Dispersion and spurious reflections of viscoelastic wave

TL;DR

This paper analyzes how numerical methods cause dispersion and false reflections in simulating viscoelastic waves, highlighting persistent issues even with refined meshes.

Contribution

It provides an analytical approach to understanding dispersion and spurious reflections in viscoelastic wave simulations using finite element and Newmark methods.

Findings

Dispersion and spurious reflections are significant even with refined meshes.

Analytical integration reveals persistent numerical artifacts.

Finite element and Newmark methods exhibit these issues in viscoelastic wave modeling.

Abstract

This article investigates the velocity dispersion and the spurious reflection of the viscoelastic wave that occur in the numerical integration of the viscoelastic wave equation. For this purpose, the classic finite element of two nodes, with a consistent and lumped mass model for spatial integration is considered, and the Newmark average acceleration method of the two-step version for integration over time is adopted. The resulting system of the difference equation is then analytically integrated in non-finite terms (numerical solution of waves) using complex notation. The numerical results reveal that, even for a refined mesh, the dispersion and spurious reflections are significant.