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

Abstract

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/ 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 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 based on the parameter. The introduced definitions are found to provide excellent results for the full Navier–Stokes equations.