There are ways to shorten the time to convergence on a difficult problem, and none of them is fiddling with relaxation factors.
1. A good initial field
You do not have to start from nothing:
- A coarse mesh solution. A quick coarse result is interpolated onto the fine mesh as a starting point. On its own this can halve the iteration count.
- A neighbouring operating point. If you are producing a curve, do not restart each point from scratch; continue from the previous solution.
- A potential flow or other simple pre-solution. Starting the field from a sensible velocity distribution avoids the shocks of the first iterations.
2. Ramping the load
Do not put the solver at the final condition in one step. Raise the flow rate, the power, the rotational speed or the buoyancy in stages. The partially converged solution at each stage is the starting point for the next.
Ramping the Mach number on compressible problems, and solving the cold flow before switching combustion on, follow the same logic. See the compressible flow note.
3. Multigrid
The low-frequency components of the error decay very slowly on a fine mesh. A multigrid method transfers the solution to coarser meshes, damps those components there quickly, and transfers back. On large meshes the gain is an order of magnitude, and it does not change the solution — it only reaches it sooner [1].
4. Scheme staging
First order at the start, then second order. This is an acceleration technique, but the final result must be obtained at second order. See the discretisation scheme note.
The illegitimate route
Loosening the convergence criterion. Raising the residual threshold and declaring convergence shortens the run but does not solve the problem; if the monitored quantities are still drifting, the solution is not finished. See the convergence note.
References
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6
- Patankar, S. V. (1980). Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing. ISBN 978-0-89116-522-4.