紧致交错网格优化差分系数二维声波方程数值模拟

Optimized difference coefficient of staggered compact finite difference scheme and 2D acoustic wave equation numerical simulation

基于频散关系保持的思路,利用最小平方法和拉格朗日乘数法,对一阶导数的紧致交错有限差分格式做了差分系数优化,并对优化格式的模拟精度、频散关系及声波方程稳定性条件进行了分析和对比。研究结果表明:①为得到相同的差分精度,优化后的紧致交错格式计算一阶导数时使用的节点个数比优化前多两个;②优化格式与优化前及常规交错格式相比,具有更小的截断误差和更低的数值频散,因而具有更高的计算精度,适用于更粗网格的计算,具有更高计算效率;③在同样差分精度条件下,二维声波方程优化格式的稳定性条件比优化前稍严格,适用的时间网格略小。分别对均匀、水平层状和Marmousi模型进行声波方程数值模拟,所得结果验证了所提方法适用于复杂介质的数值模拟,具有较高模拟精度和计算效率。

In this paper,we use the least square and Lagrange multiplier to perform difference coefficient optimization for the staggered compact finite difference scheme of first-order derivatives based on the idea of dispersion relationship preservation.Then,we analyze the optimized-scheme simulation accuracy,dispersion relation,and acoustic wave equation stability.The following understandings are obtained:A.For the same difference accuracy,the optimized staggered compact difference(OSCD)scheme uses two more nodes to calculate the first-order derivative than staggered compact difference(SCD)schemes;B.OSCD has a smaller truncation error and lower simulation dispersion than staggered difference(SD)schemes and SCD,so OSCD has higher calculation accuracy,and it is more suitable for coarse grid computing;C.For the same difference accuracy,the stability condition of OSCD for acoustic wave equation is slightly stricter than SD and SCD,and the applicable time grid size is slightly smaller.Wavefield numerical simulations of acoustic wave equation on uniform,horizontallayered,and Marmousi models demonstrate that the proposed method is suitable for complex media and it has higher accuracy and efficiency.