Parallel unsteady incompressible viscous flow computations using an unstructured multigrid method

Tai, Chin Hoe; Zhao, Yong

doi:10.1016/j.jcp.2003.07.005

Cited by 39 publications

(58 citation statements)

References 32 publications

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“…It is possible to select different numbers and directions for waves and use their corresponding compatibility relations for evaluating interface values. By selecting the above waves, to evaluate the convective flux at face * in Figure 2, the following four compatibility relations are utilized (obtained from Equation (12) for different values of ): n t du +d p = 0 on = 0 pseudo-acoustic wave…”

Section: Convective Fluxesmentioning

confidence: 99%

Genuinely multidimensional characteristic‐based scheme for incompressible flows

Razavi

Zamzamian

Farzadi

2007

Numerical Methods in Fluids

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SUMMARYThis paper presents a novel multidimensional characteristic-based (MCB) upwind method for the solution of incompressible Navier-Stokes equations. As opposed to the conventional characteristic-based (CB) schemes, it is genuinely multidimensional in that the local characteristic paths, along which information is propagated, are used. For the first time, the multidimensional characteristic structure of incompressible flows modified by artificial compressibility is extracted and used to construct an inherent multidimensional upwind scheme. The new proposed MCB scheme in conjunction with the finite-volume discretization is employed to model the convective fluxes. Using this formulation, the steady two-dimensional incompressible flow in a lid-driven cavity is solved for a wide range of Reynolds numbers. It was found that the new proposed scheme presents more accurate results than the conventional CB scheme in both their firstand second-order counterparts in the case of cavity flow. Also, results obtained with second-order MCB scheme in some cases are more accurate than the central scheme that in turn provides exact second-order discretization in this grid. With this inherent upwinding technique for evaluating convective fluxes at cell interfaces, no artificial viscosity is required even at high Reynolds numbers. Another remarkable advantage of MCB scheme lies in its faster convergence rate with respect to the CB scheme that is found to exhibit substantial delays in convergence reported in the literature. The results obtained using new proposed scheme are in good agreement with the standard benchmark solutions in the literature.

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Section: Convective Fluxesmentioning

confidence: 99%

Genuinely multidimensional characteristic‐based scheme for incompressible flows

Razavi

Zamzamian

Farzadi

2007

Numerical Methods in Fluids

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“…Unlike the parallel implementations in [7,17], where one or more 'overlapping' layers of ghost nodes are added to each partition boundary for the communication. In the present work, we propose to use a non-overlapping or 'seamless connectivity' approach.…”

Section: Parallelization Of Discrete Operatorsmentioning

confidence: 99%

“…Of course, the unstructured data management unavoidably raises the complexity of parallelization. Many references on parallelization of implicit unstructured solvers can be found in the published literatures, such as [7][8][9][10] on FVM, [11] on FEM and [12][13][14][15] on Control Volume Finite Element Method (CVFEM) (which is a mixture of FVM and FEM), just to list a few. The implicit parallel solution algorithm for Navier-Stokes equations in this work is based on the Domain Decomposition (DD) approach, which is preferable on a computer system with distributed memory.…”

Section: Introductionmentioning

confidence: 99%

Parallel computing strategy for a flow solver based on immersed boundary method and discrete stream-function formulation

Wang

Zhang

2013

Computers & Fluids

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a b s t r a c tThe development of a parallel immersed boundary solver for flows with complex geometries is presented. The numerical method for incompressible Navier-Stokes equations is based on the discrete streamfunction formulation and unstructured Cartesian grid framework. The code parallelization is achieved by using the domain decomposition (DD) approach and Single Program Multiple Data (SPMD) programming paradigm, with the data communication among processes via the MPI protocol. A 'gathering and scattering' strategy is used to handle the force computing on the immersed boundaries. Three tests, 3D lid-driven cavity flow, sedimentation of spheres in a container and flow through and around a circular array of cylinders are performed to evaluate the parallel efficiency of the code. The speedups obtained in these tests on a workstation cluster are reasonably good for the problem size up to 10 million and the number of processes in the range of 16-2048.

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“…This method has been used widely to simulate incompressible flows in different conditions, including extensions to threedimensional flows [8] and multigrid techniques [9], porous media [10], flows with various densities [11,12], turbulent flow simulation [13], and non-Newtonian flows [14]. In addition, the CB scheme was used extensively by Zhao et al to calculate incompressible flows with energy equations to address two-and three-dimensional problems with unstructured grids in conjunction with parallel computations [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…In all previous studies in this area, ordinary extrapolation from the interior cells in the domain near the wall has been used to estimate the pressure on solid walls. This is the case for incompressible flow simulations in conjunction with the AC method with various numerical characteristic-based schemes [10,[14][15][16][17]20], or the other schemes discussed above [5,6]. In the present study, we propose a new approach based on the multidimensional characteristic structure of AC equations near the solid walls together with the ghost cell concept for estimating pressure on the solid boundaries.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional characteristic-based solid boundary condition for incompressible flow calculations

Zamzamian

Hashemi

2015

Applied Mathematical Modelling

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a b s t r a c tUsing the artificial compressibility (AC) approach for incompressible flows, the NavierStokes equations are coupled together to obtain solutions for steady flows, where marching in time methods are applicable. In this study, we present a new method that employs the multidimensional characteristics of AC equations to calculate the solid boundary conditions. The first multidimensional characteristic-based scheme (MCB) for incompressible flows was proposed in a previous study. In the present study, this idea is implemented by using the characteristic structure of AC equations near solid walls together with a ghost cell method to satisfy the solid boundary conditions. We test the new proposed method with two well-known benchmark problems, where the results show that the accuracy and convergence speed of the MCB scheme is improved in many cases.

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Parallel unsteady incompressible viscous flow computations using an unstructured multigrid method

Cited by 39 publications

References 32 publications

Genuinely multidimensional characteristic‐based scheme for incompressible flows

Genuinely multidimensional characteristic‐based scheme for incompressible flows

Parallel computing strategy for a flow solver based on immersed boundary method and discrete stream-function formulation

Multidimensional characteristic-based solid boundary condition for incompressible flow calculations

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