A Numerical Study of Shock and Heating With Rarefaction for Hypersonic Flow Over a Cylinder

The numerical computation of hypersonic flows over blunt bodies is challenging due to the difficulty in robust and accurate wall heat flux prediction and proper capturing of shock waves free from the “carbuncle” phenomenon and other shock anomalies. It is important to understand how this behavior is affected due to rarefaction, which in turn will help to improve the study of aerospace vehicles flowing in rarefied and hypersonic regime. Recently, the SLAU2 convective scheme was shown to suppress the shock anomalies found in capturing strong shocks, however, it still showed a wavy pattern of heating. We have proposed a modification to the SLAU2 convective scheme to improve the accuracy of flow predictions in the presence of strong shocks. We then perform the numerical simulation of hypersonic viscous flow over a cylinder at Mach 8 and 16.34 at different Knudsen numbers. We carry out the study using the modified SLAU2 and the classical Roe schemes. We study how the shock anomalies found in the continuum hypersonic flows behave with the degree of rarefaction. It is found that the modified SLAU2 captures the shock free from the shock anomalies at all Kn, while the Roe scheme lacks robustness for Kn≲10−3. The variation of different flow properties such as heat flux, wall shear stress, and the Mach number is investigated. The peak heating value was observed to decrease with the degree of rarefaction.

Healing of the Carbuncle Phenomenon for AUSMDV Scheme on Triangular Grids

The carbuncle phenomenon, commonly occurring in solutions of compressible Euler equations, is a numerical instability associated with shock-induced anomalies. It is associated with several shock-capturing finite-volume methods designed to preserve the contact discontinuities. Due to the lack of theoretical knowledge of the carbuncle phenomenon, it is not known which numerical scheme is affected or under what circumstances that the phenomenon occur. The objective of this article is to study the numerical instability of advection upstream splitting method (AUSM) family schemes so called the AUSMD, AUSMV and AUSMDV schemes in two-dimensional structured triangular grids by examining the shock-induced anomalies produced by these original schemes in different test cases. A multidimensional dissipation technique is proposed for these schemes. The evolution of perturbations is also studied by means of a linearized discrete analysis to the odd–even decoupling problem. The recursive equations show that the AUSMDV-family schemes with the dissipation technique are less sensitive to these anomalies than the original schemes. Finally, the dissipation technique is extended to the second-order schemes and tested by several test cases.

MULTIDIMENSIONAL DISSIPATION TECHNIQUE FOR AN AUSM SCHEME ON TRIANGULAR GRIDS

Numerical instability of the AUSM scheme on two-dimensional structured triangular grids is investigated. By examining several test cases, it is found that both numerical flux formulations of the AUSM scheme (so-called the AUSM-M1 and AUSM-M2 schemes) do not have sufficiently robustness to satisfy the shock-induced anomaly so called the carbuncle phenomenon. The modified multidimensional dissipation technique is then proposed in order to heal such shock instability. The dissipation mechanism against perturbations is investigated by applying a linearized discrete analysis to the odd-even decoupling problem. The recursive equations show that the dissipation factor (δ) plays an important role in all perturbations of the AUSM-M1 scheme. But it does not have any effect on the density perturbation of the AUSM-M2 scheme. Finally, the scheme is further extended to achieve the second-order solution accuracy and evaluated theirs robustness against shock instability by solving several test cases.