Implementation of k-Exact Finite Volume Reconstruction in DLR’s Next-Generation CFD Solver: Flucs and its Comparison to Other Methods

Abstract: This thesis extended the order of the reconstruction of state for convective fluxes used by Finite Volume (FV) algorithm in DLR’s next-generation CFD solver: Flucs, from constant and linear to quadratic and cubic. Two approaches for calculating derivatives were implemented in Flucs and some test cases were tried. To allow for integration of moments within each cell and a higher-order integration of fluxes, the mesh used by Discontinuous Galerkin (DG) was fed to the FV algorithm. Insufficient geometric treatment of the boundary cells and the dummy cells in FV is believed to be detrimental to the order of error reduction in NACA0012 case and the smooth bump case. In the smooth bump case, the FV algorithms failed to show higher than second order error reduction because of this reason. The order of the schemes away from the boundaries was verified with the Ehrenfried Vortex test case. For at least structured meshes and unstructured meshes with quads, schemes of order k approached k + 1 order accuracy on sufficiently fine meshes. The original goal of this thesis was partly accomplished and some further work in the code is expected.