求解Hamilton-Jacobi方程的高精度GDQ方法

High Accurate GDQ Method for Solving Hamilton-Jacobi Equations

利用求解常微分方程的GDQ方法的思想,结合使用TVD限制器进行校正,研究求解Hamilton-Jacobi方程的高精度高分辨率数值方法,构造了一类新的高精度差分格式,并证明了它在满足一定的CFL条件下具有TVD特性;然后,推广到二维情况;最后,给出了几个典型数值算例.计算结果表明:该格式具有形式简单、边界条件易于处理、计算工作量小且分辨率高等优点.

Based on ideas of generalized differential quadrature method for ordinary differential equation and total variation diminishing limiter correction, high accuracy and high resolution methods for Hamilton-Jacobi equations are researched. A new class of high accurate difference schemes for Hamilton-Jacobi equations are present. And then, TVD property of the resulting schemes is proved under a certain CFL condition. Furthermore, the extension to two dimensional Hamihon-Jacobi equations is implemented. Finally, several typical numerical experiments show that these schemes have advantages of simplifying forms and easy to treat boundary conditions and low evaluated cost and high resolution.