一种弱数值频散的四阶Runge-Kutta方法及二维声波场模拟

The four-order Runge-Kutta method with weak numerical dispersion and acoustic wave-field simulation of two-dimension

针对二维声波方程,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,并采用四阶Runge-Kutta方法对时间导数进行四阶离散,得到了八阶NAD-RK方法.将该方法应用于双层介质模型和三层介质模型中进行波场数值模拟,同时与八阶LWC方法和八阶SG方法进行了比较.结果表明,八阶NAD-RK方法具有弱数值频散和高计算模拟效果等优势.

We gain the eight - order NAD - RK method based on the acoustic wave equation of two - dimen sion. This method uses the nearly analytic diseretization method to conduct eight - order discretization on high or der partial derivatives of the space, and employs the four - order Runge - Kutta method to conduct four - order discretization on temporal derivatives. The method is applied to wave - field numerical simulations from the two layer acoustic and three - layer acoustic models in the 2 - D case. The paper compares the method against the eighth - order LAX - Wendroff correction （ LWC ） and the eighth - order staggered - grid （SG） finite - differ ence methods. These results illustrate that the eight - order NAD - RK method has advantages such as weak nu merical dispersion and high computational simulation effect.