Convergence acceleration for multistage timeserving schemes

R. C. Swanson*, E. Turkel, C. C. Rossow, V. N. Vatsa

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The. effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 × 106 and 100.0 × 106. Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, it is demonstrated that the computational time of a well-tuned standard RK scheme can be reduced at least a factor of four.

Original languageEnglish
Title of host publicationCollection of Technical Papers - 36th AIAA Fluid Dynamics Conference
Number of pages21
StatePublished - 2006
Event36th AIAA Fluid Dynamics Confernce - San Francisco, CA, United States
Duration: 5 Jun 20068 Jun 2006

Publication series

NameCollection of Technical Papers - 36th AIAA Fluid Dynamics Conference


Conference36th AIAA Fluid Dynamics Confernce
Country/TerritoryUnited States
CitySan Francisco, CA


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