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Investigation of Relaxation Parameters and residual based truncation criteria for Reynolds averaged Navier-Stokes equations

Somasundaram, Manickam (2016) Investigation of Relaxation Parameters and residual based truncation criteria for Reynolds averaged Navier-Stokes equations. Master's. DLR-Interner Bericht. DLR-IB-AS-BS-2016-333, 57 S.

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Abstract

To solve the RANS equation and the transport equation based on one equation Spalart Allmaras model, an agglomerated non-linear multigrid scheme with implicit smoothing, based on first order approximation of the derivative ot the residual function, exists. The implicit smoothing leads to a linear system of equation that needs to be solved for every stage of the smoothing algorithm. To improve this solution method grid anisotropy is treated with the Gauss-Seidel iteration in such a way that lines with strong coupling in linear system are resolved by tridiagonal systems constructed along the direction of strong coupling. The existing methodology of solving this linear system with a line symmetric Gauss-Seidel method restricts finer meshes to reach higher CFL numbers. Therefore relaxation parameter is incorporated into the existing line symmetric Gauss-Seidel methods to investigate the change in the solution methodology. The current practice is to set the number of Gauss-Seidel sweeps to a certain number and this may lead to over-solving. Thus the extent to which the inner linear equations that needs to be solved can be truncated after the linear residual is reduced by a certain order of magnitude. In this regard too, numerical experiments demonstrate that choosing a low GS sweeps may lead to delay in converging whereas a high GS sweep value may lead to over solving thereby making it computationally expensive. Thus a truncation criteria based on a linear residual is implemented and the change is investigated. Eigenvalue analysis is done after implementation of the linear based truncation criteria to compare the asymptotic convergence of the solution method.

Item URL in elib:https://elib.dlr.de/113721/
Document Type:Monograph (DLR-Interner Bericht, Master's)
Title:Investigation of Relaxation Parameters and residual based truncation criteria for Reynolds averaged Navier-Stokes equations
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Somasundaram, ManickamUNSPECIFIEDUNSPECIFIED
Date:3 November 2016
Refereed publication:No
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Number of Pages:57
ISSN:1614-7790
Status:Published
Keywords:Reynolds averaged Navier-Stokes equations Implicit Runge-Kutta methods Relaxed Gauss-Seidel methods Analysis based on spectral information
Institution:DLR
Department:AS-BS-CASE
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
Location: Braunschweig
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > CASE, BS
Deposited By: Seyfried, Beate
Deposited On:22 Nov 2017 15:20
Last Modified:31 Jul 2019 20:11

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