Convergence study with SCHISM - Revision history

Yjzhang at 14:46, 26 May 2016

2016-05-26T14:46:21Z

Yjzhang at 14:44, 26 May 2016

2016-05-26T14:44:52Z

Yjzhang at 17:20, 18 December 2014

2014-12-18T17:20:30Z

Yjzhang: Created page with "As indicated in the SELFE main page, SELFE is an implicit model using ELM. This means that large time step is not only allowed but also encouraged! In fact the numerical diffu..."

2014-12-18T17:19:38Z

Created page with "As indicated in the SELFE main page, SELFE is an implicit model using ELM. This means that large time step is not only allowed but also encouraged! In fact the numerical diffu..."

New page

As indicated in the SELFE main page, SELFE is an implicit model using ELM. 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 when doing grid generation [[Mesh_generation]] 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: <br />

[[File:SELFE-sensitivity-timestep-Aug2012.png|Fig. 1: Model errors as a function of time step, on a fixed grid]]

This is due to the use of ELM (Baptista 1987; Zhang and Baptista 2008). 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 is often the most misunderstood part of SELFE model. No convergence is expected with dt-->0 when dx is fixed. An analogy is that in explicit models, no convergence is expected with dx-->0 when dt is fixed (due to stability condition). Both types of models converge (and are consistent) with dx,dt-->0 and dx/dt=constant. SELFE is a consistent and convergent model.

'''References'''
<UL>
<LI> Baptista, A.M. (1987) Solution of advection-dominated transport by Eulerian-Lgrangian Methods using the backwards method of characteristics. Ph.D. Dissertation, MIT, Cambridge.
<LI>Zhang, Y.-L. and Baptista, A.M. (2008) "SELFE: A semi-implicit Eulerian-Lagrangian finite-element model for cross-scale ocean circulation", Ocean Modelling, 21(3-4), 71-96.
</UL>

@@ Line 7: / Line 7: @@
 [[File:SELFE-sensitivity-timestep-Aug2012.png|Fig. 1: Model errors as a function of time step, on a fixed grid]]
-This is due to the use of ELM (Baptista 1987; Zhang and Baptista 2008). 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 (Baptista 1987; Zhang and Baptista 2008). So beware of this behavior when you reduce the time step. If you have to reduce the time step for some reason (e.g., extremely fine grid and strong wet/dry), you
 The 'peculiar' behavior is often the most misunderstood part of SCHISM model. No convergence is expected with dt-->0 when dx is fixed. An analogy is that in explicit models, no convergence is expected with dx-->0 when dt is fixed (due to stability condition). Both types of models converge (and are consistent) with dx,dt-->0 and dx/dt=constant. SCHISM is a consistent and convergent model.

← Older revision		Revision as of 14:44, 26 May 2016
Line 1:		Line 1:
−	SCHISM is an implicit model using ELM. This means that large time step is not only allowed but also encouraged! In fact the numerical diffusion in ELM of SCHISM will increase when the CFL number is below ~0.4, which may lead to undesirable results. So estimate the CFL number in your application when doing grid generation [[Mesh_generation]] 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).	+	SCHISM is an implicit model using ELM. This means that large time step is not only allowed but also encouraged! In fact the numerical diffusion in ELM of SCHISM will increase when the CFL number is below ~0.4, which may lead to undesirable results. So estimate the CFL number in your application when doing grid generation [[Mesh_generation]] and start from a large time step (e.g., 100-400s 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. For field-scale applications we typically use 100-200s step).

	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).

@@ Line 1: / Line 1: @@
-As indicated in the SELFE main page, SELFE is an implicit model using ELM. 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 when doing grid generation [[Mesh_generation]] 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).
+SCHISM is an implicit model using ELM. This means that large time step is not only allowed but also encouraged! In fact the numerical diffusion in ELM of SCHISM will increase when the CFL number is below ~0.4, which may lead to undesirable results. So estimate the CFL number in your application when doing grid generation [[Mesh_generation]] 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).
@@ Line 9: / Line 9: @@
 This is due to the use of ELM (Baptista 1987; Zhang and Baptista 2008). 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 is often the most misunderstood part of SELFE model. No convergence is expected with dt-->0 when dx is fixed. An analogy is that in explicit models, no convergence is expected with dx-->0 when dt is fixed (due to stability condition). Both types of models converge (and are consistent) with dx,dt-->0 and dx/dt=constant. SELFE is a consistent and convergent model.
+The 'peculiar' behavior is often the most misunderstood part of SCHISM model. No convergence is expected with dt-->0 when dx is fixed. An analogy is that in explicit models, no convergence is expected with dx-->0 when dt is fixed (due to stability condition). Both types of models converge (and are consistent) with dx,dt-->0 and dx/dt=constant. SCHISM is a consistent and convergent model.