Computation of hypersonic viscous flows with the thermally perfect gas model using a discontinuous Galerkin method

Abstract

AbstractThis article is concerned with the numerical simulation of high‐speed thermally perfect flows using high‐order discontinuous Galerkin (DG) methods. In these methods, the polynomial approximation of the solution is susceptible to spurious oscillations, especially in high‐gradient regions. The introduction of variable thermodynamic properties, important for hypersonic flows, can exacerbate this issue. Given the general lack of satisfactory high‐order DG simulations of these types of flows, our primary objective is to demonstrate the success of the formulation proposed here in computing flows in this regime. Secondary goals are to (a) highlight that DG schemes are significantly less sensitive than finite‐volume methods to mesh‐shock misalignment in the given setting and (b) evaluate the sensitivity of surface heating predictions to various types of no‐slip isothermal wall boundary conditions. To handle strong shocks prevalent in this flow regime, intra‐element solution variations are used to detect discontinuities and smooth artificial viscosity is employed for stabilization. We discuss the algorithmic developments for extending a standard DG discretization of the compressible Navier–Stokes equations with the calorically perfect gas model to the thermally perfect gas model. We apply the resulting DG formulation to several hypersonic test cases, including inviscid flow over a cylinder and viscous flow over a double cone. Where appropriate, our results are benchmarked against those obtained with state‐of‐the‐art finite‐volume hypersonic flow solvers. The final case entails high‐speed particle‐laden flow over a blunt body. The results of this test illuminate how the consideration of variable thermodynamic properties influences the prediction of the particle phase.