A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach

[1]  O. Burggraf Analytical and numerical studies of the structure of steady separated flows , 1966, Journal of Fluid Mechanics.

[2]  Robert J. MacKinnon,et al.  Differential‐equation‐based representation of truncation errors for accurate numerical simulation , 1991 .

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

[4]  E Weinan,et al.  Finite Difference Schemes for Incompressible Flows in the Velocity-Impulse Density Formulation , 1997 .

[5]  P. N. Shankar,et al.  The eddy structure in Stokes flow in a cavity , 1993, Journal of Fluid Mechanics.

[6]  D. Zorin,et al.  A fast solver for the Stokes equations with distributed forces in complex geometries , 2004 .

[7]  Julio M. Ottino,et al.  Experimental and computational studies of mixing in complex Stokes flows: the vortex mixing flow and multicellular cavity flows , 1994, Journal of Fluid Mechanics.

[8]  G. Carey,et al.  High‐order compact scheme for the steady stream‐function vorticity equations , 1995 .

[9]  Murli M. Gupta A fourth-order poisson solver , 1984 .

[10]  A. Cheng,et al.  Boundary element solution for steady and unsteady Stokes flow , 1994 .

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

[12]  Murli M. Gupta High accuracy solutions of incompressible Navier-Stokes equations , 1991 .

[13]  L. Collatz The numerical treatment of differential equations , 1961 .

[14]  Jiten C. Kalita,et al.  A fourth-order accurate compact scheme for the solution of steady Navier–Stokes equations on non-uniform grids , 2008 .

[15]  Kazufumi Ito,et al.  Preconditioned iterative methods on sparse subspaces , 2006, Appl. Math. Lett..

[16]  Jun Zhang,et al.  High order ADI method for solving unsteady convection-diffusion problems , 2004 .

[17]  Julio M. Ottino,et al.  Experiments on mixing due to chaotic advection in a cavity , 1989, Journal of Fluid Mechanics.

[18]  Yiping,et al.  COMPACT FOURTH-ORDER FINITE DIFFERENCE SCHEMES FOR HELMHOLTZ EQUATION WITH HIGH WAVE NUMBERS , 2008 .

[19]  K. Ito,et al.  An augmented approach for Stokes equations with a discontinuous viscosity and singular forces , 2007 .

[20]  Tao Tang,et al.  A Compact Fourth-Order Finite Difference Scheme for Unsteady Viscous Incompressible Flows , 2001, J. Sci. Comput..

[21]  J. E. Gómez,et al.  A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number , 1997 .

[22]  M. Kohr Boundary element method to the study of a Stokes flow past an obstacle in a channel , 1997 .

[23]  A. Acrivos,et al.  Steady flows in rectangular cavities , 1967, Journal of Fluid Mechanics.

[24]  S. Lele Compact finite difference schemes with spectral-like resolution , 1992 .

[25]  E. Purcell Life at Low Reynolds Number , 2008 .

[26]  R. Temam,et al.  REGULARITY RESULTS FOR LINEAR ELLIPTIC PROBLEMS RELATED TO THE PRIMITIVE EQUATIONS , 2002 .