Finite volume adaptive solutions using SIMPLE as smoother

This paper describes a new multilevel procedure that can solve the discrete Navier-Stokes system arising from finite volume discretizations on composite grids, which may consist of more than one level. SIMPLE is used and tested as the smoother, but the multilevel procedure is such that it does not exclude the use of other smoothers. Local refinement is guided by a criterion based on an estimate of the truncation error. The numerical experiments presented test not only the behaviour of the multilevel algebraic solver, but also the efficiency of local refinement based on this particular criterion.

[1]  M. Perić,et al.  EFFICIENCY AND ACCURACY ASPECTS OF A FULL-MULTIGRID SIMPLE ALGORITHM FOR THREE-DIMENSIONAL FLOWS , 1997 .

[2]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[3]  Inge K. Eliassen,et al.  A multiblock/multilevel mesh refinement procedure for CFD computations , 2001 .

[4]  P. Colella,et al.  A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains , 1998 .

[5]  Nami Matsunaga,et al.  Superconvergence of the Shortley-Weller approximation for Dirichlet problems , 2000 .

[6]  M. Hortmann,et al.  Finite volume multigrid prediction of laminar natural convection: Bench-mark solutions , 1990 .

[7]  M. Paisley.  Multigrid solution of the incompressible Navier-Stokes equations for three-dimensional recirculating flow : Coupled and decoupled smoothers compared , 1999 .

[8]  Tim Lee,et al.  Experimental and numerical investigation of 2-D backward-facing step flow , 1998 .

[9]  Sophie Papst,et al.  Computational Methods For Fluid Dynamics , 2016 .

[10]  Franz Durst,et al.  Local block refinement with a multigrid flow solver , 2002 .

[11]  G. Bergeles,et al.  A multigrid method with higher-order discretization schemes , 2001 .

[12]  J. Ferziger,et al.  An adaptive multigrid technique for the incompressible Navier-Stokes equations , 1989 .

[13]  Alexandros Syrakos,et al.  Estimate of the truncation error of a finite volume discretisation of the Navier-Stokes equations on colocated grids , 2015, ArXiv.

[14]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[15]  G. J. Shaw,et al.  A multigrid method for recirculating flows , 1988 .

[16]  A. D. Gosman,et al.  RESIDUAL ERROR ESTIMATE FOR THE FINITE-VOLUME METHOD , 2001 .

[17]  B. Armaly,et al.  Experimental and theoretical investigation of backward-facing step flow , 1983, Journal of Fluid Mechanics.

[18]  M. F. Paisley,et al.  Comparison of Multigrid Methods for Neutral and Stably Stratified Flows over Two-Dimensional Obstacles , 1998 .

[19]  Anton Schüller,et al.  Adaptive parallel multigrid solution of 2D incompressible Navier-Stokes equations , 1997 .

[20]  Michael Pernice,et al.  A Multigrid-Preconditioned Newton-Krylov Method for the Incompressible Navier-Stokes Equations , 2001, SIAM J. Sci. Comput..

[21]  Fue-Sang Lien,et al.  Multigrid acceleration for recirculating laminar and turbulent flows computed with a non-orthogonal, collocated finite-volume scheme , 1994 .

[22]  G. Gutiérrez,et al.  NUMERICAL ANALYSIS IN INTERRUPTED CUTTING TOOL TEMPERATURES , 2001 .

[23]  Horst Stoff,et al.  Calculation of three‐dimensional turbulent flow with a finite volume multigrid method , 1999 .

[24]  R. P. Fedorenko.  A relaxation method for solving elliptic difference equations , 1962 .

[25]  F. Bramkamp,et al.  An adaptive multiscale finite volume solver for unsteady and steady state flow computations , 2004 .

[26]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[27]  Surya Pratap Vanka,et al.  A multigrid procedure for three-dimensional flows on non-orthogonal collocated grids , 1993 .

[28]  G. J. Shaw,et al.  On the smoothing properties of the simple pressure-correction algorithm , 1988 .

[29]  T. Gjesdal,et al.  Comparison of pressure correction smoothers for multigrid solution of incompressible flow , 1997 .

[30]  S. Muzaferija,et al.  Adaptive finite volume method for flow prediction using unstructured meshes and multigrid approach , 1994 .

[31]  I. Demirdzic,et al.  Fluid flow and heat transfer test problems for non‐orthogonal grids: Bench‐mark solutions , 1992 .

[32]  O. Botella,et al.  BENCHMARK SPECTRAL RESULTS ON THE LID-DRIVEN CAVITY FLOW , 1998 .