Abstract
A pressure-based implicit procedure to solve the Euler and Navier ‐Stokes equations on a nonorthogonal mesh withcollocated e nitevolumeformulation is described. The boundedness criteria forthisprocedurearedetermined from total variation diminishing (TVD) schemes, which are based on characteristic variables and are applied to the e uxes of the convected quantities, including mass e ow rate. The procedure incorporates the k‐ eddy-viscosity turbulence model. Thealgorithm ise rsttested for inviscid e owsat differentMach numbers ranging from subsonic to supersonic on a bump in a channel geometry, where the results are compared with other existing numerical solutions.Themethodisthenvalidatedagainstexperimentandanothernumericalsolutionforthecaseofturbulent transonic e ow through a gas turbine rotor blade cascade for which wind-tunnel experimental data exist. The comparisons show that the quality of the resolution of the TVD scheme, as implemented in the pressure-based procedure, is similar to that obtained when applied in density-based methods.
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