Hi developers and users,
Seems I sent to wrong address last email, sorry for that.
I tried to expand the tensor form of N-S to the general PDEs as shown in
the attached picture, is this same to the governing equation that ex13
used? please correct me if i am wrong. Is any book introduce deriving
the nonlinear PDEs to the element equations? nonlinear terms in the
equation bother me a lot, I don't know how to derive their weak forms.
Another question is about the constant \theta in the ex13, which is
equal to one in the equation, the description goes like:
"Find out what the timestep size parameter is from the system, and the
value of theta for the theta method. We use implicit Euler (theta=1) for
this simulation even though it is only first-order accurate in time. "
can I understand it as the coordinator for the Crank-Nicolson method,
theta =0.5 means the classic Crank-Nicolson, theta = 0/1 means pure
forward/backward Euler method? There are no \mu and \rho in the assemble
equation, so both parameters are evaluated one?
Many thanks !
Liang
===============copy from ex13 ==================
for (unsigned int i=0; i<n_u_dofs; i++)
{
Fu(i) += JxW[qp]*(u_old*phi[i][qp] - // mass-matrix term
(1.-theta)*dt*(U_old*grad_u_old)*phi[i][qp] + // convection term
(1.-theta)*dt*p_old*dphi[i][qp](0) -
// pressure term on rhs
(1.-theta)*dt*(grad_u_old*dphi[i][qp]) +
// diffusion term on rhs
theta*dt*(U*grad_u)*phi[i][qp]);
// Newton term
Fv(i) += JxW[qp]*(v_old*phi[i][qp] -
// mass-matrix term
(1.-theta)*dt*(U_old*grad_v_old)*phi[i][qp] +
// convection term
(1.-theta)*dt*p_old*dphi[i][qp](1) -
// pressure term on rhs
(1.-theta)*dt*(grad_v_old*dphi[i][qp]) +
// diffusion term on rhs
theta*dt*(U*grad_v)*phi[i][qp]);
// Newton term
==========================================================================================
Liang wrote:
Hi developers and users,
I am looking at the nonlinear system of equations and want to borrow
some ideas from ex13, while the finite element equations in the
assemble function make me a little confused because I am not familiar
with the Stokes' equation, does any fluids expert might send me a
image format PDEs of that system? or give a link which is exact same
to the equations in ex13. I have looked at the Wikipedia but not make
sure which equations are belong to the case of ex13. Thanks a lot!
Liang
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