High-Order Spectral/hp-Based Solver for Compressible Navier-Stokes Equations

High-order spectral element methods are becoming more established for solving problems in computational fluid dynamics. In this paper, we introduce new stabilization parameters for the solution of compressible Navier-Stokes equations in conjunction with high-order spectral element methods. We previously defined a new set of stabilization parameters for Euler equations in a high-order spectral/hp framework. In this paper, we examine the definition of these stabilization parameters in the context of solutions of full Navier-Stokes equations, and we report good agreement with previously published results in the literature. We establish spectral L-2 convergence of errors for Kovasznay flow. We then validate the definition of the stabilization parameter for Couette flow, flat plate, and compression corner problems. In a later example, we solve the flow past a cylinder and benchmark results with previously published results obtained with low-order methods and other approaches in compressible flow computations. We further solve hypersonic flow past a wedge and supersonic flow past a Flight Investigation of Re-Entry program (FIRE) entry capsule. We explore the definition of the shock-capturing parameter delta based on the YZ beta parameter. The introduced definitions are found to provide excellent results for the full Navier-Stokes equations.