Solve NS on a referece domain (convection terms)

General Discussion
1

Hi everyone,

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?

Thank you!

Best wishes
Dongwei

2

Sorry I here rephrase my question here. I find out the problem why the convective term doesn’t work: the characteristic approximation u(x-u(x)*delta_t) has an independent x, which also needs a transformation as well. However the ‘convect’ term can only modify delta_t, u(x), how could I modify the ‘x’ in the code?