Development of a Novel Riemann Solver for Solid Dynamics

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.