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A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm
Blasco Lorente, Jorge; Codina, Ramon; 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
An implicit fractional-step method for the numerical solution of the time-dependent incompressible Navier-Stokes equations in primitive variables is studied in this paper. The method, which is first-order-accurate in the time step, is shown to converge to an exact solution of the equations. By adequately splitting the viscous term, it allows the enforcement of full Dirichlet boundary conditions on the velocity in all substeps of the scheme, unlike standard projection methods. The consideration of this method was actually motivated by the study of a well-known predictor-multicorrector algorithm, when this is applied to the incompressible Navier-Stokes equations. A new derivation of the algorithm in a general setting is provided, showing in what sense it can also be understood as a fractional-step method; this justifies, in particular, why the original boundary conditions of the problem can be enforced in this algorithm. Two different finite element interpolations are considered for the space discretization, and numerical results obtained with them for standard benchmark cases are presented.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
Navier-Stokes equations--Numerical solutions
incompressible Navier-Stokes equations
finite elements
fractional-step methods
predictor-multicorrector algorithm
convergence analysis
Equacions de Navier-Stokes -- Mètodes numèrics

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