基于不同时间步长时域非结构有限体积法模拟声-弹性耦合问题

介绍一种改进的时域非结构有限体积法(FVM),并将其应用于声-弹性耦合问题.在流体与固体介质中分别求解声波动方程与弹性波方程,根据交界面上的力平衡与质点振速连续条件考虑二者的相互作用.同时考虑双线性四边形单元的线性变化项及常数项,并结合常应变三角形单元处理混合网格问题.分别对三角形单元和四边形单元进行色散分析,给出声波动方程的稳定性条件.在不同介质中采用不同时间步长,提高计算效率.求解弹性波问题、声-弹性耦合问题,结果表明,改进后的方法求解声-弹性耦合问题是有效和准确的,并且具有良好的数值稳定性.

NUMERICAL SIMULATION OF ACOUSTIC-ELASTIC INTERACTION BASED ON MULTI-TIME-STEP UNSTRUCTURED FINITE VOLUME TIME DOMAIN METHOD

An improved unstructured finite volume time domain method is presented to solve the acoustic-elastic interaction problems. The computational domain is divided into acoustic and elastic sub-domains and the interaction between them is implemented by interface boundary conditions. The quadrilateral element, which is treated as the bilinear element while considering the linear term and the constant term, and the triangular element are employed to deal with mixed grid problems. The stability criterions are provided for the quadrilateral element and the triangular element respectively for the acoustic wave equation. Different time steps are adopted for different sub-domains which could improve the efficiency of the present method. One elastic wave problem and two acoustic-elastic interaction problems are solved. According to the comparisons between the calculated results and the published results, the improved method can treat the acoustic-elastic interaction problem effectively and accurately with good numerical stability.