求解粘性Hamilton-Jacobi方程的高阶方法

High-order Schemes for Viscous Hamilton-Jacobi Equations

提出了求解具有粘性项的Hamilton Jacobi方程的二阶、四阶方法.该方法以加权基本无振荡(WENO)格式为基础,通过修正数值通量函数和构造右端粘性项的基于非线性限制器的二阶近似、基于Taylor展开的四阶近似,成功地求解了一维、二维的粘性Hamilton Jacobi方程.给出的算例说明了本方法具有高分辨率、鲁棒性和无振荡特性.

Second-order and fourth-order methods for approximate solutions of viscous Hamilton-Jacobi equations are developed on the basis of the weighted essentially non-oscillator (WENO) scheme. By modifying the numerical flux, constructing the second-order approximation based on nonlinear limiter and fourth-order approximation based on Taylor expansion for viscosity term, the one-and two-dimensional viscous Hamilton-Jacobi equations are solved successfully. Numerical tests demonstrate the desired high-resolution, robustness and non-oscillatory behaviors of the schemes.