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Title:	A semi-explicit multi-step method for solving incompressible navier-stokes equations
Author:	Ryzhakov, Pavel; Martí, Julio Marcelo
Other authors:	Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. DECA - Grup de Recerca del Departament d'Enginyeria Civil i Ambiental
Abstract:	The fractional step method is a technique that results in a computationally-efficient implementation of Navier–Stokes solvers. In the finite element-based models, it is often applied in conjunction with implicit time integration schemes. On the other hand, in the framework of finite difference and finite volume methods, the fractional step method had been successfully applied to obtain predictor-corrector semi-explicit methods. In the present work, we derive a scheme based on using the fractional step technique in conjunction with explicit multi-step time integration within the framework of Galerkin-type stabilized finite element methods. We show that under certain assumptions, a Runge–Kutta scheme equipped with the fractional step leads to an efficient semi-explicit method, where the pressure Poisson equation is solved only once per time step. Thus, the computational cost of the implicit step of the scheme is minimized. The numerical example solved validates the resulting scheme and provides the insights regarding its accuracy and computational efficiency.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica -Àrees temàtiques de la UPC::Física::Física de fluids::Flux de fluids -Runge-Kutta formulas -Fluid mechanics--Mathematical models -Runge-Kutta -fractional step method -incompressible flows -finite element method -computational efficiency -Mecànica de fluids -- Mètodes numèrics
Rights:	Attribution 3.0 Spain http://creativecommons.org/licenses/by/3.0/es/
Document type:	Article - Published version Article
Published by:	Multidisciplinary Digital Publishing Institute
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