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.
Highlights
A new method is presented in this study that is simple to implement and computationally cheaper than a corresponding ADER-WENO method if only second order accuracy is required
A new numerical method based on an operator splitting, and including some analytical results, has been proposed for the GPR model of continuum mechanics
It has been demonstrated that this method is able to match current ADER-WENO methods in terms of accuracy on a range of test cases
Summary
The Godunov–Peshkov–Romenski model of continuum mechanics (as described in 1.2) presents an exciting possibility of being able to describe both fluids and solids within the same mathematical framework This has the potential to streamline development of simulation software by reducing the number of different systems of equations that require solvers, and cutting down on the amount of theoretical work required, for example in the treatment of interfaces in multimaterial problems. A new method is presented in this study that is simple to implement and computationally cheaper than a corresponding ADER-WENO method if only second order accuracy is required This may prove useful in the design of simulation software addressing problems in which not just accuracy and speed and usability are of paramount importance
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