Four spacetime dimensional simulation of rheological waves in solids and the merits of thermodynamics

TL;DR

This paper extends a thermodynamically based numerical scheme for wave propagation in viscoelastic solids to four spacetime dimensions, demonstrating its advantages in accuracy, stability, and efficiency over traditional methods.

Contribution

It introduces a four-dimensional spacetime extension of a thermodynamically conceived numerical scheme for rheological wave simulation, highlighting its benefits over conventional finite element methods.

Findings

Enhanced stability and control of numerical artefacts.

Improved accuracy, speed, and resource efficiency.

Advantages over commercial finite element software.

Abstract

The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions and in the aspect of the virtues of a thermodynamical approach. Regarding the scheme, the arrangement of which quantity is represented where in discretized spacetime, including the question of appropriately realizing the boundary conditions, is nontrivial. In parallel, placing the problem in the thermodynamical framework proves to be beneficial in regards to monitoring and controlling numerical artefacts - instability, dissipation error, and dispersion error. This, in addition to the observed preciseness, speed, and resource-friendliness, makes the thermodynamically extended symplectic approach that is presented here advantageous above commercial finite element software solutions.