The solver (nsfds3.solver)
The solver package contains the following main objects:
CfgSetup: read a configuration file and set all simulation parameters.FDTD: setup and run the FDTD simulationSourceSet: Describes a set of sourcesCustomInitialConditions: Describes custom initial conditions
The following example gives the general philosophy to use nsfds3:
from nsfds3.solver import CfgSetup, FDTD from nsfds3.cpgrid import build_mesh # Initialize simulation parameter cfg = CfgSetup() # or cfg = CfgSetup('path_to_configfile.conf') # Make the mesh msh = build_mesh(cfg) # Create and run simulation fdtd = FDTD(msh, cfg) fdtd.run() # Show result fdtd.show(view='p', nans=True, buffer=True, grid=False, obstacles=True)
- class nsfds3.solver.CfgSetup(cfgfile=None, last=False, verbose=False)[source]
Setup configuration of the solver.
- Parameters:
cfgfile (str, optional) – If None, CfgSetup takes defaults values. If a valid configuration file is provided, CfgSetup takes the value contained in this file.
last (bool, optional) – If cfgfile is not provided, try to load the last configuration used if it exists.
verbose (bool, optional) – Verbose mode
Note
Hereafter, one can find the correspondance between entries in the configuration file (on the left) and CfgSetup attributes (on the right) and their default values.
[general] version -> self.version quiet -> self.quiet = False [files] directory -> self.files.directory = 'data/' name -> self.files.name = 'tmp' overwrite -> self.files.overwrite = False [thermophysics] norm -> self.tp.norm = False rho0 -> self.tp.rho0 = 101325.0 t0 -> self.tp.T0 - self.tp.Tref = 20.0 gamma -> self.tp.gamma = 1.4 [geometry] force -> self.geo.force = False free -> self.geo.free = True file -> self.geo.file = None name -> self.geo.name = None kwargs -> self.geo.kwargs = None curvname -> self.geo.curvname = None bc -> self.geo.bc = 'WWWWWW' shape -> self.geo.shape = (128, 96, 32) origin -> self.geo.origin = None steps -> self.geo.steps = (1., 1., 1.) flat -> self.geo.flat = None bz grid points -> self.geo.bz_n = 20 bz filter order -> self.geo.bz_filter_order = 3 bz stretch order -> self.geo.bz_stretch_order = 3 bz stretch factor -> self.geo.bz_stretch_factor = 2 [sources] on -> self.src.on = False origin -> self.src.origin = (), S0 -> self.src.S0 = () Bx -> self.src.Bx = () By -> self.src.By = () Bz -> self.src.Bz = () kx -> self.src.kx = () ky -> self.src.ky = () kz -> self.src.kz = () k -> self.src.k = () R -> self.src.Rx = () evolution -> self.src.evolution = () [flow] type -> self.flw.ftype = None components -> self.flw.components = (0, 0, 0) [probes] variables -> self.prb.vars = () locations -> self.prb.locs = () [solver] mp -> self.sol.mp = False timings -> self.sol.timings = False nan_check -> self.sol.nan_check = False resume -> self.sol.resume = False viscous fluxes -> self.sol.vsc = True vorticity -> self.sol.vrt = True shock capture -> self.sol.cpt = True selective filter -> self.sol.flt = True selective filter n-strength -> self.sol.xnu_n = 0.2 selective filter 0-strength -> self.sol.xnu_0 = 0.01 nt -> self.sol.nt = 50 ns -> self.sol.ns = 10 cfl -> self.sol.cfl = 0.5 save fields -> self.sol.save = True [graphics] figures -> self.gra.fig = True probes -> self.gra.prb = True bz -> self.gra.bz = True bc -> self.gra.bc = True fps -> self.gra.fps = 24
- Attributes:
dtTime step.
frequenciesCalculate the minimum and maximum frequencies for the simulation.
has_grid_backupReturn whether a CartesianGrid or CurvilinearGrid already exist for this configuration or not.
ndimDimension of the grid.
versionVersion of configuration file.
Methods
Check version of the configuration.
Return existing CartesianGrid or CurvilinearGrid instance for this grid configuration if found, else return None.
load([cfgfile, last])Load configuration file cfgfile.
Overwrite configuration file.
parse_literal(value)Parse value.
run()Run the parser.
write(fname)Write a configuration file with current configuration.
- property dt
Time step.
Note
dt is a read only attribute. It is automatically updated if one of geo.steps, sol.cfl, tp.c0 or flw.components attributes is modified.
- property frequencies
Calculate the minimum and maximum frequencies for the simulation.
- Returns:
A tuple containing the minimum and maximum frequencies. The minimum frequency is calculated as 2 divided by the product of the time step and the number of time steps. The maximum frequency is calculated as the Courant-Friedrichs-Lewy (CFL) condition divided by 10 times the time step.
- Return type:
- get_grid_backup()[source]
Return existing CartesianGrid or CurvilinearGrid instance for this grid configuration if found, else return None.
- property has_grid_backup
Return whether a CartesianGrid or CurvilinearGrid already exist for this configuration or not.
- load(cfgfile=None, last=False)[source]
Load configuration file cfgfile. If file is not found, fallback to default configuration.
- Parameters:
- property ndim
Dimension of the grid.
- property version
Version of configuration file.
- class nsfds3.solver.CustomInitialConditions(cfg, msh)[source]
Customize initial conditions for acoustic pressure and/or velocities.
- Parameters:
cfg (CfgSetup) – Configuration of the simulation
msh (CartesianGrid, CurvilinearGrid) – Grid used for the simulation
Notes
To setup custom initial conditions, one must override the CustomInitialConditions.__post_init__ method. The following attributes can be customized:
self.p: acoustic pressure (without static pressure)
self.vx: x-component of velocity
self.vy: y-component of velocity
self.vz: z-component of velocity
Example
class Ring(CustomInitialConditions): def __post_init__(self): origin = 100, 100 k = 12 self.p = self.super_gaussian(origin, k=12)
- Attributes:
customReport whether initial conditions are provided or not.
has_old_fieldsReport whether old fields have been initialized or not.
varsReturn initial conditions that have been provided.
Methods
check()Check that initial conditions are valid ones.
Report whether there is an older run or not.
resume()Setup fields to resume last simulation with the current config.
show()Show initial conditions graphically.
super_gaussian(origin[, kx, ky, kz, k, Bx, ...])Super Gaussian distribution.
- property custom
Report whether initial conditions are provided or not.
- property has_old_fields
Report whether old fields have been initialized or not.
- resume()[source]
Setup fields to resume last simulation with the current config. Set r, ru, rv[, rw], re instance attributes to the values at the last iteration itmax reached during last simulation.
- super_gaussian(origin, kx=2, ky=2, kz=2, k=1, Bx=None, By=None, Bz=None, Rx=0)[source]
Super Gaussian distribution.
\[sg = e^{- (\sqrt{(x - x_0)^2 + (y - y_0)^2} + \sqrt{x_r^2 + y_r^2})^{eta} / (B_x \delta x))^{eta}}\]- Parameters:
- x, y, znumpy.ndarray
Axis of the grid.
- ix0, iy0, iz0int
Indices of the initial position of the pulse \((x_0, y_0)\).
- Bx, By, Bzfloat, optional
Widths \(B_x, B_y, B_z\) of the pulse in m. 0.1 by default.
- kx, ky, kz, k: float, optional
Orders \(eta\) of the pulse. Order 2 by default for axis and 1 for global.
- Rx: float, optional
Radius following x for annular source
- property vars
Return initial conditions that have been provided.
- class nsfds3.solver.FDTD(cfg, msh, ics=None, quiet=None, timings=None, overwrite=None)[source]
Solve Navier-Stokes equations using Finite Difference Time Domain (FDTD) technique.
- Parameters:
cfg (CfgSetup) – Configuration of the simulation
msh (CartesianGrid, CurvilinearGrid) – Grid used for the simulation
ics (CustomInitialConditions) – Custom Initial conditions
quiet (bool) – If True, display informations on the standard output
timings (bool) – If True, display complete timings during the simulation
overwrite (bool) – If True, automatically overwrite files
nan_check (bool) – If True, exit simulation when nan are encountered. This option may degrade computation time.
Notes
When the simulation is complete, one can use the show method to display the desired field at the last iteration, or inspect the fld object that gathers all conservative variables at the last iteration.
Finite differences schemes, Runge-Kutta algorithm and selective filter are applied using the technique described in [1]. The shock capturing procedure is applied using the technique described in [2].
References
[1]C. Bogey, C. Bailly, “A family of low dispersive and low dissipative explicit schemes for flow and noise computations”, Journal of Computational Physics, Volume 194, Issue 1, 2004, Pages 194-214.
[2]C. Bogey, N. de Cacqueray, C. Bailly, “A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations”, Journal of Computational Physics, Volume 228, Issue 5, 2009, Pages 1447-1465.
Methods
run()Run simulation.
Save cfg and msh objects.
show([view, vmin, vmax])Show results.
from_cfg
- class nsfds3.solver.SourceSet(shape, origin, flat=None, **kwargs)[source]
Set of pressure sources in Super Gaussian form.
Super Gaussian [1] can be declared as initial conditions or time evolving pressure fluctuations. To declare time evolving source, the evolution argument must be provided.
\[p_{\text{ring}} = S_0 e^{- (\sqrt{(x - x_0)^2 + (y - y_0)^2} + \sqrt{x_r^2 + y_r^2})^{\beta} / (B_x \delta x))^{\beta}}\]References
[1]S. Kang et al. « A Physics-Based Approach to Oversample Multi-Satellite, Multi-Species Observations to a Common Grid ». Preprint. Gases/Remote Sensing/Data Processing and Information Retrieval, 23 août 2018. https://doi.org/10.5194/amt-2018-253.
- Parameters:
shape (tuple) – Shape of the computational domain.
origin (tuple or (tuple, )) – Coordinates of the center. Can be a tuple or (tuple, ). If a tuple of tuples is provided, all tuples must have the same length.
flat (tuple or None) – Whether geometry is flattened or not. If a tuple is provided, it must provide (flat axis, flat index).
S0 (float or (float, ). Optional.) – Amplitude \(S_0\) of the pulse in Pa. 1 by default. Parameter amplitude is 1 by default for each source. Can be float for a single source or tuple of floats for multiple sources.
Bx (float or (float, ). Optional.) – Width \(B_x, B_y, B_z\) of the sources. Parameter width is 0.1 by default for each source. Can be positive int for a single source or tuple of positive ints for multiple sources.
By (float or (float, ). Optional.) – Width \(B_x, B_y, B_z\) of the sources. Parameter width is 0.1 by default for each source. Can be positive int for a single source or tuple of positive ints for multiple sources.
Bz (float or (float, ). Optional.) – Width \(B_x, B_y, B_z\) of the sources. Parameter width is 0.1 by default for each source. Can be positive int for a single source or tuple of positive ints for multiple sources.
k1 (int or (int, ). Optional.) – Order of the sources. Must be positive (if not, absolute is taken). Parameter order is 2 by default for each source. Can be int for a single source or tuple of positive ints for multiple sources.
k2 (int or (int, ). Optional.) – Order of the sources. Must be positive (if not, absolute is taken). Parameter order is 2 by default for each source. Can be int for a single source or tuple of positive ints for multiple sources.
k3 (int or (int, ). Optional.) – Order of the sources. Must be positive (if not, absolute is taken). Parameter order is 2 by default for each source. Can be int for a single source or tuple of positive ints for multiple sources.
k (int or (int, ). Optional.) – Order of the sources. Must be positive (if not, absolute is taken). Parameter order is 2 by default for each source. Can be int for a single source or tuple of positive ints for multiple sources.
Rx (float or (float, ). Optional.) – Radius for the case of annular source. 0 by default. Can be float for a single source or tuple of floats for multiple sources.
on (bool or (bool, ). Optional) – Whether source is on or not. Parameter on is False by default for each source. Can be bool for a single source or tuple of bool for multiple sources.
evolution (float/func, or (float/func, ). Optional.) –
Time evolution of the source. Parameter evolution is None by default for each source. If evolution is None, the source will be an initial condition. If evolution is a float, it will describe the frequency of a sinusoidal time evolution. If evolution is a function, the time evolution of the source will be the result of evolution(t) where t is the time axis calculated as follows:
import numpy as np t = np.linspace(0, nt * dt, nt + 1)
where nt and dt are the number of time step and the time step setup in the configuration, respectively.
Example
# Declare 2 initial conditions, the first one located at (100, 100) with an amplitude of 10 # and a x-width of 0.1 grid points. The second source is located at (150, 150) with the same # amplitude and a x-width of 0.2 grid points s = SourceSet(origin=((100, 100), (150, 150)), S0=10, Bx=(0.1, 0.2))
- Attributes:
Bxx-widths of the source. Will be converted to positive integer if not.
Byy-widths of the source. Will be converted to positive integer if not.
Bzz-widths of the source. Will be converted to positive integer if not.
RxRadius in the case of annular source.
S0Amplitudes of the source.
evolutionTime evolution of the sources.
kGlobal order of the source.
kwargsReturn a list of dictionnaries providing keyword arguments of the sources.
kxOrder of the source following x.
kyOrder of the source following y.
kzOrder of the source following z.
onReport whether sources must be activated or not.
- origin
Methods
update()Update parameters.
- property Bx
x-widths of the source. Will be converted to positive integer if not.
- property By
y-widths of the source. Will be converted to positive integer if not.
- property Bz
z-widths of the source. Will be converted to positive integer if not.
- property Rx
Radius in the case of annular source.
- property S0
Amplitudes of the source.
- property evolution
Time evolution of the sources.
- property k
Global order of the source. Will be converted to positive integer if not.
- property kwargs
Return a list of dictionnaries providing keyword arguments of the sources.
- property kx
Order of the source following x. Will be converted to positive integer if not.
- property ky
Order of the source following y. Will be converted to positive integer if not.
- property kz
Order of the source following z. Will be converted to positive integer if not.
- property on
Report whether sources must be activated or not.