多区域再生核有限差分法求解Burgers方程

A multi-domain reproducing kernel finite difference method forBurgers equation

针对Burgers方程,给出了一种将再生核有限差分法与惩罚法相结合的一种区域分解算法.首先将整体区域进行分区,将原问题的求解转化为在子区域上进行求解.然后,在各子区域内,空间上应用再生核方法进行离散,时间上应用四阶Runge-kutta法进行离散.对内边界则应用惩罚法进行处理,将各个子区域连同边界条件看成是一个整体进行求解,不必单独考虑边界条件.数值实验结果表明了此方法的有效性.

A multi-domain reproducing kernel finite difference method is presented for Burgers equation. It is a domain decomposition method, which combines reproducing kernel finite difference method with penalty method. Firstly, we decompose the global computational domain into a number of subdomains, hence the equation can be solved in subdomains instead of the whole domain. Then, we apply reproducing kernel finite difference method for space discretion, a fourth order Runge - Kutta scheme for time discretion in each subdomain. Finally, we apply penalty method for dealing with the inner boundary condition, so that each subdomain with inner boundary condition can be solved as a whole while not considering it independently. Numerical examples are given to test the efficiency of the represented method.