scholarly journals Unified fractional step method for Lagrangian analysis of quasi-incompressible fluid and nonlinear structure interaction using the PFEM

2016 ◽  
Vol 109 (9) ◽  
pp. 1219-1236 ◽  
Author(s):  
Minjie Zhu ◽  
Michael H. Scott
Keyword(s):  
Incompressible Fluid ◽  
Fractional Step ◽  
Lagrangian Analysis ◽  
Step Method ◽  
Fractional Step Method ◽  
Nonlinear Structure ◽  
Structure Interaction

scholarly journals A SEMI-IMPLICIT APPROACH FOR FLUID-STRUCTURE INTERACTION BASED ON AN ALGEBRAIC FRACTIONAL STEP METHOD

2007 ◽  
Vol 17 (06) ◽  
pp. 957-983 ◽  
Author(s):  
A. QUAINI ◽  
A. QUARTERONI
Keyword(s):  
Fluid Structure Interaction ◽  
Mass Effect ◽  
Added Mass ◽  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Wide Range ◽  
Structure Problem

We address the numerical simulation of fluid-structure interaction problems characterized by a strong added-mass effect. We propose a semi-implicit coupling scheme based on an algebraic fractional-step method. The basic idea of a semi-implicit scheme consists in coupling implicitly the added-mass effect, while the other terms (dissipation, convection and geometrical nonlinearities) are treated explicitly. Thanks to this kind of explicit–implicit splitting, computational costs can be reduced (in comparison to fully implicit coupling algorithms) and the scheme remains stable for a wide range of discretization parameters. In this paper we derive this kind of splitting from the algebraic formulation of the coupled fluid-structure problem (after finite-element space discretization). From our knowledge, it is the first time that algebraic fractional step methods, used thus far only for fluid problems in computational domains with rigid boundaries, are applied to fluid-structure problems. In particular, for the specific semi-implicit method presented in this work, we adapt the Yosida scheme to the case of a coupled fluid-structure problem. This scheme relies on an approximate LU block factorization of the matrix obtained after the discretization in time and space of the fluid-structure system. We analyze the numerical performances of this scheme on 2D fluid-structure simulations performed with a simple 1D structure model.

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

Numerical Study of Density-Currents Using the Non-Staggered Grid Fractional-Step-Method

2000 ◽  
Author(s):  
J. Rafael Pacheco ◽  
Arturo Pacheco-Vega ◽  
Sigfrido Pacheco-Vega
Keyword(s):  
Numerical Study ◽  
Density Variation ◽  
Staggered Grid ◽  
Mapping Technique ◽  
Fractional Step ◽  
Density Currents ◽  
Step Method ◽  
Fractional Step Method ◽  
New Approach ◽  
Flow Equations

Abstract A new approach for the solution of time-dependent calculations of buoyancy driven currents is presented. This method employs the idea that density variation can be pursued by using markers distributed in the flow field. The analysis based on the finite difference technique with the non-staggered grid fractional step method is used to solve the flow equations written in terms of primitive variables. The physical domain is transformed to a rectangle by means of a numerical mapping technique. The problems analyzed include two-fluid flow in a tank with sloping bottom and colliding density currents. The numerical experiments performed show that this approach is efficient and robust.

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