Improved solutions to the small strain continuum equations using a modified Engquist filter (Q1908760)

The authors use high resolution numerical methods to solve elastic wave propagation problems for linear, bilinear and nonlinear solids. They calculate solutions by the LAYER code for plane wave solutions for these three kinds of elastic solids. The numerical analysis shows a significant improvement over classical finite difference schemes. A two-dimensional grid system is employed to compute one-dimensional plane wave solutions. For the linear case, the nonlinear filter is very effective in eliminating Gibbs oscillations. For the bilinear case, the numerical solution is compared with a known analytical solution. It is shown that the filtered plane wave and decaying shock have sharp wave fronts with insignificant oscillations behind the fronts. This paper provides with a new numerical methods for finding solutions of a class of problems in continuum mechanics. The results of this paper would be also useful for other problems in solid and fluid mechanics.