PD Dr. Stefan Langer, DLR Braunschweig
Title: On boundary value problems for RANS equations and two-equation turbulence models – Talk 1
Currently, in engineering computations for high Reynolds number turbulent flows, turbulence modeling continues to be the most frequently used approach to represent the effects of turbulence. Such models generally rely on solving either one or two transport equations along with the Reynolds-Averaged Navier-Stokes (RANS) equations. The solution of the boundary-value problem of any system of partial differential equations (PDEs) requires the complete delineation of the equations and the boundary conditions, including any special restrictions and conditions. In the literature, such a description is often incomplete, neglecting important details related to the boundary conditions and possible restrictive conditions, such as how to ensure satisfying prescribed values of the dependent variables of the transport equations in the far field of a finite domain. In these two lectures, which build on each other, we consider the following topics:
Often a severe loss of reliability and efficiency of current solution methods for boundary-value problems for the compressible RANS equations can be observed. We discuss the possible influence of boundary values, as well as near-field and far-field behavior, on the solution of the RANS equations coupled with transport equations for turbulence modeling. An analysis is performed to analyze the near-wall and far-field behavior of the turbulence model variables. This allows an assessment of the decay rate of these variables required to realize the boundary conditions in the far field. A multigrid algorithm using implicit multistage Runge-Kutta methods as a smoother is developed. It is shown that (almost) all well known solution methods proposed in the literature about CFD are specializations of this general ansatz. It is demonstrated that for complex applications smoothers with a large amount of implicitness are required to reliably approximate steady-state solutions.
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