fluidsim.solvers.sphere.sw1l.solver
SW1L equations over a sphere (fluidsim.solvers.sphere.sw1l
)
- class fluidsim.solvers.sphere.sw1l.solver.InfoSolverSphereSW1L(only_root=False, **kargs)[source]
Bases:
InfoSolverSphericalHarmo
Contain the information on the
sphere.sw1l
solver.
- class fluidsim.solvers.sphere.sw1l.solver.SimulSphereSW1L(params)[source]
Bases:
SimulSphericalHarmo
Spherical-harmonics solver for shallow water equation.
- InfoSolver
alias of
InfoSolverSphereSW1L
- static _complete_params_with_default(params)[source]
Complete the params container (static method).
- tendencies_nonlin(state_spect=None, old=None)[source]
Compute the nonlinear tendencies.
- Parameters:
- state_spect
fluidsim.base.setofvariables.SetOfVariables
optional
Array containing the state, i.e. the vorticity, the divergence and displacement in the spectral space. If
state_spect
is provided, the variables in the physical space are computed from it, otherwise, they are taken from the global state of the simulation,self.state.state_phys
.These two possibilities are used during the time-stepping.
- old
fluidsim.base.setofvariables.SetOfVariables
optional
Array containing the previous
tendencies_sh
. This array is reused to save memory and improve performance.
- state_spect
- Returns:
- tendencies_sh
fluidsim.base.setofvariables.SetOfVariables
An array containing the tendencies for the vorticity.
- tendencies_sh
Notes
The 1-layer shallow water equations are solved in the vector-invariant form (see section 2.2.6 Vallis 2nd edition).
\[\partial_t \hat\zeta = \hat N_\zeta - \sigma(k) \hat \zeta, \partial_t \hat\delta = \hat N_\delta - \sigma(k) \hat \delta, \partial_t \hat\eta = \hat N_\eta - \sigma(k) \hat \eta,\]This function computes the nonlinear term (“tendencies”). The algorithm is as follows,
Compute \(N_u\) and \(N_v\), the tendencies for the velocities.
Take divergence and curl of the above to obtain \(N_\zeta, N_\delta\).
Subtract laplacian of total energy K.E. + hydrostatic pressure from \(N_\delta\).
Compute \(N_\eta = -\nabla.((\eta + 1)\mathbf{u})\)
Functions
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Compute cross-product of absolute potential vorticity with velocity. |
Classes
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Contain the information on the |
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alias of |
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Spherical-harmonics solver for shallow water equation. |