An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme
2008
A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-ω model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the twodimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.
Keywords:
- Reynolds-averaged Navier–Stokes equations
- Mathematical optimization
- Turbulence modeling
- K-omega turbulence model
- K-epsilon turbulence model
- Alternating direction implicit method
- Reynolds decomposition
- Classical mechanics
- Multigrid method
- Reynolds stress equation model
- Mathematics
- Applied mathematics
- Turbulence kinetic energy
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
29
References
3
Citations
NaN
KQI