A discontinuous Galerkin method for convection-dominated compressible viscous Navier-Stokes equations with an inflow boundary condition

A linearized steady-state compressible viscous Navier Stokes system with an in ow boundary condition is considered. A discontinuous Galerkin method for this system is formulated with convection-dominance and O(h) viscous functions where h is the mesh size in a given triangulation. The resulting finite element method is explicit and valid for all polynomials of degree greater than or equal to 1. We show a L-p-stability and derive error estimates for velocity and pressure, respectively. I particular, the compressibility number kappa := rho'/rho is regarded as essential in showing our stability results.open113sciescopu

Finite element model for three-dimensional compressible turbulent flows

Due to the complexity of the Navier-Stokes equations, numerical methods are widely used to analyze the flows. In this thesis, we establish a finite element model for three-dimensional compressible turbulent flows. We modified an in-house code in order to use several types of elements in a computational domain. We used four types of elements in our mesh: the 8-node hexahedron, the 4-node tetra, the 6-node prism, and the 5-node pyramid. The original code used only the 4-node tetra elements. We used the Streamline Upwind/Petrov-Galerkin stabilization technique with a shock capturing operator. We validated the code with benchmark tests using the 3D Naca0012 model and the DLR F11 model. We used different sets of Reynolds numbers, Mach numbers, and angles of attack to test the code and compare our results with other numerical and experimental results. Because of the strong nonlinearities with the increase of the angle of attack, we need to set up a solution strategy to avoid divergence of the solution. The tests of verification and validation show that the results we obtained are comparable to those of the references