I am modeling steady and transient(using explicit relation )heat flow through a fin. Now i have refined the mesh but the solution diverges(both transient and steady)
so the time step can also become too small since it depends on the grid spacing?
It should never diverge, make sure you are getting answers for the same point in all the meshes. What goes up is the medium error if you use finer mesh, but this doenst make the solution worse. Look at my paper about transient heat transfer here on research gate, also a smaller time step gives better solution
thanx, i'll verify my equations again
Ah, the tolerance for convergence was too high, needed to be reduced a bit.thanx again
More fine the mess better will be your results. but your cost of simulation will be high with fine meshes.
Check your Y+ value based on your courant number then fixed your first cell distance from the wall. Also check your input temperature values
"so the time step can also become too small since it depends on the grid spacing?"
Indeed. With a finer mesh the solver will have less numerical dissipation and it will be capturing smaller scales that perturb the flow in a different frequency. Due to all these, you will probably have to decrease your time step size to avoid abrupt gradients between timesteps.
Hope this helps.
Before giving a serious response, I would ask the type of discretization you are using. Numerical stability depends on that.
Anyway, I strongly suggest to do a grid refinement study first on a simple analytical solution.
What about the time integration? What about the cell Peclet number on the finest grid?
I believe that Newmark's scheme applies to second order ordinary differential equations, whereas heat flow is generally subject to Fourier's equation, a PDE which has a single time-derivative.
As I understand it, Fourier's equation, even with some wild and wacky boundary conditions, can be solved fairly easily using constant-step finite differences. These are central differences in space, and a simple Euler forward difference in time. If your timestep is too large, then the solutions will diverge in an oscillatory fashion in both time and space. The simple resolution is to decrease the timestep sufficiently.
This appears not to work in your case, though. Given that some of the earlier answers (and possibly mine too) seem to apply to slightly different perceptions of what you are solving, may I ask that you post the precise equations and boundary conditions that you trying to solve, with an indication of the method that you are using. At the moment we are all guessing at what your configuration is!
As you go for finer mesh your computation time will increase as more of grid points will be generated and governing equation will be applied over it. ..you must also perform grid independence test in order to validate your simulated results..
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