Conservative Finite Difference Schemes for Cosymmetric Systems

We consider the application of computer algebra for the derivation of the formula for the preservation of the cosymmetry property through discretization of partial differential equations. The finite difference approximations of differential operators for both regular and staggered grids are derived and applied to the planar filtration-convection problem.

[1]  V. I. Yudovich,et al.  Cosymmetry, degeneration of solutions of operator equations, and onset of a filtration convection , 1991 .

[2]  M. Shashkov.  Conservative Finite-Difference Methods on General Grids , 1996 .

[3]  Lynne D. Talley,et al.  Generalizations of Arakawa's Jacobian , 1989 .

[4]  C. Budd,et al.  The geometric integration of scale-invariant ordinary and partial differential equations , 2001 .

[5]  Evgenii V. Vorozhtsov,et al.  Numerical Solutions for Partial Differential Equations: Problem Solving Using Mathematica , 1996 .

[6]  V. I. Yudovich,et al.  Implicit function theorem for cosymmetric equations , 1996 .

[7]  Paul C. Abbott.  Problem Solving Using Mathematica , 1991, Programming Environments for High-Level Scientific Problem Solving.

[8]  Richard Liska,et al.  Where Numerics Can Benefit from Computer Algebra in Finite Difference Modelling of Fluid Flows , 1999, CASC.

[9]  A. Arakawa.  Computational design for long-term numerical integration of the equations of fluid motion: two-dimen , 1997 .

[10]  D. Jespersen,et al.  Arakawa's method is a finite-element method , 1974 .

[11]  Robert I McLachlan.  Spatial discretization of partial differential equations with integrals , 1998 .

[12]  V. I. Yudovich,et al.  Secondary cycle of equilibria in a system with cosymmetry, its creation by bifurcation and impossibility of symmetric treatment of it. , 1995, Chaos.

[13]  Bülent Karasözen,et al.  Finite-difference approximations and cosymmetry conservation in filtration convection problem , 1999 .

[14]  P. Moin,et al.  Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow , 1998 .