Evaluation of Euler Fluxes for Hypersonic Heating Computations

Abstract

In hypersonic flow computations, it is a key issue to predict surface heating accurately, though this is still challenging because there always are possibilities of resulting in anomalous solutions. In this paper, three properties for flux functions are proposed: 1) shock stability/robustness, 2) conservation of total enthalpy, and 3) resolving boundary layer. Then, numerical experiments are performed for widely used or recently developed flux functions, and these fluxes are categorized into five major groups based on how they satisfy the three properties. These tests reveal that no flux function investigated here possesses all the three properties. In particular, the first one is not satisfied by any flux functions, including flux-vector-splittings. Finally, contributions of those properties are compared in a two-dimensional, viscous, hypersonic blunt-body problem. Results showed that the first and the third properties are crucial, and the second one is preferred to predict hypersonic heating. A group of flux functions that best satisfies these properties is suggested, and they are recommended either to be used or designed for hypersonic heating computations.

A parameter-free upwind scheme for all speeds’ simulations

“…The free stream conditions are M ∞ =8.1, P ∞ = 370.7 Pa, T ∞ =63.73 K, and Re=1.3×10 5 (Reynolds number based on the radius r=20 mm). Also, no-slip and isothermal (Tw= 300 K) conditions are imposed at the wall [15]. The cell Reynolds number based on the minimum cell size is taken as 2 to satisfy the Klopfer and Yee's criterion of computing hypersonic heating [22].…”

“…According to ref. [11], AUSMPW+ appears to be the most robust one in practical use, especially in hypersonic heating computations. Thus, we construct the AUSMPW-M's mass flux as AUSMPW+, which can be written in the following form.…”

“…It shows numerical overshoots behind strong shock waves and oscillations near the region of small convection velocity or pressure gradient, such as near a wall or around a stagnation point [14]. Roe and his partners drew a conclusion in 2010 that AUSMPW+ was the most promising one to be used in hypersonic computations [15]. However, its dissipation is too large in low speeds' simulation like others.…”

“…Also, shortcomings of the original ones in higher Mach number flows are inherited. The Roe scheme combined with preconditioned matrix, for example, still suffers from the shock-induced anomaly [11,12] in hypersonic flows. Also, it needs to employ an entrophy fix [13] in rarefactions' simulations.…”

Improved second-order hyperbolic residual-distribution scheme and its extension to third-order on arbitrary triangular grids

“…However, it is widely accepted that accurate and smooth solution gradients cannot be achieved with conventional schemes on fully irregular unstructured grids [1,2]. In conventional schemes, the gradients are obtained typically with a lower order of accuracy (e.g., through reconstruction of primary variables), and they are usually subject to numerical oscillations on such grids.…”