# Alternative formulation of momentum equation

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 June 30, 2013, 13:05 Alternative formulation of momentum equation #1 New Member   Thomas K. Join Date: Jan 2011 Posts: 15 Rep Power: 7 Is it possible to use Code: ```fvm::div(phi, U) - fvc::div(tau)``` instead of Code: ```fvm::div(phi, U) - fvm::laplacian(fluid.nu(), U) - (fvc::grad(U) & fvc::grad(fluid.nu()))``` which is the standard formulation in non-Newtonian, steady-state solvers? I would like to modify the stress tensor before the momentum equation is solved (i.e. include the elongational viscosity in normal direction). For the energy equation this is already working: Code: ```// calculate stress tensor volTensorField gradU = fvc::grad(U); volTensorField tau = fluid.nu() * (gradU + gradU.T()); tau.component(tensor::XX) = tau.component(tensor::XX) / max(dimensionedScalar ("VSMALL", dimensionSet(0,2,-1,0,0,0,0), VSMALL), fluid.nu()) * elongFluid.nuElong(); tau.component(tensor::YY) = tau.component(tensor::YY) / max(dimensionedScalar ("VSMALL", dimensionSet(0,2,-1,0,0,0,0), VSMALL), fluid.nu()) * elongFluid.nuElong(); tau.component(tensor::ZZ) = tau.component(tensor::ZZ) / max(dimensionedScalar ("VSMALL", dimensionSet(0,2,-1,0,0,0,0), VSMALL), fluid.nu()) * elongFluid.nuElong(); // energy equation tmp TEqn ( fvm::div(phi, T) - fvm::laplacian(alpha, T) - 1.0/Cp * (tau && gradU) ); TEqn().relax(); solve(TEqn());``` However, when I use Gauss linear scheme for div((nu*(grad(U)+grad(U).T()))) the time step continuity error gets very high after only one step. Does anyone have an idea how to solve the problem? Thank you in advance!

 July 1, 2013, 12:07 Stress tensor #2 New Member   Thomas K. Join Date: Jan 2011 Posts: 15 Rep Power: 7 Even if I use Code: ```volTensorField gradU = fvc::grad(U); volTensorField tau = fluid.nu() * (gradU + gradU.T());``` without the elongational viscosity and then for the momentum equation Code: ```fvm::div(phi, U) - fvc::div(tau)``` it is not working (time step continuity error very high). How can I tell OpenFOAM to solve Code: `fvc::div(tau)` correctly?

 July 1, 2013, 13:04 Explicit (fvc) and implicit derivative (fvm) #3 New Member   Thomas K. Join Date: Jan 2011 Posts: 15 Rep Power: 7 Can it be due to the use of an explicit (fvc) instead of an implicit derivative (fvm)? Do I have to use an transient solver or should it also work for a steady-state solver like simpleFoam?

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