volumetric conservation equation in PHOENICS code
 

In case of the two methods HOL and SEM implemented in PHOENICS code for simulating free surface flows, the continuity equation was formulated in term of volumetric conservation as

D(Ln(RHO))/Dt+du/dx+dv/dy+dw/dz=0.

REF: Free surface flow and heat transfer in cavities: the sea algorithm, K.A Percilious & al 1995 ,Numerical heat transfer Part B, 27:487-507, 1995

1- what are the steps followed to discretise this equation by finite volume method ?

2- What is the discretized form of this equation ?

Thank you.

Re: volumetric conservation equation in PHOENICS c
 

The details of HOL and SEM methods for dealing with free surface flows in PHOENICS are fully described in related documentation available for on-line ordering in CHAM's cfdSHOP at http://www.simuserve.com/cfd-shop/:

1 HOL at http://www.simuserve.com/cfd-shop/tr307.htm 2 SEM at http://www.simuserve.com/cfd-shop/cfd88-4.htm

Best regards

Sergei Zhubrin

Re: volumetric conservation equation in PHOENICS c
 

I know the two methods and I use them for applications

- 1 HOL at http://www.simuserve.com/cfd-shop/tr307.htm - 2 SEM at http://www.simuserve.com/cfd-shop/cfd88-4.htm

but there isn't more on the continuity equation formulated in term of volumetric conservation as

D(Ln(RHO))/Dt+du/dx+dv/dy+dw/dz=0.

The only other reference is: REF: Free surface flow and heat transfer in cavities: the sea algorithm, K.A Percilious & al 1995 ,Numerical heat transfer Part B, 27:487-507, 1995

Re: volumetric conservation equation in PHOENICS c
 

Single-Phase Volumetric-Continuity Equation:

The volumetric continuity equation is an option which is activated, for HOL and SEM methods, in preference to mass continuity.

The equation is:

AeUe-AwUw+AnVn-AsVs+AhWh-AlWl=Sp/RHOp

It is assumed that the volume of the cell remains constant in time and

Sp stands for source of mass for the cell; RHOp is in-cell density; Ue,Uw etc are the cell face velocity components; Ae, Aw etc are the cell face areas.

The full account of all principal finite-volume equations embodied in PHOENICS can be found in TR99 at http://www.simuserve.com/cfd-shop/tr99sab.htm.

Sergei Zhubrin

Re: volumetric conservation equation in PHOENICS c
 

Thank you Sergei for your help,

My problem is in the term : D(Ln(RHO))/Dt I don't know where and how it appears in the discretised equation of continuity AeUe-AwUw+AnVn-AsVs+AhWh-AlWl=Sp/RHOp.