基于二维声波方程的八阶NAD-RK方法及数值频散研究

The Eighth-Order NAD-RK Method Based on Two-Dimensional Acoustic Wave Equation and Its Numerical Dispersion

基于二维声波方程,本文首先采用四级四阶的Runge-Kutta方法对时间导数进行四阶离散,而利用近似解析离散化方法对空间高阶偏导数进行八阶离散,从而得到了八阶NAD-RK方法.然后,从理论上和数值模拟上对该方法进行了数值频散分析,并与八阶LWC方法和八阶SG方法进行了比较.结果揭示,八阶NAD-RK方法有着很好压制数值频散和提高模拟精度等优点.

In this paper,we firstly gain the eighth-order NAD-RK method based on the 2-D acoustic wave equation.This method uses the fourth-order Runge-Kutta method to conduct fourth-order discretization on temporal derivatives,and employs the nearly analytic discretization method to conduct eighth-order discretiza-tion on high order partial derivatives of the space.Secondly,the numerical dispersion of this method is analyzed from the theory and numerical simulation.The paper finally compares the method with the eighth-order Lax-Wendroff correction （LWC）and the eighth-order staggered-grid （SG）methods.These results show that the eighth-order NAD-RK method can suppress numerical dispersion and enhance computational simulation accu-racy.