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Agglomeration multigrid methods with implicit Runge–Kutta smoothers applied to aerodynamic simulations on unstructured grids

Langer, Stefan (2014) Agglomeration multigrid methods with implicit Runge–Kutta smoothers applied to aerodynamic simulations on unstructured grids. Journal of Computational Physics, 277 (11), pp. 72-100. Elsevier. doi: 10.1016/j.jcp.2014.07.050. ISSN 0021-9991.

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Official URL: http://www.sciencedirect.com/science/article/pii/S0021999114005439


For unstructured finite volume methods an agglomeration multigrid with an implicit multistage Runge–Kutta method as a smoother is developed for solving the compressible Reynolds averaged Navier–Stokes (RANS) equations. The implicit Runge–Kutta method is interpreted as a preconditioned explicit Runge–Kutta method. The construction of the preconditioner is based on an approximate derivative. The linear systems are solved approximately with a symmetric Gauss–Seidel method. To significantly improve this solution method grid anisotropy is treated within the Gauss–Seidel iteration in such a way that the strong couplings in the linear system are resolved by tridiagonal systems constructed along these directions of strong coupling. The agglomeration strategy is adapted to this procedure by taking into account exactly these anisotropies in such a way that a directional coarsening is applied along these directions of strong coupling. Turbulence effects are included by a Spalart–Allmaras model, and the additional transport-type equation is approximately solved in a loosely coupled manner with the same method. For two-dimensional and three-dimensional numerical examples and a variety of differently generated meshes we show the wide range of applicability of the solution method. Finally, we exploit the GMRES method to determine approximate spectral information of the linearized RANS equations. This approximate spectral information is used to discuss and compare characteristics of multistage Runge–Kutta methods.

Item URL in elib:https://elib.dlr.de/91002/
Document Type:Article
Title:Agglomeration multigrid methods with implicit Runge–Kutta smoothers applied to aerodynamic simulations on unstructured grids
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Date:9 August 2014
Journal or Publication Title:Journal of Computational Physics
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:pp. 72-100
Keywords:Reynolds averaged Navier-Stokes equations High Reynolds number Agglomeration multigrid Implicit smoother Aerodynamic applications Eigenvalue analysis
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:fixed-wing aircraft
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Simulation and Validation (old)
Location: Braunschweig
Institutes and Institutions:Institute of Aerodynamics and Flow Technology > C²A²S²E - Center for Computer Applications in AeroSpace Science and Engineering
Deposited By: Langer, Dr.rer.nat. Stefan
Deposited On:16 Oct 2014 09:38
Last Modified:21 Nov 2023 14:01

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