A high-order Discontinuous Galerkin (DG) method to simulate incompressible/compressible single-/two-phase fluid flows with/without cavitation

As a part of my PhD thesis, A Nodal Discontinuous Galerkin Method (NDGM) was developed to solve different kinds of problems. The simulations can be done by selecting different options listed below:

Incompressible or compressible fluid flow
Viscous or inviscid
1D, 2D (quadrilateral or triangular grids), 3D (hexahedral or tetrahedral grids)
Immiscible multiphase or multicomponent fluid flows
Cavitation modelling: One-fluid model (table look-up approach), transport equation-based model (Merkle et al., Kunz et al. and Senocak and Shyy)
Numerical fluxes: Lax, Roe, Rusanov, Harten–Lax–van Leer (HLL), Harten–Lax–van Leer- Contact (HLLC), Low-Diffusion-Flux-Splitting (LDFS), AUSM+-up
Shock/discontinuity capturing methods: generalized MUSCL limiter, generalized exponential filter, artificial viscosity method
Temporal discretization method: Explicit Runge Kutta methods, Implicit dual-time method
Diffusion terms discretization approaches: central, local DG (LDG), internal penalty (IP)

The NDGM solver is written from scratch in the C++ programming language. It is object-oriented and has been paralleled using OpenMP. The grids were taken in from Gambit in neutral file formats. In the incompressible form of governing equations, the artificial compressibility method is used to overcome the velocity-pressure coupling problem. So, the governing equations are preconditioned to accelerate to convergence rate in pseudo times. Caution is needed for solving this class of equations because the eigenvalues and eigenvectors of the system of equations will change so an amendment is needed in the calculation of the numerical fluxes. These eigenvalues and eigenvectors were derived analytically using Maple and were used in the process of the numerical flux evaluation. The results are exported in a .dat or .plt format files to be read in Tecplot for postprocessing purposes. Although some of the results are not presented in my articles, main information are available in these papers: