Numerical solutions of 2‐D steady incompressible flow in a driven skewed cavity

The benchmark test case for non-orthogonal grid mesh, the "driven skewed cavity flow", first introduced by Demirdzice t al. (5) for skew angles of α =3 0 ◦ and α =4 5 ◦ , is reintroduced with a more variety of skew angles. The benchmark problem has non-orthogonal, skewed grid mesh with skew angle (α). The governing 2-D steady incompressible Navier-Stokes equations in general curvilinear coordinates are solved for the solution of driven skewed cavity flow with non-orthogonal grid mesh using a numerical method which is efficient and stable even at extreme skew angles. Highly accurate numerical solutions of the driven skewed cavity flow, solved using a fine grid (512 × 512) mesh, are presented for Reynolds number of 100 and 1000 for skew angles ranging between 15 ◦ α 165 ◦ . c

[1]  C. Zenger,et al.  An asymptotic solution for the singularity at the angular point of the lid driven cavity , 1994 .

[2]  Chao Zhang,et al.  Study of the effect of the non‐orthogonality for non‐staggered grids—The results , 1998 .

[3]  A. Shklyar,et al.  Numerical method for calculation of the incompressible flow in general curvilinear co‐ordinates with double staggered grid , 2003 .

[4]  H. B. Keller,et al.  Driven cavity flows by efficient numerical techniques , 1983 .

[5]  R. T. Fenner,et al.  Boundary element analysis of driven cavity flow for low and moderate Reynolds numbers , 2001 .

[6]  W. Spotz Accuracy and performance of numerical wall boundary conditions for steady, 2D, incompressible streamfunction vorticity , 1998 .

[7]  L. Quartapelle,et al.  A review of vorticity conditions in the numerical solution of the ζ–ψ equations , 1999 .

[8]  Chao Zhang,et al.  Numerical calculations of laminar flows using contravariant velocity fluxes , 2000 .

[9]  T. Corke,et al.  Numerical Solutions of Laminar Incompressible Flow Past Parabolic Bodies at Angles of Attack , 2004 .

[10]  E. Erturk,et al.  Numerical solutions of 2‐D steady incompressible driven cavity flow at high Reynolds numbers , 2004, ArXiv.

[11]  P. Tucker,et al.  A Cartesian cut cell method for incompressible viscous flow , 2000 .

[12]  M. Peric ANALYSIS OF PRESSURE-VELOCITY COUPLING ON NONORTHOGONAL GRIDS , 1990 .

[13]  P. Wesseling,et al.  Schwarz domain decomposition for the incompressible Navier-Stokes equations in general co-ordinates , 2000 .

[14]  B. Fornberg,et al.  A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations , 1995 .

[15]  A. Thom,et al.  The flow past circular cylinders at low speeds , 1933 .

[16]  Sarit K. Das,et al.  An efficient solution method for incompressible N-S equations using non-orthogonal collocated grid , 1999 .

[17]  E. Brakkee,et al.  International Journal for Numerical Methods in Fluids Schwarz Domain Decomposition for the Incompressible Navier–stokes Equations in General Co-ordinates , 2022 .

[18]  V. Denny,et al.  On the convergence of numerical solutions for 2-D flows in a cavity at large Re , 1979 .

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

[20]  J. Pacheco,et al.  NONSTAGGERED BOUNDARY-FITTED COORDINATE METHOD FOR FREE SURFACE FLOWS , 2000 .

[21]  Kim Dan Nguyen,et al.  AN EFFICIENT FINITE DIFFERENCE TECHNIQUE FOR COMPUTING INCOMPRESSIBLE VISCOUS FLOWS , 1997 .

[22]  Nobuyuki Satofuka,et al.  Higher‐order solutions of square driven cavity flow using a variable‐order multi‐grid method , 1992 .

[23]  H. K. Moffatt Viscous and resistive eddies near a sharp corner , 1964, Journal of Fluid Mechanics.

[24]  P. Wesseling,et al.  Benchmark solutions for the incompressible Navier–Stokes equations in general co‐ordinates on staggered grids , 1993 .

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

[26]  B. Wetton,et al.  Discrete Compatibility in Finite Difference Methods for Viscous Incompressible Fluid Flow , 1996 .

[27]  E. Erturk,et al.  Fourth‐order compact formulation of Navier–Stokes equations and driven cavity flow at high Reynolds numbers , 2004, ArXiv.

[28]  Murli M. Gupta,et al.  Nature of viscous flows near sharp corners , 1981 .

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

[30]  N. G. Wright,et al.  An efficient multigrid approach to solving highly recirculating flows , 1995 .

[31]  S. Komori,et al.  On the improvement of the SIMPLE-like method for flows with complex geometry , 2000 .

[32]  Yuying Yan,et al.  The effect of choosing dependent variables and cell‐face velocities on convergence of the SIMPLE algorithm using non‐orthogonal grids , 2001 .

[33]  Jian‐Guo Liu,et al.  Vorticity Boundary Condition and Related Issues for Finite Difference Schemes , 1996 .