波动方程数值模拟的隐式差分法

Wave equation modeling with implicit difference technique.

中国石油大学, 北京102200

China Petroleum University, Beijing 100083,China

在有限差分波动方程数值模拟中,通常采用高阶差分方法来提高空间导数的数值逼近精度,以实现降低数值频散,提高数值模拟精度的目的。首先对差分频散进行了理论分析;然后讨论了估计一阶空间导数的隐式差分格式,并与通常采用的高阶精度显式差分格式进行了对比分析,结果表明,隐式差分格式能够在更宽的波数范围使差分频散控制在可接受的水平,如8阶精度的显式差分格式所适应的波数带宽约为O．55kmax,而隐式差分格式所适应的波数带宽约为0．7kmax;最后通过模型试算,对隐式差分格式的有效性进行了验证。模拟结果表明,用隐式差分格式在一定程度上降低了差分频散,提高了模拟精度。

The restraint of numerical dispersion is the key issue in wave-equation modeling. High order definite difference is usually used to improve the estimating accuracy of spatial derivatives in wave-equation modeling. Based on theoretic analysis, an implicit form of definite difference is introduced to estimate spatial derivatives. By applying implicit form of difference, the numerical dispersion is controlled within a wider range of wave number. For instance, the conventional explicit difference of 8-order accuracy gives a good result only within the range of [0,0. 55kmax] while the implicit difference can widen the range to [0,0.7 k^max]. The results prove that the implicit form of difference has advantage in both reducing numerical dispersion and improving the simulation results.