Having problem with Discrete Ordinates Mathod (DOM). I want to discuss with someone who are doing the same. Can you please reply me then I will write details.

Regards Manosh

Hi Manosh,

You are invited to share your problems with me, either here or by e-mail.

Rami

What's the problem?

Nuray Kayakol

Dear Rami/Nuray

The problem is having 'Negative Intencities'! How do you reduce negative intencities in (DOM)?

Manosh

Hi,

This is very well-known problem of DOM when cell-centered differencing scheme is used. It appears when the walls are very hot compared to gas for furnace applications. The common practice is to use a negative intensity fix-up procedure (use of up-wind differencing scheme )for the cells having negative intensity. In your coding you need to change the value of alpha (averaging coeff. which is 0.5 for cell-centered diff. scheme) from 0.5 to 1.0 when negative intensity is encountered.

Here is a simple example; Consider a control volume next to a hot wall. (Intensity values are completely unrealistic for the sake of simple calculation)

I_bw(wall intensity)=11 I_p(cell-centered intensity)=5. I_bw is known from wall Temp. I_p is calculated from recurrence of DOM equation. I_cf(cell-faced intensity leaving the control volume)=?

I_p=(I_bw+I_cf)/2

This equation tells you that the intensity at the centre is the arithmatic average of cell-faced intencities. =(11-1)/2=5 Therofore I_cf=-1 which is unrealistic.

Then accept I_cf=I_p

Read following paper for further information

N. Selçuk and N. Kayakol, Evaluation of Angular Quadrature and Spatial Differencing Schemes for Discrete Ordinates Method in Rectangular Furnaces, Proceeding of 31st National Heat Transfer Conference, ASME HDT-Vol.325, 3, 151-158, Houston, Texas (1996).

Best Regards N. Kayakol

Dear Manosh,

In the method we developed (Fiterman, A., Ben-Zvi, R., and Kribus, A., DOTS: Pseudo-Time-Stepping solution of the Discrete-Ordinate Equations, Numerical Heat Transfer B 25, 163-183, 1999) you are guaranteed that negative intensities are impossible if non-negative intensities are used as the initial guess. For details and proof please refer to the Appendix of the above reference.

Besides that, this method is very efficient due to its explicitness and use of mult-grid. Recently we demonstrated (in a paper accepted by Numerical Heat Transfer B, but not published yet) it also has high parallel efficiency.

Rami