ON DISCRETE PROJECTION AND NUMERICAL BOUNDARY CONDITIONS FOR THE NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

• 来源期刊: 计算数学（英文版）
• 学科: 数学
• 关键词: Differential algebraic equations Discrete projection Numerical boundary con-ditions.
• 年，卷（期）: 2002,（1）
• 页码范围: 35-56
• 页数: 22页
• 分类号: O1
• 语种: 英文

摘要

The unsteaiy incompressible Navier-Stokes equations are discretized in space and stud-ied on the fixed mesh as a system of differential algebraic equations. With discrete projec-tion defined, the local errors of Crank Nicholson schemes with three projection methodsare derived in a straightforward manner. Then the approximate factorization of relevantmatrices are used to study the time accuracy with more detail, especially at points adjacentto the boundary. The effects of numerical boundary conditions for the auxiliary velocityand the discrete pressure Poisson equation on the time accuracy are also investigated. Re-sults of numerical experiments with an analytic example confirm the conclusions of ouranalysis.