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Appl. Sci. 2018, 8(1), 119; doi:10.3390/app8010119

A Semi-Explicit Multi-Step Method for Solving Incompressible Navier-Stokes Equations

Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Edifici C1 Campus Nord UPC C/ Gran Capità, S/N 08034 Barcelona, Spain
Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya (UPC), 08034 Barcelona, Spain
Author to whom correspondence should be addressed.
Received: 19 December 2017 / Revised: 10 January 2018 / Accepted: 14 January 2018 / Published: 16 January 2018
(This article belongs to the Section Mechanical Engineering)
View Full-Text   |   Download PDF [444 KB, uploaded 16 January 2018]   |  


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. View Full-Text
Keywords: Runge–Kutta; fractional step method, incompressible flows; finite element method; computational efficiency Runge–Kutta; fractional step method, incompressible flows; finite element method; computational efficiency

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ryzhakov, P.; Marti, J. A Semi-Explicit Multi-Step Method for Solving Incompressible Navier-Stokes Equations. Appl. Sci. 2018, 8, 119.

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