Moving geometry in compressible flows using Cartesian grid and high order Discontinuous Galerkin Method

In this contribution we present how the interactions between moving geometry and compressible flows can be realized using high order method on Cartesian grids. To maintain the accuracy of the boundary conditions on geometry equivalent to the scheme order, the geometry has to be represented accordingly. Therefore we consider an immersed boundary method, representing the geometry as a porous material with artificial porosity and permeability coefficients as functions in space and time, known as Brinkman penalization[1]. The surface is obtained by projecting the surface function to a representing polynomial on the computational grid, resulting in the same accuracy as the underlying scheme. Our simulations are carried out using our in-house CFD Framework called APES[2]. 

REFERENCE

 [1]Q. Liu, O.V. Vasilyev, A Brinkman method for compressible flows in complex geometries, In Journal of Computational Physics 227, Elsevier Inc. 2007

[2]S. Roller, J. Bernsdorf, H. Klimach, M. Hasert, D. Harlacher, M. Cakircali, S. Zimny, K. Masilamani, L. Didinger, and J. Zudrop. An adaptable simulation framework based on a linearized octree. In M. Resch, X. Wang, W. Bez, E. Focht, H. Kobayashi, and S. Roller, editors, High Performance Computing on Vector Systems 2011, Springer Berlin Heidelberg, 2012