论文信息 - An Improved HLLE Method for Hypersonic Viscous Flows

An Improved HLLE Method for Hypersonic Viscous Flows

Dissipation mechanisms of Godunov-type schemes are presented in the framework of unified representation. We first examined the causes of inaccuracy at the contact discontinuity and the dissipation mechanism in the numerical mass flux of the HLLEM scheme. Through a linear perturbation analysis on the oddeven decoupling problem, we discuss necessary conditions for designing a shock stable scheme. The curing methods for each specified problem are also presented. A new improved HLLE(HLLE+) scheme is proposed and analyzed on its dissipation mechanism. The diffusivity of the Godunov-type schemes is examined by computing two-dimensional hypersonic viscous flow. It is shown that the present method can accurately predict the surface heating rates without grid dependency.

Jang-Hyuk Kwon | Su Hong Park | J. Kwon | Su Hong Park

[1] Hong-Chia Lin,et al. Dissipation additions to flux-difference splitting , 1991 .

[2] Shigeru Obayashi,et al. Practical formulation of a positively conservative scheme , 1994 .

[3] Meng-Sing Liou,et al. Mass Flux Schemes and Connection to Shock Instability , 2000 .

[4] P. Lax,et al. On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[5] S. Imlay,et al. Blunt-body flow simulations , 1988 .

[6] P. Roe,et al. On Godunov-type methods near low densities , 1991 .

[7] J. Quirk. A Contribution to the Great Riemann Solver Debate , 1994 .

[8] Bernd Einfeld. On Godunov-type methods for gas dynamics , 1988 .

[9] T. Pulliam,et al. A diagonal form of an implicit approximate-factorization algorithm , 1981 .

[10] Probing numerical fluxes - Mass flux, positivity, and entropy-satisfying property , 1997 .

[11] D. Gaitonde,et al. Accuracy of flux-split algorithms in high-speed viscous flows , 1993 .

[12] W. K. Anderson,et al. Comparison of Finite Volume Flux Vector Splittings for the Euler Equations , 1985 .