Vertex-centered MEV MUSCL scheme in mixed-element meshes
Résumé
In the context of fluid dynamics calculations, unstruc-
tured mesh adaptation has proven to reduce significantly the mesh size
while keeping a high level of accuracy and automating the process
of mesh generation [2]–[5]. However some kinds of phenomena,
such as boundary layers, are better captured by numerical schemes
designed for structured meshes that are aligned with the boundary
of the domain. In order to take advantage of unstructured mesh
adaptation and meet some directional requirements, mixed-element
meshes appear to be a good compromise.
In this talk, we describe how gradient discretization in such cases
is clearly not trivial and three different formulations are required to
maintain a second-order accuracy. Convective fluxes are discretized
using an appropriate modified version of the Vertex Centered Mixed
Element-Volume (V4) MUSCL scheme [1], enabling the treatment of
quadrilateral and prismatic elements. Viscous fluxes are discretized
using the APproximated Finite Element (APFE) method [6]. Nodal
gradients in boundary and sources terms are discretized with a
generalization of Clement’s L2-operator for mixed-element meshes.
Some numerical results for 3D mixed-element meshes involving
tetrahedra, prisms and pyramids will be shown. Some of these will
be those obtained on best practice meshes of AIAA DPW6.