Abstract
Nonlinear entropy stability analysis is used to derive entropy stable no-slip wall boundary conditions for the Eulerian model proposed by Svärd (Phys A Stat Mech Appl 506:350–375, 2018). The spatial discretization is based on entropy stable collocated discontinuous Galerkin operators with the summation-by-parts property for unstructured grids. A set of viscous test cases of increasing complexity are simulated using both the Eulerian and the classic compressible Navier–Stokes models. The numerical results obtained with the two models are compared, and similarities and differences are then highlighted. However, the differences are very small and probably smaller than what the current experimental technology allows to measure.
Highlights
The classical compressible Navier–Stokes (CNS) equations can be derived based on the material (Lagrangian) derivative formulation [29]
Nonlinear entropy stability analysis is used to derive entropy stable no-slip wall boundary conditions for the Eulerian model proposed by Svärd (Phys A Stat Mech Appl 506:350–375, 2018)
The above equations have exactly the same structure as the local discontinuous Galerkin (LDG)-IP approach used for the imposition of the solid wall boundary conditions except for the boundary penalty interface terms, g(xbi,)r,· in Eq (33), which are replaced by the interior penalty interface coupling terms, g(xIi,nr ),· in Eqs. (52)
Summary
The classical compressible Navier–Stokes (CNS) equations can be derived based on the material (Lagrangian) derivative formulation [29]. In the Lagrangian sense, diffusion between gas pockets is non-existent, and the continuity equation is hyperbolic. In the Eulerian model of Svärd [32], air molecules diffuse into other parts of the domain, and the continuity equation is modeled as a parabolic equation. This article is part of the section “Computational Approaches” edited by Siddhartha Mishra
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