# fluidsim.solvers.sphere.sw1l.solver¶

## SW1L equations over a sphere (fluidsim.solvers.sphere.sw1l)¶

class fluidsim.solvers.sphere.sw1l.solver.InfoSolverSphereSW1L(**kargs)[source]

Contain the information on the sphere.sw1l solver.

_init_root(self)[source]

Init. self by writting the information on the solver.

class fluidsim.solvers.sphere.sw1l.solver.SimulSphereSW1L(params)[source]

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(self, state_spect=None, old=None)[source]

Compute the nonlinear tendencies.

Parameters
state_spectfluidsim.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.

oldfluidsim.base.setofvariables.SetOfVariables

optional

Array containing the previous tendencies_sh. This array is reused to save memory and improve performance.

Returns
tendencies_shfluidsim.base.setofvariables.SetOfVariables

An array containing the tendencies for the vorticity.

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

 compute_Frot(rot, ux, uy, f_radial) Compute cross-product of absolute potential vorticity with velocity.

Classes

 InfoSolverSphereSW1L(**kargs) Contain the information on the sphere.sw1l solver. Simul SimulSphereSW1L(params) Spherical-harmonics solver for shallow water equation.