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

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 f...

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Vydáno v:Applied sciences Ročník 8; číslo 1; s. 119
Hlavní autoři: Ryzhakov, Pavel, Marti, Julio
Médium: Journal Article Publikace
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.01.2018
Multidisciplinary Digital Publishing Institute
Témata:
Anàlisi numèrica
computational efficiency
finite element method
Finite volume method
Fluid mechanics
Flux de fluids
fractional step method
Física
Física de fluids
incompressible flows
Matemàtiques i estadística
Mathematical models
Mecànica de fluids
Mètodes numèrics
Navier-Stokes equations
Runge-Kutta
Runge-Kutta formulas
Àrees temàtiques de la UPC
ISSN:2076-3417, 2076-3417
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Shrnutí: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.
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ISSN:2076-3417
2076-3417
DOI:10.3390/app8010119