Algebraic Construction of a Strongly Consistent, Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow

摘要: By using symbolic algebraic computation, we construct a strongly-consistent second-order finite difference scheme for steady three-dimensional Stokes flow and Cartesian solution grid. The has the second order of accuracy incorporates pressure Poisson equation. This equation is integrability condition discrete momentum continuity equations. Our approach to construction schemes suggested by third authors combines volume method, numerical integration, elimination. We make use techniques differential Janet/Grobner bases performing related computations. To prove strong consistency generated scheme, these correlate ideal polynomials in equations with constructed scheme. As this takes place, our conservative inherits permutation symmetry flow. For obtained compute modified system it analyze scheme’s accuracy.