Development of a Novel Riemann Solver for Solid Dynamics

TL;DR

This paper introduces a new finite volume method with a Roe-type Riemann solver for solid dynamics, improving stability and accuracy in hyperbolic conservation law solutions for multidimensional problems.

Contribution

It develops a novel Roe-type Riemann solver within a momentum-deformation framework, advancing numerical methods for solid dynamics beyond traditional displacement-based approaches.

Findings

Demonstrates robustness and accuracy on 2D and 3D elasticity benchmarks

Enhances stability and multidimensional handling of hyperbolic problems

Provides a foundation for nonlinear and fluid-structure interaction extensions

Abstract

This work presents a new finite volume framework for solid dynamics based on a momentum-deformation formulation. Building on the C-TOUCH methodology [1], a novel Roe-type Riemann solver is developed to enhance the stability and accuracy of hyperbolic conservation law solutions in solids. The approach naturally handles multidimensional problems and provides a foundation for future extensions to nonlinear and fluid-structure interaction cases. Validation against standard two- and three-dimensional linear elasticity benchmarks demonstrates the method's robustness and accuracy relative to traditional displacement-based approaches, highlighting its promise for large-scale dynamic simulations.