Numerical Study of an Unsteady Confined Jet. Application to Crossflow Filtration

1996 ◽  
Vol 118 (1) ◽  
pp. 74-80
Author(s):  
C. Maranges ◽  
G. Arroyo ◽  
C. Fonade ◽  
J. L. Estivalezes
Keyword(s):  
Numerical Calculation ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Numerical Study ◽  
Main Flow ◽  
Permeate Flux ◽  
Crossflow Filtration ◽  
Bentonite Suspension ◽  
Jet Velocities

This paper deals with the influence of a new flow unsteadiness on the permeate flux in crossflow filtration. A pneumatically controlled valve generates intermittent jets from the main flow, leading to the formation of large vortices moving downstream along the tubular membrane. A numerical calculation of this flow is achieved using a finite difference scheme. Influences of tube diameter and jet velocities are discussed. Application of this technique is carried out by filtering a bentonite suspension through an ultrafiltration membrane.

scholarly journals A Parallel Second Order Cartesian Method for Elliptic Interface Problems

2012 ◽  
Vol 12 (5) ◽  
pp. 1562-1587 ◽  
Author(s):  
Marco Cisternino ◽  
Lisl Weynans
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Numerical Study ◽  
Elliptic Problems ◽  
Two Dimensions ◽  
Transmission Conditions ◽  
Second Order ◽  
Interface Problems ◽  
Elliptic Interface Problems

AbstractWe present a parallel Cartesian method to solve elliptic problems with complex immersed interfaces. This method is based on a finite-difference scheme and is second-order accurate in the whole domain. The originality of the method lies in the use of additional unknowns located on the interface, allowing to express straightforwardly the interface transmission conditions. We describe the method and the details of its parallelization performed with the PETSc library. Then we present numerical validations in two dimensions, assorted with comparisons to other related methods, and a numerical study of the parallelized method.

NUMERICAL STUDY OF THE WAVE INSTABILITY PROBLEM WITH THE EFFECT OF THE TRANSVERSE VELOCITY COMPONENT TEX SYSTEM

2001 ◽  
Vol 09 (03) ◽  
pp. 1055-1065
Author(s):  
B. S. ATTILI
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Velocity Component ◽  
Finite Difference Scheme ◽  
Numerical Study ◽  
Transverse Velocity ◽  
Numerical Results ◽  
Wave Instability ◽  
Transverse Velocity Component ◽  
Instability Problem

We will numerically investigate the wave instability problem with the effect of the transverse velocity component. An accurate and easy to program finite difference scheme will be developed for this purpose. The eigenfunctions will be normalized and computed simultaneously with the eigenvectors. Numerical results will also be presented.

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

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