【摘要】 基于分部求和(Summation By Parts)方法和同时逼近项(Simultaneous Approximation Terms)技术建立的有限差分方法,具有更高的精度和稳定性。同时在介质几何不连续、参数突变条件具有较大的优势。国内对SBP-SAT方法的相关研究目前较少,论文对该方法的研究背景,方法发展过程进行了介绍并基于SBP-SAT方法和弹性波动理论,结合初边值条件,推导出曲线网格条件下的弹性波动SBP-SAT离散方程。最后,通过数值模拟实现地震波传播过程,介绍该方法在地震数值模拟领域中的应用价值和前景。更多还原

【Abstract】 Summation by parts with simultaneous approximation terms has a set of properties that leads to provable time stability and higher order spatial discretization of partial differential equations. The finite difference methods based on this theory can establish a scheme that has incomparable advantages for simulating geometric discontinuity or complex media. At present, there are few researches on SBP-SAT methods in China. Therefore, this paper reviews the history of SBP-SAT methods and their application to the numerical solution of partial differential equations. Then, the discrete equations of elastic wave under the curvilinear coordinates were derived. At last, combining initial value conditions and boundary conditions, a simple simulation for imitating seismic wave propagation was performed. The potential and the application value were present.更多还原