Hi, I am trying to create my own finite element code based upon the semi-implicit characteristic based split scheme for incompressible viscous flow. Now my problem is that in the last step the velocities are determined by means of an explicit equation. Could someone please explain to me how exactly I am meant to enforce the no-slip boundary conditions in this step as there are no simultaneous equations to solve.

Thanks in advance,

Chris

If you're using a lumped mass formulation, your solution will look like

u[ i ] = rhs[ i ]/M[ i ];

where M is your (diagonal) lumped mass matrix. So, you could just make

M[ i ] = 1.;

and

rhs[ i ] = wall_velocity;

where "i" denotes the nodes where the no-slip condition is applied.

I'm working with FEM too. What kind of formulation do you use?

regards

Márcio Ricardo

Yea, thanks that was what I thaught. However, what I am working on is trying to apply the Scaled Boundary Finite Element Method to incompressible viscous flow. This method is a boundary method where you have an analytical solution in the radial direction, and apply finite element techniques in the tangential direction. So what my problem is, is that for the explicit velocity correction equation, the RHS is a polynomial, not values at discreet points so I cannot see a way of enforcing the no slip boundary conditions at that step. Any suggestions? Maybe if there was an implicit velocity correction it would be straight forward.

Anyway, thanks

Chris