Dear Libmesher,
I tried to write an incompressible Naiver-Stokes solver based Libmesh.
Following features includes:
coupled pressure-velocity method
TransientNonlinearImplicitSystem used with
compute_jacobian(..) and compute_residual(..) run separatedly
Lid-driven cavity case for initial tests
BDF1 time marching
QUAD4 element,
vel_order=2, pres-order=1, both LAGRANGE elements
Pressure pinned at node_id=0
I tried DirichletBoundary class to impose the velocity BC, the code runs OK.
Now the problem is :
I coded myself the common penalty method for term
\int_{\Gamma_D}dt*\gamma/h*u*v,
and applied the forms in boundary integral part of jacobian function
Jxw_face[qp_face]*dt*penalty/h_elem*phi_face_[j][qp_face] *phi_face_[i][qp_face]
and
Jxw_face[qp_face]*dt*penalty/h_elem*phi_face_[i][qp_face] *(u-u_bc)
at counterparts of residual function
the results show the boundary velocity not fully applied ,esp. at the side
walls near
the two top corners. Actually there are nonzero u normal to the local side wall.
So I wonder anybody here will kindly show me some hints.
Furthermore, I tried applied the weak Dirichlet conditions by add futher
boundary integrals like
dt\int_{\partial\Omega} (-\mu\nabla \vec{ u}+pII)\cdot \vec{n}\cdot\vec{v} +
dt\int_{\partial\Omega} (-\mu\nabla \vec{ v}+qII)\cdot \vec{n}\cdot\vec{u}
at left and
dt\int_{\partial\Omega} (-\mu\nabla \vec{ v}+qII)\cdot \vec{n}\cdot\vec{u_bc}
at right hand side
But the case is even worse.
I also attached the code here, and I am looking forward to any suggestions.
Many thanks.
Zhenyu------------------------------------------------------------------------------
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