High-Order Accurate Entropy Stable Finite Difference Schemes for the Compressible Euler Equations with the van der Waals Equation of State on Adaptive Moving Meshes (Communications in Computational Physics, 2025)
This paper develops the high-order entropy stable finite difference schemesfor multi-dimensional compressible Euler equations with the van der Waals equationof state on adaptive moving meshes. Semi-discrete schemes are first nontrivially constructed on the newly derived high-order entropy conservative (EC) fluxes in curvilinear coordinates and scaled eigenvector matrices as well as the multi-resolution WENOreconstruction, and then the fully-discrete schemes are given by using the high-orderexplicit strong-stability-preserving Runge-Kutta time discretizations. The high-orderEC fluxes in curvilinear coordinates are derived by using the discrete geometric conservation laws and the linear combination of the two-point symmetric EC fluxes, whilethe two-point EC fluxes are delicately selected by using their sufficient condition, thethermodynamic entropy and the technically selected parameter vector. The adaptivemoving meshes are iteratively generated by solving the mesh redistribution equations,in which the fundamental derivative related to the occurrence of non-classical waves isinvolved to produce high-quality mesh. Several numerical tests are conducted to validate the accuracy, the ability to capture the classical and non-classical waves, and thehigh efficiency of our schemes in comparison with their counterparts on the uniformmesh.
Keywords: Entropy stable scheme; entropy conservative scheme; mesh redistribution; van der Waals equation of state.