# Source terms linearisation

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 February 10, 2006, 11:01 Source terms linearisation #1 Mehdi BEN HAJ Guest   Posts: n/a Hi every body, Is it a paper or a document for the linearisation (patch & coval) of complex source terms in PHOENICS equations. Thanks.

 February 10, 2006, 13:52 Re: Source terms linearisation #2 Mick Guest   Posts: n/a Document, papers books. Since Spalding inventing this formulation years ago everyone uses it. Book: Patankar and Spalding "Numerical Heat Transfer" Lecture : E:\phoenics\d_polis\d_lecs\GENERAL\BCOND.HTM

 February 13, 2006, 12:13 Re: Source terms linearisation #3 Mehdi BEN HAJ Guest   Posts: n/a Yes, but I need some special examples. I want to linearise a source term for a water wave generation sourec which contains third order of stokes expression. Can I send expressions (JPG Format) on PHOENICS User Forum or to PHOENICS experts. Seriously yours.

 February 16, 2006, 05:14 Re: Source terms linearisation #4 Mick Guest   Posts: n/a Yes, the text book, "Numerical Heat Transfer" by Patankar and Spalding is a great book for understanding this concept, its easy to read and was the text that made the whole thing understandable to everyone. In Polis, (the PHOENICS encyclopedia), there is a lecture regarding the mathematics behind CFD finite Volume, this has a boundary condition section: Polis.htm \phoenics\d_polis\d_lecs\GENERAL\BCOND.HTM Now quickly, 'boundary conditions' and 'source terms' are handled the same way in CFD codes. They need to be set as BC = T.Co(Val-Phi) T is a geometric multiplier usually area or volume Co stands for coefficient and Val for Value and PHI is the value of the solved variable at the cell in question. So as an example : ---------------- Take a radiation source sigma.emmisivity(Tv^4-Tp^4) sigma = stephan boltzman emmisivity(e) = emmissivity Tv^4 is 'receiving temperature' i.e. that responsible for heating/cooling Tp^4 is temperature in the cell, that being solved for. step 1/ work out the units of this source = Watts/m^2, so the source needs to have a geometric multiplier of AREA type to make it into WATTS for the energy equation. step2/ Rearrange source in linear form if possible i.e. T.Co(Val-Phi)form --> (Tv^4-Tp^4)= (Tv+Tp)(Tv^2+Tp^2)[Tv-Tp] step3/ Source = Area.sigma.e.(Tv+Tp)(Tv^2+Tp^2)[Tv-Tp] So T=Area ; Co = sigma.e.(Tv+Tp)(Tv^2+Tp^2); Val=Tv step4/ apply in PHOENICS as PATCH and COVAL, through sources panel in menu, or inform or by hand, many types of sources are automatically handled by PHOENICS. so PATCH -> defines the region over which this source will exist COVAL -> defines the source step5/ IN this case the source will be , (assuming north facing wall) : Patch(RADIAT1,NORTH,1,nx,ny,ny,1,nz,1,lstep) Coval(RADIAT,TEM1,sigma.e.(Tv+Tp)(Tv^2+Tp^2),Tv) This should give a nett source in WATTS at the bottom of the RESULT file for you to check. Write down your source and see if you can linearise it, but remember some sources can not be linearised, and certainly if it does not contain the variable for which you are solving. In these cases we just lump the whole source in using Co=FIXFLU and VAL='the SOURCE', with an appropriate geometric multiplier to give the correct units for the equation. For momentum = Newtons For Temperature = Watts Look at the lectures and read the Patankar/Spalding book.

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