Dear all,
I am trying to couple a simulation with two codes, say code A and code B (different discretizations). For code A we solve simply the conduction equation (solid), while in B we solve the NS + temperature convection/diffusion (fluid).
The coupling is explicit, while the time scheme for each code is implicit.
at each iteration, code A gives code B the heat flux to impose at the boundary of domain B, while code B gives code A the temperature to impose at the boundary of domain A. So in short, the coupling is done via a Neumann/Dirichlet BCs.
I am facing stability issues that don't allow me to finish correctly the transient solution.
Let us focus only on domain A (code A). When code A receives the temperature values from code B to apply a Dirichlet BC, the values are stocked in a layer of cells; so called the ghost cells. We denote these values as T_wall.
Now, we need to compute the heat flux at the boundary to give to code B. There are two possibilities to compute such a flux :
1- use T_wall and one inner temperature value
2- use 2 or 3 inner temperature values to calculate the flux, and then extrapolate it to the boundary.
I am getting serious instabilities if I calculate the flux via the first approach (T_wall and 1 inner temperature value). Otherwise, with the second approach (only inner temperature values), the simulation is stable and a steady-state is reached.
Can I have please your opinion on this subject. Have you ever faced such kind of problems ?
Is it really true that computing the flux with the second approach leads to a stable solution, but to a non-consevative scheme ?
Best regards
Elie Saikali
The stability condition is Fo Bi < 1 (CAST3M club presentation in 2019 at the CAST3M website by myself)... and serious references on the question :
Giles, M. B. "Stability analysis of numerical interface conditions in fluid–structure thermal analysis." International journal for numerical methods in fluids 25.4 (1997): 421-436.
Errera, Marc Paul, and Florent Duchaine, 2015. "STABLE AND FAST NUMERICAL SCHEMES FOR CONJUGATE HEAT TRANSFER."
Hi Frederic,
Thank you very much for the references. They really precise what I am looking for.
So if I understand correctly, in case of a thermal fluid/solid coupling, the scheme will be stable if a Dirichlet condition is prescribed at the fluid boundary, while a Neumann at the solid (surely the continuity of the flux is required). This is true as far as in this case the condition r
The heat exchange between fluids takes place through of the structure of the solid. The heat flows pass by convection between the fluids and the metallic structure via waves. Concerning the mesh (the discretization of your domain), you can combine a hydrodynamic mesh and a thermal mesh. With the passage classes, the definition of thermal interfaces makes it possible to establish the links between thermal meshes of two neighboring entities (solid and fluid).
To obtain a stable coupling, it is necessary to know the temporal schems for the two types of heat transfer. You can try combinations of the boundary conditions on the passing classes, for example the Dirichlet type conditions on the fluid border and the other on the solid border or even the Cauchy conditions on the solid border. But the temporal patterns are quite unstable. So I advise you to use the Newton-Raphson method in which the convergence criteria is based on the infinite norm of the residuals.
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