A well-conditioned augmented system for solving Navier-Stokes equations in irregular domains

JOURNAL OF COMPUTATIONAL PHYSICS

卷:228

Article

Ito, Kazufumi^1,2  Lai, Ming-Chih³  Li, Zhilin^1,2 

[1] N Carolina State Univ, Ctr Res Sci Computat, Raleigh, NC 27695 USA

[2] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[3] Natl Chiao Tung Univ, Dept Appl Math, Hsinchu 30050, Taiwan

关键词: Navier-Stokes equations;    Embedding technique;    Immersed interface method;    Irregular domain;    Augmented system;    Projection method;    Level set representation;   

DOI  :  10.1016/j.jcp.2008.12.028

来源: Elsevier

【 摘 要 】

An augmented method based on a Cartesian grid is proposed for the incompressible Navier-Stokes equations in irregular domains. The irregular domain is embedded into a rectangular one so that a fast Poisson solver can be utilized in the projection method. Unlike several methods suggested in the literature that set the force strengths as unknowns, which often results in an ill-conditioned linear system, we set the jump in the normal derivative of the velocity as the augmented variable. The new approach improves the condition number of the system for the augmented variable significantly. Using the immersed interface method, we are able to achieve second order accuracy for the velocity. Numerical results and comparisons to benchmark tests are given to validate the new method. A lid-driven cavity flow with multiple obstacles and different geometries are also presented. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free