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The recent results attained from a thermodynamically conceived numericalscheme applied on wave propagation in viscoelastic/rheological solids aregeneralized here, both in the sense that the scheme is extended to fourspacetime dimensions and in the aspect of the virtues of a thermodynamicalapproach. Regarding the scheme, the arrangement of which quantity isrepresented where in discretized spacetime, including the question ofappropriately realizing the boundary conditions, is nontrivial. In parallel,placing the problem in the thermodynamical framework proves to be beneficial inregards to monitoring and controlling numerical artefacts - instability,dissipation error, and dispersion error. This, in addition to the observedpreciseness, speed, and resource-friendliness, makes the thermodynamicallyextended symplectic approach that is presented here advantageous abovecommercial finite element software solutions.

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