Title: A Fast Numerical Scheme for the Godunov-Peshkov-Romenski Model of Continuum Mechanics,
Abstract: 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.