Four Spacetime Dimensional Simulation of Rheological Waves in Solids and the Merits of Thermodynamics

Area of Science:

• Computational physics
• Solid mechanics
• Numerical analysis

Background:

• Wave propagation in viscoelastic solids presents numerical challenges.
• Existing numerical schemes may struggle with accuracy and stability.
• Thermodynamic principles can guide numerical method development.

Purpose of the Study:

• To generalize a thermodynamically conceived numerical scheme for wave propagation.
• Extend the scheme to four spacetime dimensions.
• Evaluate the benefits of a thermodynamic approach for numerical simulations.

Main Methods:

• Development of a thermodynamically extended symplectic numerical scheme.
• Application to wave propagation in viscoelastic/rheological solids.
• Extension to four spacetime dimensions with careful boundary condition implementation.

Main Results:

• The generalized scheme accurately simulates wave propagation.
• The thermodynamic framework effectively monitors and controls numerical artifacts like instability, dissipation error, and dispersion error.
• The approach demonstrates preciseness, speed, and resource-friendliness.

Conclusions:

• The thermodynamically extended symplectic approach offers significant advantages over commercial finite element software.
• This method provides a robust and efficient tool for simulating wave propagation in complex materials.
• The integration of thermodynamics enhances the reliability and performance of numerical simulations.