A Sliding-Mesh Strategy Based on the Mixing of Continuous and Discontinuous Finite Element Methods for Compressible Flow Problems

Abstract

There are flow problems in which different parts of the domain are in relative motion. This occurs, for instance, in turbomachinery, in internal combustion engines with ports for gas exchange (two-stroke engines and rotary engines), etc. The computational simulation of such problems becomes simpler if the flow domain is split into sub-domains with different motion or deformation rate. These sub-domains could have a common boundary over which, due to the relative motion, they slide one with respect to the other. In this article a sliding-mesh strategy is presented, which is useful to solve the kind of problems cited above when the involved flow is compressible. The strategy is based on the use of standard (i.e., continuous) finite elements at the interior of the domain and a layer of discontinuous elements at the ‘sliding’ surface between two adjacent sub-domains. It must be pointed out that the inter-element discontinuity appears between elements of neighbor sub-domains, which share a facet lying on the ‘sliding’ surface. Therefore, nonconformal meshes at sub-domain boundaries can be used. The solution is continuous across element faces lying inside each sub-domain. The finite element formulation applied at the interior of the sub-domains is stabilized by means of the Streamline-Upwind/Petrov-Galerkin (SUPG) technique. A shock-capturing term is added to the formulation in order to stabilize the computations in the presence of sharp gradients. At the discontinuous elements layer, an interior penalization Discontinuos Galerkin (DG) method is applied. The Lax-Friedrichs fluxes are used in this work in order to define the numerical fluxes arising in the DG method. For the penalization coefficients involved in the Lax-Friedrichs flux, the definitions given in the literature and modifications of them are tested. In some cases, due to the relative motion between sub-domains, the faces of the elements belonging to the discontinuous layer could change their location from the portion of surface shared by two adjacent sub-domains to another portion of the border where boundary conditions must be specified. These boundary conditions are enforced through numerical fluxes properly designed. Wall boundary conditions and open boundary conditions are addressed here. Some numerical examples are presented in order to show the performance of the proposed strategy.