Interpolation

interpolate_line(start, end_, n_points, semi, ref_system, sol; endpoint=true,
                 smoothing_length=initial_smoothing_length(ref_system), cut_off_bnd=true,
                 clip_negative_pressure=false)

Interpolates properties along a line in a TrixiParticles simulation. The line interpolation is accomplished by generating a series of evenly spaced points between start and end_. If endpoint is false, the line is interpolated between the start and end points, but does not include these points.

See also: interpolate_points, interpolate_plane_2d, interpolate_plane_2d_vtk, interpolate_plane_3d.

Arguments

• start: The starting point of the line.
• end_: The ending point of the line.
• n_points: The number of points to interpolate along the line.
• semi: The semidiscretization used for the simulation.
• ref_system: The reference system for the interpolation.
• sol: The solution state from which the properties are interpolated.

Keywords

• endpoint=true: A boolean to include (true) or exclude (false) the end point in the interpolation.
• smoothing_length=initial_smoothing_length(ref_system): The smoothing length used in the interpolation.
• cut_off_bnd=true: Boolean to indicate if quantities should be set to NaN when the point is "closer" to the boundary than to the fluid in a kernel-weighted sense. Or, in more detail, when the boundary has more influence than the fluid on the density summation in this point, i.e., when the boundary particles add more kernel-weighted mass than the fluid particles.
• clip_negative_pressure=false: One common approach in SPH models is to clip negative pressure values, but this is unphysical. Instead we clip here during interpolation thus only impacting the local interpolated value.

Returns

• A NamedTuple of arrays containing interpolated properties at each point along the line.

Examples

# Interpolating along a line from [1.0, 0.0] to [1.0, 1.0] with 5 points
results = interpolate_line([1.0, 0.0], [1.0, 1.0], 5, semi, ref_system, sol)

interpolate_plane_2d(min_corner, max_corner, resolution, semi, ref_system, sol;
                     smoothing_length=initial_smoothing_length(ref_system), cut_off_bnd=true,
                     clip_negative_pressure=false)

Interpolates properties along a plane in a TrixiParticles simulation. The region for interpolation is defined by its lower left and top right corners, with a specified resolution determining the density of the interpolation points.

The function generates a grid of points within the defined region, spaced uniformly according to the given resolution.

See also: interpolate_plane_2d_vtk, interpolate_plane_3d, interpolate_line, interpolate_points.

Arguments

• min_corner: The lower left corner of the interpolation region.
• max_corner: The top right corner of the interpolation region.
• resolution: The distance between adjacent interpolation points in the grid.
• semi: The semidiscretization used for the simulation.
• ref_system: The reference system for the interpolation.
• sol: The solution state from which the properties are interpolated.

Keywords

• smoothing_length=initial_smoothing_length(ref_system): The smoothing length used in the interpolation.
• cut_off_bnd=true: Boolean to indicate if quantities should be set to NaN when the point is "closer" to the boundary than to the fluid in a kernel-weighted sense. Or, in more detail, when the boundary has more influence than the fluid on the density summation in this point, i.e., when the boundary particles add more kernel-weighted mass than the fluid particles.
• clip_negative_pressure=false: One common approach in SPH models is to clip negative pressure values, but this is unphysical. Instead we clip here during interpolation thus only impacting the local interpolated value.

Returns

• A NamedTuple of arrays containing interpolated properties at each point within the plane.

Examples

# Interpolating across a plane from [0.0, 0.0] to [1.0, 1.0] with a resolution of 0.2
results = interpolate_plane_2d([0.0, 0.0], [1.0, 1.0], 0.2, semi, ref_system, sol)

interpolate_plane_2d_vtk(min_corner, max_corner, resolution, semi, ref_system, sol;
                         smoothing_length=initial_smoothing_length(ref_system), cut_off_bnd=true,
                         clip_negative_pressure=false, output_directory="out", filename="plane")

Interpolates properties along a plane in a TrixiParticles simulation and exports the result as a VTI file. The region for interpolation is defined by its lower left and top right corners, with a specified resolution determining the density of the interpolation points.

The function generates a grid of points within the defined region, spaced uniformly according to the given resolution.

See also: interpolate_plane_2d, interpolate_plane_3d, interpolate_line, interpolate_points.

Arguments

• min_corner: The lower left corner of the interpolation region.
• max_corner: The top right corner of the interpolation region.
• resolution: The distance between adjacent interpolation points in the grid.
• semi: The semidiscretization used for the simulation.
• ref_system: The reference system for the interpolation.
• sol: The solution state from which the properties are interpolated.

Keywords

• smoothing_length=initial_smoothing_length(ref_system): The smoothing length used in the interpolation.
• output_directory="out": Directory to save the VTI file.
• filename="plane": Name of the VTI file.
• cut_off_bnd=true: Boolean to indicate if quantities should be set to NaN when the point is "closer" to the boundary than to the fluid in a kernel-weighted sense. Or, in more detail, when the boundary has more influence than the fluid on the density summation in this point, i.e., when the boundary particles add more kernel-weighted mass than the fluid particles.
• clip_negative_pressure=false: One common approach in SPH models is to clip negative pressure values, but this is unphysical. Instead we clip here during interpolation thus only impacting the local interpolated value.

Examples

# Interpolating across a plane from [0.0, 0.0] to [1.0, 1.0] with a resolution of 0.2
results = interpolate_plane_2d([0.0, 0.0], [1.0, 1.0], 0.2, semi, ref_system, sol)

interpolate_plane_3d(point1, point2, point3, resolution, semi, ref_system, sol;
                     smoothing_length=initial_smoothing_length(ref_system), cut_off_bnd=true,
                     clip_negative_pressure=false)

Interpolates properties along a plane in a 3D space in a TrixiParticles simulation. The plane for interpolation is defined by three points in 3D space, with a specified resolution determining the density of the interpolation points.

The function generates a grid of points on a parallelogram within the plane defined by the three points, spaced uniformly according to the given resolution.

See also: interpolate_plane_2d, interpolate_plane_2d_vtk, interpolate_line, interpolate_points.

Arguments

• point1: The first point defining the plane.
• point2: The second point defining the plane.
• point3: The third point defining the plane. The points must not be collinear.
• resolution: The distance between adjacent interpolation points in the grid.
• semi: The semidiscretization used for the simulation.
• ref_system: The reference system for the interpolation.
• sol: The solution state from which the properties are interpolated.

Keywords

• smoothing_length=initial_smoothing_length(ref_system): The smoothing length used in the interpolation.
• cut_off_bnd=true: Boolean to indicate if quantities should be set to NaN when the point is "closer" to the boundary than to the fluid in a kernel-weighted sense. Or, in more detail, when the boundary has more influence than the fluid on the density summation in this point, i.e., when the boundary particles add more kernel-weighted mass than the fluid particles.
• clip_negative_pressure=false: One common approach in SPH models is to clip negative pressure values, but this is unphysical. Instead we clip here during interpolation thus only impacting the local interpolated value.

Returns

• A NamedTuple of arrays containing interpolated properties at each point within the plane.

Examples

# Interpolating across a plane defined by points [0.0, 0.0, 0.0], [1.0, 0.0, 0.0], and [0.0, 1.0, 0.0]
# with a resolution of 0.1
results = interpolate_plane_3d([0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], 0.1, semi, ref_system, sol)

interpolate_points(point_coords::AbstractMatrix, semi, ref_system, sol;
                   smoothing_length=initial_smoothing_length(ref_system),
                   cut_off_bnd=true, clip_negative_pressure=false)

Performs interpolation of properties at specified points in a TrixiParticles simulation. The interpolation utilizes the same kernel function of the SPH simulation to weigh contributions from nearby particles.

See also: interpolate_line, interpolate_plane_2d, interpolate_plane_2d_vtk, interpolate_plane_3d, .

Arguments

• point_coords: A matrix of point coordinates, where the $i$-th column holds the coordinates of particle $i$.
• semi: The semidiscretization used in the SPH simulation.
• ref_system: The reference system defining the properties of the SPH particles.
• sol: The current solution state from which properties are interpolated.

Keywords

• smoothing_length=initial_smoothing_length(ref_system): The smoothing length used in the interpolation.
• cut_off_bnd=true: Boolean to indicate if quantities should be set to NaN when the point is "closer" to the boundary than to the fluid in a kernel-weighted sense. Or, in more detail, when the boundary has more influence than the fluid on the density summation in this point, i.e., when the boundary particles add more kernel-weighted mass than the fluid particles.
• clip_negative_pressure=false: One common approach in SPH models is to clip negative pressure values, but this is unphysical. Instead we clip here during interpolation thus only impacting the local interpolated value.

Returns

• A NamedTuple of arrays containing interpolated properties at each point.

Examples

# For a single point create a 2x1 matrix
result = interpolate_points([1.0; 0.5;;], semi, ref_system, sol)

# For multiple points
points = [1.0 1.0 1.0; 0.5 0.6 0.7]
results = interpolate_points(points, semi, ref_system, sol)