2D sediment transport formulation¶
Governing equations¶
Suspended sediment transport is modelled in two dimensions
using an advectiondiffusion equation
(7).
If solved in nonconservative form, the prognostic variable
is the passive tracer concentration,
\(T\). The corresponding field in Thetis is called
'sediment_2d'
.
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
ModelOptions2d.use_sediment_conservative_form
option.
Bedload transport is modelled in two dimensions using the
Exner equation
(2).
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
ModelOptions2d.solve_suspended_sediment
and
ModelOptions2d.solve_exner
options to
True
.
Spatial discretization¶
Thetis currently only supports suspended sediment in P1DG space.
LaxFriedrichs 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
ModelOptions2d.timestepper_type
option.
Note that the same time integration method will be used for both the shallow
water equations and the 2D sediment model.
Time integrator 
Thetis class 
Unconditionally stable 
Description 


No 
Forward Euler method 


Yes 
Backward Euler method 


Yes 
CrankNicolson 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.