# fluidsim.solvers.sphere.ns2d.solver¶

## NS2D equations over a sphere (fluidsim.solvers.sphere.ns2d)¶

class fluidsim.solvers.sphere.ns2d.solver.InfoSolverSphereNS2D(**kargs)[source]

Contain the information on a base pseudo-spectral solver.

_init_root(self)[source]

Init. self by writting the information on the solver.

class fluidsim.solvers.sphere.ns2d.solver.SimulSphereNS2D(params)[source]

Pseudo-spectral base solver.

InfoSolver

alias of InfoSolverSphereNS2D

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, in Fourier space. If state_spect, the variables vorticity and the velocity are computed from it, otherwise, they are taken from the global state of the simulation, self.state.

These two possibilities are used during the Runge-Kutta time-stepping.

Returns
tendencies_shfluidsim.base.setofvariables.SetOfVariables

An array containing the tendencies for the vorticity.

Notes

The 2D Navier-Stokes equation can be written

$\partial_t \hat\zeta = \hat N(\zeta) - \sigma(k) \hat \zeta,$

This function compute the nonlinear term (“tendencies”) $$N(\zeta) = - \mathbf{u}\cdot \mathbf{\nabla} \zeta$$.

Classes

 InfoSolverSphereNS2D(**kargs) Contain the information on a base pseudo-spectral solver. Simul SimulSphereNS2D(params) Pseudo-spectral base solver.