A fully-conservative sliding grid algorithm for compressible flows using an Isogeometric Discontinuous Galerkin scheme

A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows

The modern vision of a flow solver necessarily includes adaptivity. In particular, mesh adaptivity enables the solution strategy to allocate the resources efficiently, in that cells are concentrated in areas where they are needed, as opposed to uniform mesh refinement. Multiresolution-based mesh adaptivity using biorthogonal wavelets has been quite successful with finite volume solvers for comp...

Discontinuous Galerkin Finite Element Method for Inviscid Compressible Flows

This paper presents the development of an algorithm based on the discontinuous Galerkin finite element method (DGFEM) for the Euler equations of gas dynamics. The DGFEM is a mixture of a finite volume and finite element method. In the DGFEM the unknowns in each element are locally expanded in a polynomial series and thus the information about the flow state at the element faces can be directly ...

Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows

A discontinuous Galerkin conservative level set scheme for interface capturing in multiphase flows

The accurate conservative level set (ACLS) method of Desjardins et al. [O. Desjardins, V. Moureau, H. Pitsch, An accurate conservative level set/ghost fluid method for simulating turbulent atomization, J. Comput. Phys. 227 (18) (2008) 8395–8416] is extended by using a discontinuous Galerkin (DG) discretization. DG allows for the scheme to have an arbitrarily high order of accuracy with the smal...

Multipatch Discontinuous Galerkin Isogeometric Analysis

Isogeometric analysis (IgA) uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get flexibility in the geometrical representation. This multi-patch representation corresponds to a decomposition of the computational domain into non-overlapping sub...