2D sediment transport formulation¶
Governing equations¶
Suspended sediment transport is modelled in two dimensions
using an advection-diffusion equation
(6).
If solved in non-conservative form, the prognostic variable
is the passive tracer concentration,
\(T\). The corresponding field in Thetis is called
'sediment_2d'.
The sediment model is defined by specifying parameters in
ModelOptions2d.sediment_model_options.
See
SedimentModelOptions
for a list of all available parameters.
A conservative suspended sediment transport model is also
available. In this case, the equation is solved for
\(q=HT\), where
\(H\) is the total water depth.
The conservative tracer model is specified using the
SedimentModelOptions.use_sediment_conservative_form
option.
Bedload transport is modelled in two dimensions using the
Exner equation
(1).
It is solved for the bedlevel,
\(z_b\), which is the bathymetry. The corresponding field
in Thetis is called
'bathymetry_2d'.
To activate the 2D sediment model, set the
SedimentModelOptions.solve_suspended_sediment
and
SedimentModelOptions.solve_exner
options to
True.
Spatial discretization¶
Thetis currently only supports suspended sediment in P1DG space.
Lax-Friedrichs stabilization is used by default and may be
controlled using the
ModelOptions2d.use_lax_friedrichs_tracer
option. The scaling parameter used by this scheme may be controlled
using the
ModelOptions2d.lax_friedrichs_tracer_scaling_factor
option.
The function space used for the bedlevel is determined by that used for the bathymetry. Typically, this is P1.
Temporal discretization¶
Thetis supports different time integration methods, set by the
SedimentModelOptions.sediment_timestepper_type
and
SedimentModelOptions.exner_timestepper_type
options. Use the
ModelOptions2d.set_timestepper_type
method to set the same timestepper for all 2D model components.
Time integrator |
Thetis class |
Unconditionally stable |
Description |
|---|---|---|---|
|
No |
Forward Euler method |
|
|
Yes |
Backward Euler method |
|
|
Yes |
Crank-Nicolson method |
|
|
Yes |
DIRK(2,3,2) method |
|
|
Yes |
DIRK(3,4,3) method |
|
|
No |
SSPRK(3,3) method |
Table 1. Time integration methods for 2D sediment model.