An Example of Transient Laminar Countercurrent Flow

1987 ◽  
Vol 109 (3) ◽  
pp. 262-267 ◽  
Author(s):  
I. K. Tsanis ◽  
H. J. Leutheusser
Keyword(s):  
Experimental Study ◽  
Finite Difference ◽  
Pressure Gradient ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Time Dependent ◽  
Countercurrent Flow ◽  
Governing Equations ◽  
Numerical Predictions ◽  
Explicit Finite Difference

This paper presents a numerical and experimental study of transient laminar countercurrent flow in which the pressure gradient is time-dependent. An explicit finite-difference scheme is used to solve numerically the governing equations. Experimental results are obtained with a new kind of apparatus and are found to verify the numerical predictions.

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.

A NUMERICAL METHOD FOR 1D TIME-DEPENDENT SCHRÖDINGER EQUATION USING RADIAL BASIS FUNCTIONS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341010 ◽  
Author(s):  
TONGSONG JIANG ◽  
ZHAOLIN JIANG ◽  
JOSEPH KOLIBAL
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Radial Basis Functions ◽  
Finite Difference Scheme ◽  
Good Accuracy ◽  
Basis Functions ◽  
Time Dependent ◽  
Numerical Examples ◽  
Radial Basis

This paper proposes a new numerical method to solve the 1D time-dependent Schrödinger equations based on the finite difference scheme by means of multiquadrics (MQ) and inverse multiquadrics (IMQ) radial basis functions. The numerical examples are given to confirm the good accuracy of the proposed methods.

scholarly journals A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiaojie Li ◽  
Zhoushun Zheng ◽  
Shuang Wang ◽  
Jiankang Liu
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
One Dimensional ◽  
Explicit Finite Difference ◽  
Boltzmann Method

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. TheL2, L∞and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.

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