Finite volume methods for acoustics and elasto-plasticity with damage in a heterogeneous medium.

摘要

High-resolution finite-volume numerical methods originally developed for shock capturing in the context of nonlinear conservation laws are found to be very useful for solving acoustic and elasto-plastic problems in heterogeneous media. These methods are based on solving Riemann problems at the interface between grid cells. The solution method is introduced in the context of acoustics problems with periodic or random media in one and two space dimensions. Test problems are used to show how the method can be extended to solve problems that are elasto-plastic in nature and may include material damage. The use of constrained minimization techniques in conjunction with linear elasticity to solve elasto-plastic problems is introduced and found to be useful in multi-dimensional problems. In one dimension exact Riemann solutions can be computed and have been used to validate the minimization approach. The minimization algorithms are then extended to two-dimensional problems and used to find numerical solutions to a variety of physically interesting 2D examples.