pyLBM.Scheme¶

class pyLBM.Scheme(dico, stencil=None)¶

Create the class with all the needed informations for each elementary scheme.

Parameters:

dico : a dictionary that contains the following key:value dim : spatial dimension (optional if the box is given) scheme_velocity : the value of the ratio space step over time step (la = dx / dt) schemes : a list of dictionaries, one for each scheme generator : a generator for the code, optional (see Generator) ode_solver : a method to integrate the source terms, optional (see ode_solver) test_stability : boolean (optional)

Notes

Each dictionary of the list schemes should contains the following key:value

• velocities : list of the velocities number
• conserved moments : list of the moments conserved by each scheme
• polynomials : list of the polynomial functions that define the moments
• equilibrium : list of the values that define the equilibrium
• relaxation_parameters : list of the value of the relaxation parameters
• source_terms : dictionary do define the source terms (optional, see examples)
• init : dictionary to define the initial conditions (see examples)

If the stencil has already been computed, it can be pass in argument.

Examples

see demo/examples/scheme/

Attributes

dim	(int) spatial dimension
dx	(double) space step
dt	(double) time step
la	(double) scheme velocity, ratio dx/dt
nscheme	(int) number of elementary schemes
stencil	(object of class Stencil) a stencil of velocities
P	(list of sympy matrix) list of polynomials that define the moments
EQ	(list of sympy matrix) list of the equilibrium functions
s	(list of list of doubles) relaxation parameters (exemple: s[k][l] is the parameter associated to the lth moment in the kth scheme)
M	(sympy matrix) the symbolic matrix of the moments
Mnum	(numpy array) the numeric matrix of the moments (m = Mnum F)
invM	(sympy matrix) the symbolic inverse matrix
invMnum	(numpy array) the numeric inverse matrix (F = invMnum m)
generator	(Generator) the used generator ( NumpyGenerator, CythonGenerator, ...)
ode_solver	(ode_solver,) the used ODE solver ( explicit_euler, heun, ...)

Methods

create_moments_matrix :	Create the moments matrices
create_relaxation_function :	Create the relaxation function
create_equilibrium_function :	Create the equilibrium function
create_transport_function :	Create the transport function
create_f2m_function :	Create the function f2m
create_m2f_function :	Create the function m2f
generate :	Generate the code
equilibrium :	Compute the equilibrium
transport :	Transport phase
relaxation :	Relaxation phase
f2m :	Compute the moments from the distribution functions
m2f :	Compute the distribution functions from the moments
onetimestep :	One time step of the Lattice Boltzmann method
set_initialization :	set the initialization functions for the conserved moments
set_source_terms :	set the source terms functions
set_boundary_conditions :	Apply the boundary conditions
compute_amplification_matrix_relaxation :	compute the amplification matrix of the relaxation
compute_amplification_matrix(wave_vector) :	compute the amplification matrix of one time step of the scheme for the given wave vector
vp_amplification_matrix(wave_vector) :	compute the eigenvalues of the amplification matrix for a given wave vector
is_L2_stable :	test the L2 stability of the scheme
is_monotonically_stable :	test the monotonical stability of the scheme