Hello everyone, I’m trying to solve a steady flow with the Boussinesq equation. I have three equations with no nonlinear terms, but I still have this error: ‘End of String could not be found.’ Thank you so much for your help.
boussinesq.edp (1.8 KB)
Hello, here is your code with several modifications. I hope it will help you.
boussinesq_eqn.edp (1.9 KB)
If you give me your schemes ( i.e, set of equations that you implemented here) and exact solution, i can check order of convergences.
Thanks in advance!.
thank you so much for you answer ,my equations are basically ΔP + a ∂T/∂y = 0
2. μv = K(∇P + aTe_z)
3. v·∇T = ∇·(D∇T)
and in the weak form i get
4. ∫_Ω ∇P·∇Q dΩ = a∫_Ω (∂_y T)Q dΩ
5. velocity :
v_x = (K/μ) ∂P/∂x
v_y = (K/μ) (∂P/∂y + aT)
6. then temperature:
∫_Ω v·∇T ϕ dΩ + ∫_Ω D∇T·∇ϕ dΩ = 0. and thanks again for your help
Can you please share it’s details reference (that is paper)??.
i’m sorry,i just derived them by myself
Actually, i need exact solutions to check order of convergence. I asked for that reason. It is fine you give me exact solution and source function.
oh yeah i know,but there is no exact solution for this probleme(as much as i know),but i think there is a problem in the converging,because T never converge with my dirichlet conditions