An Implicit Fractional-Step Method for Efficient Transient Simulation of Incompressible Flows

2005 ◽  
Author(s):  
Sung-Eun Kim ◽  
Boris Makarov
Keyword(s):  
Incompressible Flows ◽  
Transient Simulation ◽  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method

scholarly journals A comparative study of fractional step method in its quasi-implicit, semi-implicit and fully-explicit forms for incompressible flows

2016 ◽  
Vol 26 (3/4) ◽  
pp. 595-623 ◽  
Author(s):  
Rhodri LT Bevan ◽  
Etienne Boileau ◽  
Raoul van Loon ◽  
R.W. Lewis ◽  
P Nithiarasu
Keyword(s):  
Incompressible Flows ◽  
Transient Flow ◽  
Stokes Equations ◽  
Second Order ◽  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method ◽  
Content Type ◽  
Time Stepping ◽  
Implicit Form

Purpose – The purpose of this paper is to describe and analyse a class of finite element fractional step methods for solving the incompressible Navier-Stokes equations. The objective is not to reproduce the extensive contributions on the subject, but to report on long-term experience with and provide a unified overview of a particular approach: the characteristic-based split method. Three procedures, the semi-implicit, quasi-implicit and fully explicit, are studied and compared. Design/methodology/approach – This work provides a thorough assessment of the accuracy and efficiency of these schemes, both for a first and second order pressure split. Findings – In transient problems, the quasi-implicit form significantly outperforms the fully explicit approach. The second order (pressure) fractional step method displays significant convergence and accuracy benefits when the quasi-implicit projection method is employed. The fully explicit method, utilising artificial compressibility and a pseudo time stepping procedure, requires no second order fractional split to achieve second order or higher accuracy. While the fully explicit form is efficient for steady state problems, due to its ability to handle local time stepping, the quasi-implicit is the best choice for transient flow calculations with time independent boundary conditions. The semi-implicit form, with its stability restrictions, is the least favoured of all the three forms for incompressible flow calculations. Originality/value – A comprehensive comparison between three versions of the CBS method is provided for the first time.

scholarly journals Comparison of Efficient Explicit Schemes for Shallow-Water Equations—Characteristics-Based Fractional-Step Method and Multimoment Eulerian Scheme

2007 ◽  
Vol 46 (3) ◽  
pp. 388-395 ◽  
Author(s):  
Yohsuke Imai ◽  
Takayuki Aoki ◽  
Magdi Shoucri
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Parallel Architecture ◽  
Fractional Step ◽  
Processing Unit ◽  
Step Method ◽  
Fractional Step Method ◽  
Central Processing ◽  
Explicit Schemes ◽  
Coarse Meshes

Abstract Two explicit schemes for the numerical solution of the shallow-water equations are examined. The directional-splitting fractional-step method permits relatively large time steps without an iterative process by using a treatment based on the characteristics of the governing equations. The interpolated differential operator (IDO) scheme has fourth-order accuracy in time and space by using a Hermite interpolation function covering local domains, and accurate results are obtained with coarse meshes. It is shown that the two schemes are very efficient for hydrostatic meteorological models from the viewpoints of numerical accuracy and central processing unit time, and the fact that they are explicit makes them suitable for computers with parallel architecture.

The fully discrete fractional-step method for the Oldroyd model

2018 ◽  
Vol 129 ◽  
pp. 83-103 ◽  
Author(s):  
Tong Zhang ◽  
Yanxia Qian ◽  
JinYun Yuan
Keyword(s):  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method ◽  
Oldroyd Model ◽  
Fully Discrete
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