A NOTE ON PRESSURE APPROXIMATION OF FIRST AND HIGHER ORDER PROJECTION SCHEMES FOR THE NONSTATIONARY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

• 来源期刊: 计算数学（英文版）
• 关键词: Incompressible Navier-Stokes equation Time discretization Projection method
• 年，卷（期）: 2009,（2）
• 页码范围: 338-347
• 页数: 10页
• 语种: 英文

摘要

Projection methods are efficient operator-splitting schemes to approximate solutions of the incompressible Navier-Stokes equations. As a major drawback, they introduce spurious layers, both in space and time. In this work, we survey convergence results for higher order projection methods, in the presence of only strong solutions of the limiting problem; in particular, we highlight concomitant difficulties in the construction process of accurate higher order schemes, such as limited regularities of the limiting solution, and a lack of accurate initial data for the pressure. Computational experiments are included to compare the presented schemes, and illustrate the difficulties mentioned.