Analysis and realization of fractional step filters of order (1+α)

2022 ◽  
pp. 337-372
Author(s):  
Gagandeep Kaur ◽  
A.Q. Ansari ◽  
M.S. Hashmi
Keyword(s):  
Fractional Step

scholarly journals Goal-Oriented Error Estimation for the Fractional Step Theta Scheme

2014 ◽  
Vol 14 (2) ◽  
pp. 203-230 ◽  
Author(s):  
Dominik Meidner ◽  
Thomas Richter
Keyword(s):  
Time Discretization ◽  
Posteriori Error ◽  
Numerical Dissipation ◽  
Error Estimator ◽  
Fractional Step ◽  
Weighted Residual Method ◽  
Time Stepping ◽  
Backward Euler ◽  
Galerkin Formulation ◽  
Theta Method

Abstract. In this work, we derive a goal-oriented a posteriori error estimator for the error due to time-discretization of nonlinear parabolic partial differential equations by the fractional step theta method. This time-stepping scheme is assembled by three steps of the general theta method, that also unifies simple schemes like forward and backward Euler as well as the Crank–Nicolson method. Further, by combining three substeps of the theta time-stepping scheme, the fractional step theta time-stepping scheme is derived. It possesses highly desired stability and numerical dissipation properties and is second order accurate. The derived error estimator is based on a Petrov–Galerkin formulation that is up to a numerical quadrature error equivalent to the theta time-stepping scheme. The error estimator is assembled as one weighted residual term given by the dual weighted residual method and one additional residual estimating the Galerkin error between time-stepping scheme and Petrov–Galerkin formulation.

Fractional step two-phase flow lattice Boltzmann model implementation

2009 ◽  
Vol 2009 (06) ◽  
pp. P06014 ◽  
Author(s):  
Pablo M Dupuy ◽  
Maria Fernandino ◽  
Hugo A Jakobsen ◽  
Hallvard F Svendsen
Keyword(s):  
Lattice Boltzmann ◽  
Two Phase Flow ◽  
Lattice Boltzmann Model ◽  
Fractional Step ◽  
Phase Flow ◽  
Two Phase ◽  
Boltzmann Model

Field programmable analogue array implementation of fractional step filters

2010 ◽  
Vol 4 (6) ◽  
pp. 514 ◽  
Author(s):  
T.J. Freeborn ◽  
B. Maundy ◽  
A.S. Elwakil
Keyword(s):  
Fractional Step ◽  
Field Programmable

Numerical investigation of magnetic multiphase flows by the fractional-step-based multiphase lattice Boltzmann method

2020 ◽  
Vol 32 (8) ◽  
pp. 083309 ◽  
Author(s):  
Xiang Li ◽  
Zhi-Qiang Dong ◽  
Peng Yu ◽  
Xiao-Dong Niu ◽  
Lian-Ping Wang ◽  
...  
Keyword(s):  
Lattice Boltzmann Method ◽  
Numerical Investigation ◽  
Lattice Boltzmann ◽  
Multiphase Flows ◽  
Fractional Step ◽  
Boltzmann Method

scholarly journals Implementation of the fractional-step, artificial compressibility with pressure projection (FSAC-PP) method into openfoam for unsteady flows

2021 ◽  
Vol 11 (5) ◽  
pp. 85-91
Author(s):  
Jesús Miguel Sánchez Gil ◽  
Tom-Robin Teschner ◽  
László Könözsy
Keyword(s):  
Time Derivative ◽  
Unsteady Flows ◽  
Time Discretization ◽  
Projection Methods ◽  
Fractional Step ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method ◽  
Start Up ◽  
2D Flow ◽  
Pressure Projection

Commercial and open-source CFD solvers rely mostly on incompressible approximate projection methods to overcome the pressure-velocity decoupling, such as the SIMPLE (Patankar, 1980) or PISO (Issa, 1986) algorithm. Incompressible methods based on the Artificial Compressibility method (Chorin, 1967) lack a mechanism to evolve in time and need to be supplemented by a real time derivative through the dual time scheme. The current study investigates the implementation of the explicit dual time discretization of the Artificial Compressibility method into OpenFOAM and extends on that by applying the dual time scheme to the incompressible FSAC-PP method (Könözsy, 2012). Applied to the Couette 2D flow at Re=100 and Re=1000, results show that for both methods accurate time evolutions of the velocity profiles are presented, where the FSAC-PP methods seemingly produces smoother profiles compared to the AC method, especially during the start-up of the simulation.

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