22nd Congress of International Council of the Aeronautical Sciences, Harrogate, UK, 28 August - 1st September, 2000
Paper ICAS 2000-7.3.2

EFFECTS OF TREATMENT OF THE SOURCE TERMS IN TURBULENT MODELS ON THE CONVERGENCE RATE

J. B. Zhang
University of Tokyo, Japan

Keywords: aerodynamics, cfd, turbulence model, positivity property

After substantial progress has been made in solving flow field accurately, the robustness of a numerical scheme has raised growing interest in CFD community. Solution of turbulence model equations poses additional difficulties compared with the solution of mean-flow equations. Method to ensure the discrete positivity of turbulence eddy viscosity is proposed by Baldwin & Barth and later expanded by Spalart & Allmaras in the solution of their respective one-equation turbulence models. It is noticed during the current research that the strategy proposed by Spalart and Allmaras is a sufficient but unnecessarily restrictive condition for the solution procedure to be positively conservative, and that there is no fundamental reason to split the Jacobian of the combined source term into two parts. The presence of the temporal term allows more information from the exact Jacobian of the combined source term to be extracted. A new strategy of treatment of source terms, having the potential to give even better convergence characteristic, is proposed. In addition, previous works have been restricted to firstorder accurate discretization of convection terms in the turbulence model. A way to extend the positivity property to second-order accurate discretization of convection terms is proposed.

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