From: Liang <goeasyon@gm...>  20100321 20:25:30

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 NS 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 firstorder accurate in > time. " > > can I understand it as the coordinator for the CrankNicolson method, > theta =0.5 means the classic CrankNicolson, 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] >  // massmatrix 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] >  // massmatrix 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 >> > > >  > 