Efficient upwind algorithms for solution of the Euler and Navier-stokes equations

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dc.contributor.advisor Roe, P. L.
dc.contributor.advisor Qin, N.
dc.contributor.author McNeil, C. Y.
dc.date.accessioned 2010-01-16T10:13:03Z
dc.date.available 2010-01-16T10:13:03Z
dc.date.issued 1995-10
dc.identifier.uri http://hdl.handle.net/1826/4147
dc.description.abstract An efficient three-dimensionasl tructured solver for the Euler and Navier-Stokese quations is developed based on a finite volume upwind algorithm using Roe fluxes. Multigrid and optimal smoothing multi-stage time stepping accelerate convergence. The accuracy of the new solver is demonstrated for inviscid flows in the range 0.675 :5M :5 25. A comparative grid convergence study for transonic turbulent flow about a wing is conducted with the present solver and a scalar dissipation central difference industrial design solver. The upwind solver demonstrates faster grid convergence than the central scheme, producing more consistent estimates of lift, drag and boundary layer parameters. In transonic viscous computations, the upwind scheme with convergence acceleration is over 20 times more efficient than without it. The ability of the upwind solver to compute viscous flows of comparable accuracy to scalar dissipation central schemes on grids of one-quarter the density make it a more accurate, cost effective alternative. In addition, an original convergencea cceleration method termed shock acceleration is proposed. The method is designed to reduce the errors caused by the shock wave singularity M -+ 1, based on a localized treatment of discontinuities. Acceleration models are formulated for an inhomogeneous PDE in one variable. Results for the Roe and Engquist-Osher schemes demonstrate an order of magnitude improvement in the rate of convergence. One of the acceleration models is extended to the quasi one-dimensiona Euler equations for duct flow. Results for this case d monstrate a marked increase in convergence with negligible loss in accuracy when the acceleration procedure is applied after the shock has settled in its final cell. Typically, the method saves up to 60% in computational expense. Significantly, the performance gain is entirely at the expense of the error modes associated with discrete shock structure. In view of the success achieved, further development of the method is proposed. en_UK
dc.language.iso en en_UK
dc.publisher Cranfield University en_UK
dc.title Efficient upwind algorithms for solution of the Euler and Navier-stokes equations en_UK
dc.type Thesis or dissertation en_UK
dc.type.qualificationlevel Doctoral en_UK
dc.type.qualificationname PhD en_UK

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