Boundary conditions specification

[SHAIMA MAGDALINE DSOUZA]

Can we apply delP=0 boundary conditions in simvascular?
Also can we specify the dirchlet and the neuman conditions on the weak form of Navier Stokes?

[Weiguang Yang]

For delP=0, do you mean you want to impose dP/dx=0, dP/dy=0, dP/dz=0? To my knowledge, simvascular doesn't have a way to impose this BC. Can you clarify physically what you want to impose?
Simvascular solves Navier-Stokes using finite element methods. The NS eqns are written in a weak form and solved. The boundary conditions (Dirchlet and Neumann) appear in the weak form of the NS eqns.

[SHAIMA MAGDALINE DSOUZA]

I want to specify the outlet boundary condition by setting zero pressure gradient.
Can we have the access to the variational form of the Navier Stokes equation? So that one can specify the required boundary condition directly?

[Weiguang Yang]

In the conventional Neumann boundary condition for the N-S equation, we specify T \cdot n=h(x,t) on the Neumann boundary \Gamma_h , where T=-pI+\mu( \nabla u +\nabla u^T). In the weak form, integrating by parts generates a term for \Gamma_h, which is -\int_{\Gamma_h}w \cdot h d\Gamma. When one wants to impose a pressure boundary condition for an outlet, one can specify \mathbf{h}(\mathbf{u},p,\mathbf{x},t)=-P(t)\mathbf{n}, where P(t) is a user defined pressure function that can be a constant or based on a lumped parameter model. The pressure is assumed to be the same everywhere on the outlet face. Thus the pressure gradient on the outlet plane is 0 but the gradient in the normal direction is not enforced. I am not sure if it is possible to impose the gradient in the normal direction to be 0 because the boundary condition is supposed to be lower order than the differential equation itself. Hope these help.