# Discretization

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 September 6, 2011, 19:29 Discretization #1 Member   ,... Join Date: Apr 2011 Posts: 92 Rep Power: 6 Hi Guys As you all may know, the form of the discretized momentum equation that have been used in OpenFOAM's icoFoam solver is based on the general Scalar Transport equation which has term "del.(U Phi)" and has been discretized in the following way "fvm :: div(phi, U)" My question is that how can I discretize it based on familar N.S. equation form which includes U.del(Phi). I tried "U & (fvc::grad(phi))" but it produced the follwoing error "no match for ‘operator&’ in ‘Foam:perator+(const Foam::tmp >&, const Foam:imensionedField&)" I would appriciate your commments.

September 7, 2011, 17:30
#2
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Daniel P. Combest
Join Date: Mar 2009
Location: St. Louis, USA
Posts: 584
Rep Power: 20
Quote:
 Originally Posted by mahdiiowa Hi Guys As you all may know, the form of the discretized momentum equation that have been used in OpenFOAM's icoFoam solver is based on the general Scalar Transport equation which has term "del.(U Phi)" and has been discretized in the following way "fvm :: div(phi, U)" My question is that how can I discretize it based on familar N.S. equation form which includes U.del(Phi). I tried "U & (fvc::grad(phi))" but it produced the follwoing error "no match for ‘operator&’ in ‘Foam:perator+(const Foam::tmp >&, const Foam:imensionedField&)" I would appriciate your commments.
div(phi,U) is actually your div(UU) term in the NS equation. As you probably know already:

div(UU) = U & grad(U) + U*div(U)

for incompressible flow at a low residual...div(U) goes to zero and

so...div(UU) is considered the conservative form of the equation. hope this helps.

Dan

 September 7, 2011, 17:56 #3 Member   ,... Join Date: Apr 2011 Posts: 92 Rep Power: 6 Daniel Thank you for your help.

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