I am trying to solve 2D Navier stokes equations on a reference domain through a mapping function T. It works well with all the terms in the weak formulations (by multiplying deformation gradient F and jacobian of F, etc) except the convection terms.
I intend to use the ‘convect’ operator which will be easy to implement instead of changing it to a newton approximation. However, it seems that the ‘convect’ approximation u^n dot X^n doesn’t work if I just by multiplying it with a Jacobian of F. For example,
int2d(Th)(convect([uold,vold], -dt, uold)*uh/dt*J(FX,FY))
I am wondering if you have any suggestions for this kind of situation?