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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 >> > > >  > 
From: Liang <goeasyon@gm...>  20100321 03:17:00

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 > 