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Implementation of a stabilized finite element formulation for the incompressible Navier-Stokes equations based on a pressure gradient projection
Codina, Ramon; Blasco Lorente, Jorge; Buscaglia, G C; Huerta, Antonio
Universitat Politècnica de Catalunya. Departament de Resistència dels Materials i Estructures en Enginyeria; Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions; Universitat Politècnica de Catalunya. (MC)2 - Grup de Mecànica Computacional en Medis Continus; Universitat Politècnica de Catalunya. LACÀN - Centre Específic de Recerca de Mètodes Numèrics en Ciències Aplicades i Enginyeria
We discuss in this paper some implementation aspects of a finite element formulation for the incompressible Navier-Stokes equations which allows the use of equal order velocity-pressure interpolations. The method consists in introducing the projection of the pressure gradient and adding the difference between the pressure Laplacian and the divergence of this new field to the incompressibility equation, both multiplied by suitable algorithmic parameters. The main purpose of this paper is to discuss how to deal with the new variable in the implementation of the algorithm. Obviously, it could be treated as one extra unknown, either explicitly or as a condensed variable. However, we take for granted that the only way for the algorithm to be efficient is to uncouple it from the velocity-pressure calculation in one way or another. Here we discuss some iterative schemes to perform this uncoupling of the pressure gradient projection (PGP) from the calculation of the velocity and the pressure, both for the stationary and the transient Navier-Stokes equations. In the first case, the strategies analyzed refer to the interaction of the linearization loop and the iterative segregation of the PGP, whereas in the second the main dilemma concerns the explicit or implicit treatment of the PGP.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Navier-Stokes equations--Numerical solutions
finite element
incompressible flow
Navier-Stokes equations
pressure gradient projection
Equacions de Navier-Stokes -- Mètodes numèrics
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