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提出了一种优化交错变网格有限差分算法,并在二维速度-应力关系的弹性波方程中实现.利用频散关系守恒准则构造了四阶精度的差分算子,该算法属于连续变网格方法,不需要在精细网格和粗糙网格之间进行插值.将优化算法的数值结果与解析解及八阶规则交错网格差分算法进行了比较,验证了该算法的精度.与基于Taylor展开的变网格有限差分算法比较可知,优化算法的频散特性较好,在数值模拟中可使用更粗糙的网格.将提出的优化算法应用于复杂的井间声波模型.该数值实例表明,优化算法可以节省大量的计算内存和计算时间,同时具有优良的稳定性.
An improved finite difference method for staggered variable mesh is proposed and implemented in a two-dimensional elastic-wave equation of velocity-stress relationship.The fourth-order difference operator is constructed by using the conservative rule of dispersion relation, which belongs to continuous variable network Grid method without interpolation between the fine grid and the coarse grid.The numerical results of the optimization algorithm are compared with the analytical solution and the eighth-order grid staggered grid difference algorithm to verify the accuracy of the algorithm, Expanding the finite difference algorithm of variable mesh shows that the optimization algorithm has better dispersion characteristics and a more coarse mesh can be used in the numerical simulation.The proposed optimization algorithm is applied to the complex crosswell acoustic model.The numerical example shows that , The optimization algorithm can save a lot of computing memory and computing time, and has excellent stability.