A Fast Numerical Scheme for the Godunov-Peshkov-Romenski Model of Continuum Mechanics
This work provides a faster alternative for solving the GPR model, benefiting researchers in continuum mechanics who need efficient simulations.
The authors propose a second-order numerical scheme for the Godunov-Peshkov-Romenski model that is computationally cheaper than existing ADER-WENO schemes, achieving sufficient accuracy for practical applications. Convergence studies demonstrate second-order accuracy.
A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO reconstruction, and the temporal ODEs are solved using some analytic results presented here. Whilst it is not possible to attain arbitrary-order accuracy with this scheme (as with ADER-WENO schemes used previously), the attainable order of accuracy is often sufficient, and solutions are computationally cheap when compared with other available schemes. The new scheme is compared with an ADER-WENO scheme for various test cases, and a convergence study is undertaken to demonstrate its order of accuracy.