fluidsim.solvers.ns3d.bouss.solver
Boussinesq NS3D solver (fluidsim.solvers.ns3d.bouss.solver
)
- class fluidsim.solvers.ns3d.bouss.solver.InfoSolverNS3DBouss(only_root=False, **kargs)[source]
Bases:
InfoSolverNS3DStrat
- class fluidsim.solvers.ns3d.bouss.solver.Simul(params)[source]
Bases:
Simul
Pseudo-spectral solver 3D incompressible Navier-Stokes equations.
Notes
This class is dedicated to solve with a pseudo-spectral method the incompressible Navier-Stokes equations (possibly with hyper-viscosity):
\[\partial_t \textbf{v} + \textbf{v} \cdot \boldsymbol{\nabla} \textbf{v} = - \boldsymbol{\nabla} p - \nu_\alpha (-\Delta)^\alpha \textbf{v},\]where \(\textbf{v}\) is the non-divergent velocity (\(\boldsymbol{\nabla} \cdot \textbf{v} = 0\)), \(p\) is the pressure, \(\Delta\) is the 3D Laplacian operator.
In Fourier space, these equations can be written as:
\[\partial_t \hat v = N(v) + L \hat v,\]where
\[N(\textbf{v}) = -P_\perp \widehat{\boldsymbol{\nabla} \cdot \textbf{v} \textbf{v}},\]\[L = - \nu_\alpha |\textbf{k}|^{2\alpha},\]with \(P_\perp = (1 - \hat{\textbf{e}}_\textbf{k} \hat{\textbf{e}}_\textbf{k} \cdot)\) the operator projection on the plane perpendicular to the wave number \(\textbf{k}\). Since the flow is incompressible (\(\textbf{k} \cdot \textbf{v} = 0\)), the effect of the pressure term is taken into account with the operator \(P_\perp\).
- InfoSolver
alias of
InfoSolverNS3DBouss
- tendencies_nonlin(state_spect=None, old=None)[source]
Compute the nonlinear tendencies.
This function has to be overridden in a child class.
- Returns:
- tendencies_fft
fluidsim.base.setofvariables.SetOfVariables
An array containing only zeros.
- tendencies_fft
Classes
|
|
|
Pseudo-spectral solver 3D incompressible Navier-Stokes equations. |