不可压N-S方程的基于粘接元的区域分裂解法

首先,简单介绍了基于粘接元的无重叠区域分裂方法.这种方法利用变分原理,非常适合有限元近似.然后,着重讨论了这种区域分裂方法在求解不可压Navier-Stokes方程中的应用,具体包括等价变分公式的建立、通过算子分裂的时间离散、区域分裂情形下广义Stokes问题的共轭梯度迭代求解方法、空间的有限元离散.最后,以数值实验结果验证了这种区域分裂方法应用于不可压Navier-Stokes方程求解时的可靠性.

A Domain Decomposition Method Based on Mortar Elements for Incompressible Navier-Stokes Equations

At first,the domain decomposition method based on mortar element is introduced briefly,which takes advantage of the variational principles and is well suitable for finite element approximation.Then,the emphasis is put on the application to the solution of Navier-Stokes equations for incompressible viscous flow,including construction of the equivalent variational formulation,time discretization by operator splitting,conjugate gradient iterative solution to the generalized Stoke problem with domain decomposition and finite element approximation.Finally,the results of numerical experiments validate the application of this domain decomposition method to the incompressible Navier-Stokes equations.