Dr. Xiaojing Zhang, (ICMSEC, AMSS)

Application of Difference Algebra in Difference Scheme for Nonlinear Differential Equations

10 月 12 日（周二） 上午 10:00-11:00 数学院南楼 202 教室

We construct a strongly-consistent explicit finite difference scheme for 3D constant viscosity incompressible Navier-Stokes equations by using of symbolic algebraic computation. The difference scheme is space second order accurate and temporal first order accurate. It is proved that difference Grobner basis algorithm is correct. By using of difference Gro ̈bner basis computation method, an element in Gr ̈obner basis of difference scheme for momentum equations is a difference scheme for pressure Poisson equation. We prove that, for strongly consistent difference scheme, each element in the difference Gro bner basis of such difference scheme always approximates a differential equation which vanishes on the analytic solutions of Navier-Stokes equations. To prove the strongly consistency of this difference scheme, the differential Thomas decomposition theorem for nonlinear differential equations and difference Grobner basis theorems for difference equations are applied. Numerical test certifies that strongly consistent difference scheme is effective. 

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