论文信息 - Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids

Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids

A parallel Jacobian-free solver for supersonic flows on unstructured hybrid meshes is proposed. An edge-based Finite Element formulation is used for spatial discretization with flow stabilized via either AUSM+-up or a Roe scheme. The Jacobian-free Newton-Krylov method is used as linear system solver and the lower-upper symmetric Gauss-Seidel method is used for matrix-free preconditioning. In the present formulation, second order approximations of spatial derivatives of the inviscid fluxes are introduced efficiently. Numerical results for Mach 1.93 flow past a sphere, Mach 4 flow past a waverider, and Mach 10.01 flow past a sphere, are presented.

[1] L. Landau,et al. CHAPTER VII – SURFACE PHENOMENA , 1959 .

[2] Leonardo C. Scalabrin,et al. Numerical simulation of weakly ionized hypersonic flow over reentry capsules , 2007 .

[3] P. Roe. Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[4] V. Selmin,et al. Simulation of hypersonic flows on unstructured grids , 1992 .

[5] Rainald Löhner,et al. A fast, matrix-free implicit method for compressible flows on unstructured grids , 1998 .

[6] Meng-Sing Liou,et al. A sequel to AUSM, Part II: AUSM+-up for all speeds , 2006, J. Comput. Phys..

[7] V. Selmin,et al. The node-centred finite volume approach: bridge between finite differences and finite elements , 1993 .

[8] D. Keyes,et al. Jacobian-free Newton-Krylov methods: a survey of approaches and applications , 2004 .

[9] Homer F. Walker,et al. Choosing the Forcing Terms in an Inexact Newton Method , 1996, SIAM J. Sci. Comput..

[10] Leonardo C. Scalabrin,et al. Numerical Simulation of Weakly Ionized Hypersonic Flow for Reentry Configurations , 2006 .