求解二维Hamilton-Jacobi方程的一类无波动的耗散差分格式

A Class of Non-oscillatory Dissipative Difference Schemes for Solving Two Dimensional Hamilton-Jacobi Equations

摘要: 将二维Hamilton-Jacobi方程转换成双曲型守恒律方程组,然后利用求解一维H-J方程的一类无波动无自由参数的耗散差分格式的思想,构造了一类求解二维H-J方程的差分格式.数值实验结果表明:该格式易于计算且分辨率较高.

Abstract: Based on the dissipative difference schemes for one dimensional Hamilton-Jacobi(H-J) equations and the relations between two dimensional H-J equations and hyperbolic conservation laws,a class of difference schemes for two dimensional H-J equations is constructed.Some typical numerical experiments show that these schemes have advantages of low evaluated cost and high resolution.