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Viscous computations using a direct solver. (English) Zbl 0692.76026

Summary: Newton’s method is used to compute viscous fluid flows in a robust manner. Spatial discretization of the inviscid fluxes is performed using Roe’s approximate Riemann solver. The viscous fluxes are discretized using central differences. Marching in time is done by a fully implicit procedure. The system of equations that arises as a result of linearization in time is solved directly by applying sparse matrix methods. Quadratic convergence is realized by using the exact linearization of Roe’s scheme. It is shown that steady state solutions can be obtained typically in 3-4 iterations. It is further shown that the convergence histories are fairly independent of the Reynolds number. Results are presented for laminar test cases. Localized distortions in the pressure field are observed in the case of detached boundary layers which disappear upon better resolution. An embedded mesh procedure, in which regions of interest are better resolved, is shown to be useful in this regard. Issues concerning the computation of high Reynolds number laminar flows are also addressed.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

Software:

YSMP; symrcm
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Full Text: DOI

References:

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