Hi developers and users,
I have my nonlinear problem done, so please forget my previous questions
on ex13 although the ex13 still doesn't convince me in the Newton term
input. Thanks!
Liang
Liang wrote:
> 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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