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.

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

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

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

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.