A parallel implicit adaptive-mesh-refinement scheme is proposed for the solution of the Navier-Stokes equations as applied to two-dimensional steady-state hypersonic laminar flows in conjunction with an equilibrium high-temperature equation of state. A finite-volume discretization is applied to the governing equations. Limited piecewise-linear solution reconstruction and Riemann solvers (Roe and HLLE, both modified for a general equation of state) are used to evaluate the inviscid fluxes. The gradients in the viscous fluxes are calculated using diamond-path reconstruction. The system of non-linear algebraic equations resulting from the finite-volume discretization are solved using an inexact Newton method with GMRES to solve the update step of the Newton method. GMRES is preconditioned with Schwarz preconditioning with local block-fill incomplete lower-upper factorization. Multigrid and pseudo-transient continuation are used for startup. Numerical results, including flows at Mach numbers of 7.0, are discussed and demonstrate the validity and efficiency of the scheme.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/11173 |
| Date | 30 July 2008 |
| Creators | Wood, Alistair Henry Cameron |
| Contributors | Groth, Clinton P. T. |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
| Format | 27858183 bytes, application/pdf |
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