regular structures around vortices (vortex cores), which correspond to domains with $\mathrm{KAM}$ curves. An expression for the radius of the cores is obtained. The robust nature of vortex cores, demonstrated numerically, is explained. In the near-integrable case of weak chaotization, a separatrix map is used to find the width of the stochastic layer. Numerical simulations reveal a variety of structures in the pattern of advection, such as a hierarchy of island chains and sticky bands around the vortex cores.
TL;DR: In this paper, a method for computing unsteady incompressible viscous flows on moving or deforming meshes is described using a well-established time-marching finite-volume flow solver, developed for steady compressible flows past rigid bodies.
Abstract: A method for computing unsteady incompressible viscous flows on moving or deforming meshes is described. It uses a well-established time-marching finite-volume flow solver, developed for steady compressible flows past rigid bodies. Time-marching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. Such methods can be extended to steady incompressible flows using an artificial compressibility scheme. A time-accurate scheme for unsteady incompressible flows is achieved by using an implicit real-time discretization and a dual-time approach, which uses a technique similar to the artificial compressibility scheme. Results are presented for test cases on both fixed and deforming meshes. Experimental, numerical and theoretical data have been included for comparison where available and reasonable agreement has been achieved. © 1998 John Wiley & Sons, Ltd.
TL;DR: In this article, a front tracking method to study multi-fluid flows in which a sharp interface separates incompressible fluids of different densities and viscosities is adopted to simulate the unsteady motion of an infinitely thin premixed flame characterized by significant chemical heat release and hence thermal expansion.
TL;DR: A stabilization technique for Finite Element numerical solution of 2D and 3D incompressible flow problems, which may be applied to stabilize the discretization of the pressure gradient, and also of any individual operator term such as the convection, curl or divergence operators, with specific levels of numerical diffusion.
Abstract: This paper introduces a stabilization technique for Finite Element numerical solution of 2D and 3D incompressible flow problems. It may be applied to stabilize the discretization of the pressure gradient, and also of any individual operator term such as the convection, curl or divergence operators, with specific levels of numerical diffusion for each one of them. Its computational complexity is reduced with respect to usual (residual-based) stabilization techniques. We consider piecewise affine Finite Elements, for which we obtain optimal error bounds for steady Navier-Stokes and also for generalized Stokes equations (including convection). We include some numerical experiment in well known 2D test cases, that show its good performances.