GMRES physics-based preconditioner for all Reynolds and Mach numbers: numerical examples

Nigro, Norberto M.; Storti, Mario A.; Idelsohn, Sergio

doi:10.1002/(sici)1097-0363(19971230)25:12<1347::aid-fld608>3.0.co;2-c

Cited by 6 publications

(3 citation statements)

References 28 publications

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“…Such an approach, very popular in the context of scientific computing for a large class of flow regimes and pattern (e.g. [25,26,33,34]), is able to offer invaluable advantages with respect to the computational industry standard for turbomachine aerodynamics. With reference to the numerical oscillations and instabilities that might be encountered when the flow involves high Reynolds and/or sharp boundary layers, the proposed stabilized formulation follows the most notable and referenced techniques based on PG weighted residual approaches.…”

Section: Numerical Formulationmentioning

confidence: 99%

A finite element overlapping scheme for turbomachinery flows on parallel platforms

Borello¹,

Corsini²,

Rispoli³

2003

Computers & Fluids

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Section: Numerical Formulationmentioning

confidence: 99%

A finite element overlapping scheme for turbomachinery flows on parallel platforms

Borello¹,

Corsini²,

Rispoli³

2003

Computers & Fluids

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“…The preconditioning matrix applied here was proposed by Choi and Merkle [3] to solve steady compressible flows using the Finite Volume method. Nigro et al [16,17] applied this preconditioning matrix to formulate a stabilized Finite Element Method (FEM) able to solve steady compressible flow problems. Since we are interested in the resolution of problems with deformable domains, an Arbitrary Lagrangian Eulerian (ALE) strategy is incorporated to the equations.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, we obtain the following expression for the characteristic polynomial: The eigenvalues of matrix G are given by Equation (16).…”

mentioning

confidence: 99%

Stabilized finite element method based on local preconditioning for unsteady compressible flows in deformable domains with emphasis on the low Mach number limit application

López

Nigro

Sarraf

et al. 2011

Numerical Methods in Fluids

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SUMMARY Flows with low Mach numbers represent a limit situation in the solution of compressible flows. The preconditioning of flow equations is one of the classical approaches proposed to capture the solution in the low Mach number limit. In this method, the time derivatives are premultiplied by a suitable preconditioning matrix in order to achieve a well‐conditioned system by means of the scaling of the system eigenvalues. Hence, the modified equations have only steady‐state solutions in common with the original system. For the application of these methods to unsteady problems, the dual time‐stepping technique has emerged, where the physical time derivative terms are treated as source and/or reactive terms. The use of a preconditioning matrix defined to compute steady‐state solutions may not be a good choice for unsteady problems, as showed by Vigneronit et al. (European Conference on Computational Fluid Dynamics, 2006). However, such matrices can be adapted to perform the computation of transient flows by means of the appropriate redefinition of some coefficients. The application of a ‘steady‐state’ preconditioning matrix to unsteady problems with an ALE (Arbitrary Lagrangian Eulerian) approach is presented. The equations are discretized in space using a stabilized Finite Element method and in time using finite differences. The preconditioning of the governing equations is not applied in the numerical scheme but is used, through the eigenvalues of the preconditioned system, to design appropriately the stabilization term. Several test cases are solved, including incompressible flows and the in‐cylinder flow in a motored opposed‐piston engine. Copyright © 2011 John Wiley & Sons, Ltd.

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A new finite element formulation for both compressible and nearly incompressible fluid dynamics

Sampaio

Moreira

2000

Int. J. Numer. Meth. Fluids

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GMRES physics-based preconditioner for all Reynolds and Mach numbers: numerical examples

Cited by 6 publications

References 28 publications

A finite element overlapping scheme for turbomachinery flows on parallel platforms

A finite element overlapping scheme for turbomachinery flows on parallel platforms

Stabilized finite element method based on local preconditioning for unsteady compressible flows in deformable domains with emphasis on the low Mach number limit application

A new finite element formulation for both compressible and nearly incompressible fluid dynamics

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