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

• Autor: Ryzhakov, Pavel ; Marti, Julio
• Assuntos: Anàlisi numèrica ; computational efficiency ; Computational fluid dynamics ; Computer applications ; Computing time ; Finite difference method ; Finite element method ; Finite volume method ; Fluid flow ; Fluid mechanics ; Flux de fluids ; fractional step method ; Física ; Física de fluids ; Galerkin method ; incompressible flows ; Integration ; Matemàtiques i estadística ; Mathematical models ; Mecànica de fluids ; Mètodes numèrics ; Navier-Stokes equations ; Poisson equation ; Predictor-corrector methods ; Runge-Kutta ; Runge-Kutta formulas ; Runge-Kutta method ; Solvers ; Stokes law (fluid mechanics) ; Time integration ; Àrees temàtiques de la UPC
• É parte de: Applied sciences, 2018-01, Vol.8 (1), p.119
• Descrição: 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.
  
• Editor: Basel: MDPI AG
  
• Idioma: Inglês