Development of a Novel Riemann Solver for Solid Dynamics

Khoder Alhamwi Alshaar; J C Mandal

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arXiv · 2508.07954

Development of a Novel Riemann Solver for Solid Dynamics

Khoder Alhamwi Alshaar·J C Mandal

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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.

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Khoder Alhamwi Alshaar, J C Mandal. 2025-07-28. Development of a Novel Riemann Solver for Solid Dynamics. https://arxiv.org/abs/2508.07954

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