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Question in definition of terms in solve

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Old   March 19, 2009, 17:02
Question Question in definition of terms in solve
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Antonio Martins
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Dear Foamers,

I am trying to model a problem that involves solving an equation in terms of the stress tensor that includes the convected derivative of the stress tensor and the deformation rate tensor, in the form

(convected derivative of the stress Tensor)+K*deformation rate & stress tensor)+K*(stress tensor & deformation rate)=viscosity*deformation rate

where & means inner product. The convected derivative is a combination of four terms, in the form

ddt(stress tensor)+gradient (velocity & stress tensor) - stress tensor & gradient (velocity) - gradient (transpose of the velocity) & stress tensor

When I represent this equation in OpenFoam, i only consider implicitly two terms:
- ddt (stress tensor): fvc::ddt(stresstensor)
- gradient (velocity & stress tensor)= div(phi,stresstensor)

The remaining terms are not discretized neither explicitly or implicitly. The final expression is in form

solve (
fvc::ddt(stresstensor) + div(phi,stresstensor) = viscosity*Deformation rate + stresstensor & Deformation rate + transpose(deformation rate) & stresstensor-K*(deformation rate & stress tensor) - K*(stress tensor & deformation rate)
);

In the right side none of the terms is written in the form fvc::.. Only the deformation rate involves the calculation of the gradient of the velocity field, in the form fvc::grad(velocity). Is this enough to ensure that the remaining terms are represented also as fvc::?

The expression that I wrote compiles but is it O.K? Should I discretize, using perhaps fvc, the terms in the right side? I have tried to do that directly but with no sucess. I got errors of invalid operation or problems in the units. However, in all the solvers that I analysed when solving equations the terms in the right side involve allways fvc.

Can anyone help me out?

Titio

A possible solution involves the definition of
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