虚拟区域法及其在流体力学中的应用

讨论了一类椭圆型算子Dirichlet问题的一种基于Lagrange乘子的虚拟区域方法;由此导出的鞍点问题用共轭梯度法迭代求解.为加速迭代收敛,构建了合适的预处理器.着重考虑了这种方法在不可压粘性流动数值模拟中的应用.通过基于算子分裂的劋laMarchukYanenko时间离散格式,将虚拟区域情形下的不可压NavierStokes方程分裂成非线性对流扩散方程、准Stokes方程和虚拟区域情形下的线性椭圆型方程三个子问题.给出了绕固定和运动圆二维流动的数值实验结果.

A Fictitious Domain Decomposition Method and Its Applications in Fluid Mechanics

Lagrange-multiplier based fictitious domain method for the Dirichlet problem for a class of elliptic operators is discussed and the resulting saddle point problem is solved via a preconditioned conjugate gradient algorithm. The emphasis is then put on the application to numerical simulation of incompressible viscous flows. The methodology for the Navier-Stokes equations described here takes advantage of time discretization by la Marchuk-Yanenko operator splitting in order to treat separately advection, imbedding and incompressibility. Finally, numerical results of two-dimensional flows around a fixed and moving disk are presented.