CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

Fifth order anti diffusive scheme for 1D hyperbolic heat transfer

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   November 3, 2010, 05:48
Default Fifth order anti diffusive scheme for 1D hyperbolic heat transfer
New Member
Join Date: Oct 2010
Posts: 1
Rep Power: 0
areffallah is on a distinguished road

Recently, Wensheng Shen et al published a paper as "anti-diffusive methods for hyperbolic heat transfer" that consider WENO as one of the anti-diffusive methods.

Link to download this paper:

I am trying to review this paper and want to solve 1D hyperbolic heat transfer equation using fifth-order WENO. I have studied some papers about applying WENO, as listed below, But they couldn't solve my problem.
[1] A finite volume high order ENO scheme for two dimensional hyperbolic systems. By: Casper and Atkins
[2] Efficient Implementation of Weighted ENO Schemes. By: Jiang and Shu
[3] Essentially non_oscillatory and weighted essentially non_oscillatory schemes for hyperbolic conservation laws. By: Chi_Wang Shu
From This Paper I mean “anti-diffusive methods for hyperbolic heat transfer”.

I have two basic problems:
Considering This Paper, the corresponding mathematical model consists of the following two equations:

Where the following equation of characteristic variables will be obtained:

1) I want to apply boundary and initial conditions as below:
The dimensionless temperature of the slab is kept at T = 0 initially, and the temperature at the left boundary is increased to T = 1 at time t > 0. Two types boundary conditions are considered at the right end of the slab, given temperature (T = 0) and zero heat flux (q = 0).
Main problem is: How should I apply boundary and initial conditions. Because I can only specify either T or q but not both at boundaries. For initial conditions, I have only T and for left and right boundary conditions I have only one of T or q, therefore what should I do for another variable value? T and q or W1 and W2.
W1 = 0.5*(T + q) and W2 = 0.5*(T - q)

2) As explained in procedure 2.9. [3], I got the procedure for solving this problem as below:
At each fixed X(i+1/2)
1) Compute the right eigenvectors the left eigenvectors and the eigenvalues.
2) Using left eigenvectors, transform [T q] vector to [W1 W2].
3) Perform weno reconstruction procedure on W1 and W2 to obtain W1(i+1/2) and W2(i+1/2).
4) Transform back from characteristic to physical domain using right eigenvectors:
[T(i+1/2) q(i+1/2)] = R*[W1(i+1/2) W2(i+1/2)]
Where : R = right eigenvectors and Inv(R) = left eigenvectors.
5) Form the scheme below:


And I consider two equations separately to solve (in this step I mean).

Is this procedure True? If not, please tell me what is my fault here.

Last edited by areffallah; November 3, 2010 at 06:04.
areffallah is offline   Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
Thin Wall Heat Transfer BC for rhoSimpleFoam swahono OpenFOAM Running, Solving & CFD 12 October 4, 2013 11:49
MRF and Heat transfer calculation Susan YU FLUENT 0 June 2, 2010 08:46
Heat transfer problem seojaho CFX 6 May 6, 2010 00:32
flow/heat transfer through heat sink (with fins)? Pei-Ying Hsieh Main CFD Forum 1 January 26, 2008 07:33
Convective Heat Transfer - Heat Exchanger Mark CFX 6 November 15, 2004 16:55

All times are GMT -4. The time now is 02:39.