Ongoing development of non-reflective boundary conditions for euler and navier-stokes equations via the discontinuous galerkin framework

In an effort to implement non-reflective boundary conditions (NRBCs) in the context of the high-order discontinuous Galerkin (dG) finite element method (FEM), the perfectly matched layer (PML) and the Navier-Stokes characteristic boundary condition (NSCBC) are considered for the compressible Navier-Stokes and Euler equations. A conservative-formulation Cartesian-based two-dimensional nodal dG solver and an entropy-formulation curvilinear-based three-dimensional modal dG solver are used. For the first, a low-storage fourth-order Runge-Kutta (LSRK4) is employed for time marching, while for the second, a strong-stability-preserving third-order Runge-Kutta (SSPRK3) is selected. Results include classical problems such as the isentropic vortex and the Kelvin-Helmholtz instability for the nodal solver, while a spherical pressure disturbance and a flow past a hump are considered for the modal solver. Both PML and NSCBC prove very promising in the context of the dG method. Future work will entail the development and testing of the PML in their viscous-term inclusion, as well as the compatibility conditions on edges and corners for the NSCBC on more rigorous test cases.