Difference between revisions of "Convergence study with SELFE"
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| − | As indicated in the SELFE main page, SELFE is an implicit model. This means that large time step is not only allowed but also encouraged! In fact the numerical diffusion in SELFE will increase when the CFL number is below ~0.4, which may lead to undesirable results. So estimate the CFL number in your application and start from a large time step (e.g., a 5 min step for barotropic applications; for baroclinic applications, the time step is constrained by the internal Courant number and so may need to be slightly smaller). | + | As indicated in the SELFE main page, SELFE is an implicit model. This means that large time step is not only allowed but also encouraged! In fact the numerical diffusion in ELM of SELFE will increase when the CFL number is below ~0.4, which may lead to undesirable results. So estimate the CFL number in your application and start from a large time step (e.g., a 5 min step for barotropic applications; for baroclinic applications, the time step is constrained by the internal Courant number and so may need to be slightly smaller). |
If you are doing a convergence study, you need to keep the CFL number fixed while reducing the time step (which means you have to reduce the grid spacing). | If you are doing a convergence study, you need to keep the CFL number fixed while reducing the time step (which means you have to reduce the grid spacing). | ||
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[[File:SELFE-sensitivity-timestep-Aug2012.png|Fig. 1: Model errors as a function of time step, on a fixed grid]] | [[File:SELFE-sensitivity-timestep-Aug2012.png|Fig. 1: Model errors as a function of time step, on a fixed grid]] | ||
| − | So beware of this behavior when you reduce the time step. If you have to reduce the time step for some reason (e.g., very fine grid and strong wet/dry), you have to refine the grid to satisfy the condition CFL>0.4; see [http://ccrm.vims.edu/w/index.php/Mesh_generation#Beware_of_CFL_number] for more info. | + | This is due to the use of ELM (ref). So beware of this behavior when you reduce the time step. If you have to reduce the time step for some reason (e.g., very fine grid and strong wet/dry), you have to refine the grid to satisfy the condition CFL>0.4; see [http://ccrm.vims.edu/w/index.php/Mesh_generation#Beware_of_CFL_number] for more info. |
| + | |||
| + | The 'peculiar' behavior of ELM is the most misunderstood part of SELFE model. No convergence is expected with dt when dx is fixed. An analogy is that in explicit models no convergence is expected with dx when dt is fixed (due to stability condition). Both types of models converge (and are consistent) with dx,dt-->0 and dx/dt=constant. Therefore SELFE is a consistent and convergent model. | ||
| + | |||
| + | References | ||
| + | <UL> | ||
| + | Baptista | ||
| + | </UL> | ||
Revision as of 11:08, 29 August 2013
As indicated in the SELFE main page, SELFE is an implicit model. This means that large time step is not only allowed but also encouraged! In fact the numerical diffusion in ELM of SELFE will increase when the CFL number is below ~0.4, which may lead to undesirable results. So estimate the CFL number in your application and start from a large time step (e.g., a 5 min step for barotropic applications; for baroclinic applications, the time step is constrained by the internal Courant number and so may need to be slightly smaller).
If you are doing a convergence study, you need to keep the CFL number fixed while reducing the time step (which means you have to reduce the grid spacing).
For a given grid, the errors changes with dt in a nonlinear manner, as shown in the plot below:
This is due to the use of ELM (ref). So beware of this behavior when you reduce the time step. If you have to reduce the time step for some reason (e.g., very fine grid and strong wet/dry), you have to refine the grid to satisfy the condition CFL>0.4; see [1] for more info.
The 'peculiar' behavior of ELM is the most misunderstood part of SELFE model. No convergence is expected with dt when dx is fixed. An analogy is that in explicit models no convergence is expected with dx when dt is fixed (due to stability condition). Both types of models converge (and are consistent) with dx,dt-->0 and dx/dt=constant. Therefore SELFE is a consistent and convergent model.
References
-
Baptista
