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

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.

arXiv comment24 pages, 101 figures; v3: 4 typos corrected

References in corpus (12)

• Contact variational integrators
• Distinguished rheological models in the framework of a thermodynamical internal variable theory
• Thermodynamical extension of a symplectic numerical scheme with half space and time shift demonstrated on rheological waves in solids
• Kinematic quantities of finite elastic and plastic deformation
• Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor
• Variational discretization of the nonequilibrium thermodynamics of simple systems
• Galilean relativistic fluid mechanics
• First report of long term measurements of the {MGGL} laboratory in the {M}átra mountain range
• Long term measurements from the Mátra Gravitational and Geophysical Laboratory
• Kluitenberg-Verhás rheology of solids in the GENERIC framework
• Numerics for Hyperbolic Conservation Laws with Help from the Physical Entropy
• Elastic, thermal expansion, plastic and rheological processes - theory and experiment

Cited by in corpus (4)

• Holographic fluids: a thermodynamic road to quantum physics
• Thermodynamically extended symplectic numerical simulation of viscoelastic, thermal expansion and heat conduction phenomena in solids
• New directions for contact integrators
• Field equation of thermodynamic gravity and galactic rotational curves