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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Published in:	Applied sciences Vol. 8; no. 1; p. 119
Main Authors:	Ryzhakov, Pavel, Marti, Julio
Format:	Journal Article Publication
Language:	English
Published:	Basel MDPI AG 01.01.2018 Multidisciplinary Digital Publishing Institute
Subjects:	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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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.
AbstractList	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. 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. Peer Reviewed
Author	Ryzhakov, Pavel Marti, Julio
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Snippet	The fractional step method is a technique that results in a computationally-efficient implementation of Navier–Stokes solvers. In the finite element-based... The fractional step method is a technique that results in a computationally-efficient implementation of Navier-Stokes solvers. In the finite element-based...
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SubjectTerms	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
Title	A Semi-Explicit Multi-Step Method for Solving Incompressible Navier-Stokes Equations
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