Smooth Particle Hydrodynamics

Functions for constructing and interpolation via SPH.

Kernels

fiesta.sph.cubic_kernel(r: float | ndarray, h: float | ndarray, dim: int = 3) → float | ndarray

Cubic spline kernel.

Parameters:

  • r (float or array) – Distance to center point.

  • h (float or array) – Kernel size.

Returns:

w – Kernel weights.

Return type:

float or array

fiesta.sph.dcubic_kernel(r: float | ndarray, h: float | ndarray, dim: int = 3) → float | ndarray

Cubic derivative spline kernel.

Parameters:

  • r (float or array) – Distance to center point.

  • h (float or array) – Kernel size.

Returns:

w – Kernel weights.

Return type:

float or array

SPH Objects

class fiesta.sph.SPH1D

Class for computing Smooth Particle Hydrodynamic (SPH) density and field estimation in 1D.

assign_mass(mass: ndarray | None = None) → None

Assign particles mass, if none they will be assigned

Parameters:

mass (array, optional) – Particle mass.

clean() → None

Reinitialises the class.

estimate(x: ndarray, dens: ndarray | None = None) → ndarray

Estimates field at points given.

Parameters:

  • x (array) – Cartesian coordinates.

  • dens (array) – Density at cartesian coordinates, if None this will be computed but will require double the time.

Returns:

f_est – Field estimation.

Return type:

array

get_density(x: ndarray) → ndarray

Calculates density based on SPH k neighbours.

Parameters:

x (array) – Cartesian coordinates.

Returns:

dens – Density estimation.

Return type:

array

kernel(r: float | ndarray, h: float | ndarray) → float | ndarray

Returns the SPH kernel value.

Parameters:

  • r (float or array) – Radius from a given neighbour.

  • h (float or array) – Smoothing length.

set_field(f: ndarray) → None

Sets the field values for SPH field estimation.

Parameters:

f (array) – Field values at KDTree points.

setup(k: int = 20, mass: ndarray | None = None) → None

Set basic settings for the SPH data.

Parameters:

  • k (int, optional) – Neighbours for nearest neighbour SPH calculation.

  • mass (array, optional) – For assigning masses to the particles.

sph_estimate(x: ndarray, f: ndarray | None = None, dens: ndarray | None = None) → ndarray

Estimates a field based on SPH k neighbours.

Parameters:

  • x (array) – Cartesian coordinates.

  • f (array) – Field values at KDTree points.

  • dens (array) – Density at cartesian coordinates, if None this will be computed but will require double the time.

Returns:

f_est – Field estimation.

Return type:

array

class fiesta.sph.SPH2D

Class for computing Smooth Particle Hydrodynamic (SPH) density and field estimation in 2D.

assign_mass(mass: ndarray | None = None) → None

Assign particles mass, if none they will be assigned.

clean() → None

Reinitialises the class.

estimate(x: float | ndarray, y: float | ndarray, dens: ndarray = None) → float | ndarray

Estimates field at points given.

Parameters:

  • x (float or array) – Cartesian coordinates.

  • y (float or array) – Cartesian coordinates.

  • dens (array) – Density at cartesian coordinates, if None this will be computed but will require double the time.

Returns:

f_est – Field estimation.

Return type:

float or array

get_density(x: ndarray, y: ndarray) → ndarray

Calculates density based on SPH k neighbours.

Parameters:

  • x (array) – Cartesian coordinates.

  • y (array) – Cartesian coordinates.

Returns:

dens – Density estimation.

Return type:

array

kernel(r: float | ndarray, h: float | ndarray) → float | ndarray

Returns the SPH kernel value.

Parameters:

  • r (float or array) – Radius from a given neighbour.

  • h (float or array) – Smoothing length.

set_field(f: ndarray) → None

Sets the field values for SPH field estimation.

Parameters:

f (array) – Field values at KDTree points.

setup(k: int = 20, mass: ndarray | None = None) → None

Set basic settings for the SPH data.

Parameters:

  • k (int, optional) – Neighbours for nearest neighbour SPH calculation.

  • mass (array, optional) – For assigning masses to the particles.

sph_estimate(x: float | ndarray, y: float | ndarray, f: ndarray | None = None, dens: ndarray | None = None) → float | ndarray

Estimates a field based on SPH k neighbours.

Parameters:

  • x (float or array) – Cartesian coordinates.

  • y (float or array) – Cartesian coordinates.

  • f (array) – Field values at KDTree points.

  • dens (array) – Density estimation.

Returns:

f_est – Field estimation.

Return type:

float or array

class fiesta.sph.SPH3D

Class for computing Smooth Particle Hydrodynamic (SPH) density and field estimation in 3D.

assign_mass(mass: ndarray | None = None) → None

Assign particles mass, if none they will be assigned.

clean() → None

Reinitialises the class.

estimate(x: float | ndarray, y: float | ndarray, z: float | ndarray, dens: ndarray | None = None) → float | ndarray

Estimates field at points given.

Parameters:

  • x (array) – Cartesian coordinates.

  • y (array) – Cartesian coordinates.

  • z (array) – Cartesian coordinates.

  • dens (array) – Density at cartesian coordinates, if None this will be computed but will require double the time.

Returns:

f_est – Field estimation.

Return type:

array

get_density(x: float | ndarray, y: float | ndarray, z: float | ndarray) → float | ndarray

Calculates density based on SPH k neighbours.

Parameters:

  • x (array) – Cartesian coordinates.

  • y (array) – Cartesian coordinates.

  • z (array) – Cartesian coordinates.

Returns:

dens – Density estimation.

Return type:

array

kernel(r: float | ndarray, h: float | ndarray) → float | ndarray

Returns the SPH kernel value.

Parameters:

  • r (float or array) – Radius from a given neighbour.

  • h (float or array) – Smoothing length.

set_field(f: float | ndarray) → None

Sets the field values for SPH field estimation.

Parameters:

f (array) – Field values at KDTree points.

setup(k: int = 50, mass: ndarray = None) → None

Set basic settings for the SPH data.

Parameters:

  • k (int, optional) – Neighbours for nearest neighbour SPH calculation.

  • mass (array, optional) – For assigning masses to the particles.

sph_estimate(x: float | ndarray, y: float | ndarray, z: float | ndarray, f: ndarray | None = None, dens: ndarray | None = None) → float | ndarray

Estimates a field based on SPH k neighbours.

Parameters:

  • x (array) – Cartesian coordinates.

  • y (array) – Cartesian coordinates.

  • z (array) – Cartesian coordinates.

  • f (array) – Field values at KDTree points.

  • dens (array) – Density estimation.

Returns:

f_est – Field estimation.

Return type:

array

SPH to grid

fiesta.sph.sph4grid2D(x: ndarray, y: ndarray, boxsize: float | List[float], ngrid: int | List[int], f: ndarray | None = None, origin: float | List[float] = 0.0, mass: ndarray | None = None, k: int = 20, periodic: bool = True, subsampling: int = 1, outputgrid: bool = False) → ndarray | Tuple[ndarray, ndarray, ndarray]

Estimates a field on a regular grid based on SPH k neighbours.

Parameters:

  • x (array) – Cartesian coordinates of the input points.

  • y (array) – Cartesian coordinates of the input points.

  • boxsize (float or list of float) – Size of the box in each dimension.

  • ngrid (int or list of int) – Number of grid points in each dimension.

  • f (array, optional) – Field values at the input points.

  • origin (float or list of float, optional) – Origin of the grid.

  • mass (array, optional) – Mass of the input points. If not provided, it is assumed to be 1 for all points.

  • k (int, optional) – Number of nearest neighbors to consider.

  • periodic (bool or list of bool, optional) – Whether to use periodic boundary conditions.

  • subsampling (int, optional) – Subsampling factor for the output grid.

  • outputgrid (bool, optional) – Whether to output the grid coordinates.

Returns:

  • dgrid (array) – Density field on the regular grid, if f is None.

  • fgrid (array) – Estimated field on the regular grid, if f is provided.

  • x2d, y2d (array) – Grid coordinates, if outputgrid is True.

fiesta.sph.sph4grid3D(x: ndarray, y: ndarray, z: ndarray, boxsize: float | List[float], ngrid: int | List[int], f: ndarray | None = None, origin: float | List[float] = 0.0, mass: ndarray | None = None, k: int = 32, periodic: bool = True, subsampling: int = 1, outputgrid: bool = False) → ndarray | Tuple[ndarray, ndarray, ndarray]

Estimates a field on a regular grid based on SPH k neighbours.

Parameters:

  • x (array) – Cartesian coordinates of the input points.

  • y (array) – Cartesian coordinates of the input points.

  • z (array) – Cartesian coordinates of the input points.

  • boxsize (float or list of float) – Size of the box in each dimension.

  • ngrid (int or list of int) – Number of grid points in each dimension.

  • f (array, optional) – Field values at the input points.

  • origin (float or list of float, optional) – Origin of the grid.

  • mass (array, optional) – Mass of the input points. If not provided, it is assumed to be 1 for all points.

  • k (int, optional) – Number of nearest neighbors to consider.

  • periodic (bool or list of bool, optional) – Whether to use periodic boundary conditions.

  • subsampling (int, optional) – Subsampling factor for the output grid.

  • outputgrid (bool, optional) – Whether to output the grid coordinates.

Returns:

  • dgrid (array) – Density field on the regular grid, if f is None.

  • fgrid (array) – Estimated field on the regular grid, if f is provided.

  • x3d, y3d, z3d (array) – Grid coordinates, if outputgrid is True.

fiesta.sph.mpi_sph4grid2D(x: ndarray, y: ndarray, boxsize: float | List[float], ngrid: int | List[int], MPI: object, f: ndarray | None = None, origin: float | List[float] = 0.0, mass: ndarray | None = None, k: int = 20, periodic: bool = True, subsampling: int = 1, outputgrid: bool = False, buffer_length: float = 0.0) → ndarray | Tuple[ndarray, ndarray, ndarray]

Estimates a field on a regular grid based on SPH k neighbours.

Parameters:

  • x (array) – Cartesian coordinates of the input points.

  • y (array) – Cartesian coordinates of the input points.

  • boxsize (float or list of float) – Size of the box in each dimension.

  • ngrid (int or list of int) – Number of grid points in each dimension.

  • MPI (object) – shift.mpiutils MPI object.

  • f (array, optional) – Field values at the input points.

  • origin (float or list of float, optional) – Origin of the grid.

  • mass (array, optional) – Mass of the input points. If not provided, it is assumed to be 1 for all points.

  • k (int, optional) – Number of nearest neighbors to consider.

  • periodic (bool or list of bool, optional) – Whether to use periodic boundary conditions.

  • subsampling (int, optional) – Subsampling factor for the output grid.

  • outputgrid (bool, optional) – Whether to output the grid coordinates.

  • buffer_length (float, optional) – Buffer length, must be smaller than the slab x-axis length.

Returns:

  • dgrid (array) – Density field on the regular grid, if f is None.

  • fgrid (array) – Estimated field on the regular grid, if f is provided.

  • x2d, y2d (array) – Grid coordinates, if outputgrid is True.

fiesta.sph.mpi_sph4grid3D(x: ndarray, y: ndarray, z: ndarray, boxsize: float | List[float], ngrid: int | List[int], MPI: object, f: ndarray | None = None, origin: float | List[float] = 0.0, mass: ndarray | None = None, k: int = 20, periodic: bool = True, subsampling: int = 1, outputgrid: bool = False, buffer_length: float = 0.0) → ndarray | Tuple[ndarray, ndarray, ndarray]

Estimates a field on a regular grid based on SPH k neighbours.

Parameters:

  • x (array) – Cartesian coordinates of the input points.

  • y (array) – Cartesian coordinates of the input points.

  • z (array) – Cartesian coordinates of the input points.

  • boxsize (float or list of float) – Size of the box in each dimension.

  • ngrid (int or list of int) – Number of grid points in each dimension.

  • MPI (object) – shift.mpiutils MPI object.

  • f (array, optional) – Field values at the input points.

  • origin (float or list of float, optional) – Origin of the grid.

  • mass (array, optional) – Mass of the input points. If not provided, it is assumed to be 1 for all points.

  • k (int, optional) – Number of nearest neighbors to consider.

  • periodic (bool or list of bool, optional) – Whether to use periodic boundary conditions.

  • subsampling (int, optional) – Subsampling factor for the output grid.

  • outputgrid (bool, optional) – Whether to output the grid coordinates.

  • buffer_length (float, optional) – Buffer length, must be smaller than the slab x-axis length.

Returns:

  • dgrid (array) – Density field on the regular grid, if f is None.

  • fgrid (array) – Estimated field on the regular grid, if f is provided.

  • x2d, y2d (array) – Grid coordinates, if outputgrid is True.