Momentum equation
momentum_equation
Derived terms and associated equations for the Stokes system.
All terms are considered as if they were on the righthand side of the equation, leading
to the following UFL expression returned by the residual
method:
This sign convention ensures compatibility with Thetis's time integrators. In general,
however, we like to think about the terms as they are on the lefthand side. Therefore,
in the residual methods below, we first sum the terms in the variable F
as if they
were on the lefthand side, i.e.
and then return F
.
Users should not interact with these classes; instead, please use the solver provided in the stokes_integrators module.
ViscosityTerm(test_space, trial_space, dx, ds, dS, **kwargs)
Bases: BaseTerm
Viscosity term \(nabla * (mu nabla u)\) in the momentum equation.
Using the symmetric interior penalty method, the weak form becomes
where σ is a penalty parameter (see Epshteyn and Riviere, 2007).
Epshteyn, Y., & Rivière, B. (2007). Estimation of penalty parameters for symmetric interior penalty Galerkin methods. Journal of Computational and Applied Mathematics, 206(2), 843872.
Source code in gadopt/gadopt/equations.py
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MomentumEquation(test_space, trial_space, quad_degree=None, **kwargs)
Bases: BaseEquation
Momentum equation with viscosity, pressure gradient, and source terms.
Source code in gadopt/gadopt/equations.py
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ContinuityEquation(test_space, trial_space, quad_degree=None, **kwargs)
Bases: BaseEquation
Mass continuity equation with a single divergence term.
Source code in gadopt/gadopt/equations.py
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StokesEquations(test_space, trial_space, quad_degree=None, **kwargs)
Stokes system involving the momentum and mass continuity equations.
Parameters:
Name  Type  Description  Default 

test_space 
WithGeometry

Firedrake function space of the test function 
required 
trial_space 
WithGeometry

Firedrake function space of the trial function 
required 
quad_degree 
Optional[int]

Quadrature degree. Default value is 
None

Returns:
Type  Description 

list[BaseEquation]

A list of equation instances for the Stokes system. 
Source code in gadopt/gadopt/momentum_equation.py
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