A multigrid method for convergence acceleration is used for solving coupled fluid and turbulence transport equations. For turbulence closure a low-Reynolds-number q-ω turbulence model is employed, which requires very fine grids in the near wall regions. Due to the use of fine grids, convergence of most iterative solvers slows down, making the use of multigrid techniques especially attractive. However, special care has to be taken on the strong nonlinear turbulent source terms during restriction from fine to coarse grids. Due to the hyperbolic character of the governing equations in supersonic flows and the occurrence of shock waves, modifications to standard multigrid techniques are necessary. A simple and effective method is presented that enables the multigrid scheme to converge. A strong reduction in the required number of multigrid cycles and work units is achieved for different test cases, including a Mack 2 flow over a backward facing step.
An Implicit Multigrid Scheme for the Compressible Navier-Stokes Equations With Low-Reynolds-Number Turbulence Closure
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Gerlinger, P., and Bru¨ggemann, D. (June 1, 1998). "An Implicit Multigrid Scheme for the Compressible Navier-Stokes Equations With Low-Reynolds-Number Turbulence Closure." ASME. J. Fluids Eng. June 1998; 120(2): 257–262. https://doi.org/10.1115/1.2820642
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