迎风紧致格式求解Hamilton-Jacobi方程

基于Hamilton Jacobi(H J)方程和双曲型守恒律之间的关系,将三阶和五阶迎风紧致格式推广应用于求解H J方程,建立了高精度的H J方程求解方法.给出了一维和二维典型数值算例的计算结果,其中包括一个平面激波作用下的Richtmyer Meshkov界面不稳定性问题.数值试验表明,在解的光滑区域该方法具有高精度,而在导数不连续的不光滑区域也获得了比较好的分辨效果.相比于同阶精度的WENO格式,本方法具有更小的数值耗散,从而有利于多尺度复杂流动的模拟中H J方程的求解.

Upwind Compact Schemes for Hamilton-Jacobi Equations

Based on the close relationship between Hamilton-Jacobi(H-J) equations and hyperbolic conservation laws,a high-order numerical method is developed to solve the H-J equations in the 3rd order and 5th order compact schemes.The upwind compact schemes are tested on a variety of one-dimensional and two-dimensional problems,including a problem related to the Richtmyer-Meshkov instability accelerated by planar shocks.Numerical results show that these schemes yield uniform high-order accuracy in smooth regions and satisfactorily resolve discontinuities in the derivatives.Moreover,since the present methods have less numerical dissipation than WENO scheme with the same order,they could be used to solve the H-J equations more accurately in the simulation of multi-scale complex flows.