A modified Taylor Galerkin scheme for turbulent compressible flow simulation

As already demonstrated by different authors, the Taylor-Galerkin (TG) scheme, in the context of the Finite Element Method (FEM), is particularly suitable for the solution of supersonic flows. The TG scheme, using hexahedral finite elements with analytical evaluation of element matrices, is applied...

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Autores principales: Burbridge, Horacio Pedro, Scarabino, Ana Elena, Awruch, Armando Miguel
Formato: Articulo
Lenguaje:Inglés
Publicado: 2019
Materias:
Ingeniería Aeronáutica
Compressible
Turbulent
FEM
Taylor-Galerkin
CBS
Spalart-Allmaras
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/137595
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-137595
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ingeniería Aeronáutica
Compressible
Turbulent
FEM
Taylor-Galerkin
CBS
Spalart-Allmaras
spellingShingle Ingeniería Aeronáutica
Compressible
Turbulent
FEM
Taylor-Galerkin
CBS
Spalart-Allmaras
Burbridge, Horacio Pedro
Scarabino, Ana Elena
Awruch, Armando Miguel
A modified Taylor Galerkin scheme for turbulent compressible flow simulation
topic_facet Ingeniería Aeronáutica
Compressible
Turbulent
FEM
Taylor-Galerkin
CBS
Spalart-Allmaras
description As already demonstrated by different authors, the Taylor-Galerkin (TG) scheme, in the context of the Finite Element Method (FEM), is particularly suitable for the solution of supersonic flows. The TG scheme, using hexahedral finite elements with analytical evaluation of element matrices, is applied in this work. Tools to avoid locking and a shock capturing technique for the solution of supersonic viscous and non-viscous compressible flows are also employed. However, TG scheme usually presents instabilities in subsonic flows. Even in cases in which the free stream Mach number corresponds to supersonic flows, there are always flow regions, specifically near the walls of the immersed obstacles, where the speed is lower and the local Mach number corresponds to a subsonic flow. The CharacteristicBased Split (CBS) scheme was developed in order to obtain a single method to improve the behavior with respect to TG method in subsonic and supersonic regimes. In the last two decades some works have shown advantages in convergence rates of the CBS method when compared to the TG algorithm. However, simulation time increases in the CBS method since split operations, typical of this algorithm, imply in additional element loops. In this paper a hybrid algorithm called Modified-Taylor-Galerkin scheme (MTG) is proposed. This algorithm presents advantages with respect to TG and CBS schemes in terms of convergence properties and computational processing time. In order to get an efficient algorithm, the element matrices are analytically integrated. This is performed with two different approaches. In the first approach the inverse matrix and the determinant of the Jacobian matrix at element level are evaluated with a reduced integration form, using the point located in the center of the element for mass, convective, diffusive and stabilization element matrices; all these matrices are integrated analytically. In the second approach, mass and convective matrices are calculated by a complete integration scheme (including the inverse matrix and the determinant of the Jacobian matrix at element level in the analytical expression to be integrated) and the diffusive and stabilization matrices are calculated with a reduced integration form, using the point located at the center of the element to calculate the inverse matrix and the determinant of the Jacobian matrix at element level. Finally, this work incorporates the Spalart-Allmaras (S-A) turbulence model using a conservative version of the transport equation, as proposed by the authors of the original S-A model in a later paper. Algorithms are tested to determine convergence rate improvements in both laminar and turbulent cases and for different Mach numbers (supersonic, transonic and subsonic flows).
format Articulo
Articulo
author Burbridge, Horacio Pedro
Scarabino, Ana Elena
Awruch, Armando Miguel
author_facet Burbridge, Horacio Pedro
Scarabino, Ana Elena
Awruch, Armando Miguel
author_sort Burbridge, Horacio Pedro
title A modified Taylor Galerkin scheme for turbulent compressible flow simulation
title_short A modified Taylor Galerkin scheme for turbulent compressible flow simulation
title_full A modified Taylor Galerkin scheme for turbulent compressible flow simulation
title_fullStr A modified Taylor Galerkin scheme for turbulent compressible flow simulation
title_full_unstemmed A modified Taylor Galerkin scheme for turbulent compressible flow simulation
title_sort modified taylor galerkin scheme for turbulent compressible flow simulation
publishDate 2019
url http://sedici.unlp.edu.ar/handle/10915/137595
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AT scarabinoanaelena modifiedtaylorgalerkinschemeforturbulentcompressibleflowsimulation
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