[Sereff]

Hi Foamers,

This might be a stupid question, but please bear with me. I am trying to understand pisoFoam source code in mathematical equations, and it is quite confusing. In UEqn.H the matrix of momentum equation for prediction stage is given by, the follwing code, and has a dimention of [m^4/s^2],

fvVectorMatrix UEqn
(
    fvm::ddt(U) + fvm::div(phi, U)
  + MRF.DDt(U)
  + turbulence->divDevReff(U)
 ==
    fvOptions(U)
);

However on the solving step we have, with dimension of [m/s^2]

solve(UEqn == -fvc::grad(p));

It seems that the UEqn is acceleration integrated over a control volume, however fvc::grad(p) on the RHS of solve() returns just acceleration. Could anyone please explain why are the dimensions not matching?


kind regards,

[hjasak]

Easy. p means P/rho, where P Is in Pascal and rho in kg/m^3

[Sereff]

Sir thank you for you reply,

Yes, I understant that "p" in pisoFoam is dynamic pressure which means Pascal over density, which is why p has dimension of [m^2/s^2] and fvc::grad(p) has dimension of [m/s^2]. What confuses me is that in the following line,

solve(UEqn == -fvc::grad(p));

term UEqn on the lhs has different dimension than the rhs which is -fvc::grad(p). It seems that fv<Type>Matrix class is integrated over control volume whereas the pressure gradient term isn't.


kind regards,

[tas38]

Originally Posted by Sereff

Sir thank you for you reply,

Yes, I understant that "p" in pisoFoam is dynamic pressure which means Pascal over density, which is why p has dimension of [m^2/s^2] and fvc::grad(p) has dimension of [m/s^2]. What confuses me is that in the following line,

solve(UEqn == -fvc::grad(p));

term UEqn on the lhs has different dimension than the rhs which is -fvc::grad(p). It seems that fv<Type>Matrix class is integrated over control volume whereas the pressure gradient term isn't.


kind regards,

It is unclear how you came to the conclusion that the lhs, i.e. the UEqn has units of [m^4/s^2]. It has units of [m/s^2] consistent with the pressure term to which it is equated. This units are most obvious in looking at the transient term... fvm::ddt(U). This is the first temporal derivative of the velocity field w.r.t time and has units 1/s * (m/s) = m/s^2.

[Sereff]

Hi tas38

thank you for you reply. I agree with you that UEqn is supposed to have dimension of [m/s^2]. However, I came to this conclusion because I included the following line after UEqn is constructed.

Info << "dimension of UEqn is: " << UEqn.dimensions() << endl;

and the terminal prints out

dimension of UEqn is: [0 4 -2 0 0 0 0]

kind regards,

[hjasak]

Yes - at the point of solution, the equation is multiplied by the volume - as will be the case with the rhs. This is "integrated over the control volume"

Hrv