dpivsoft.Postprocessing

dpivsoft.Postprocessing.vorticity(x, y, u, v, method)

Vorticity omega = dv/dx - du/dy

Calculates the vorticity of a vector field u,v in a domain x,y, by different methods. The methods are described in Markus Raffel, Christian E. Willert, Steven T. Wereley, Jürgen Kompenhans Experimental Fluid Mechanics Particle image velocimetry: a practical guide [2nd ed.] Springer-Verlag

WARNING: Only works for equispaced data with x and y produced by meshgrid.

The output is omega of size

leastsq = (Nx-4)*(Ny-4) centered = (Nx-2)*(Ny-2) richardson = (Nx-4)*(Ny-4) circulation = (Nx-2)*(Ny-2) curl = (Nx-2)*(Ny-2)

12. Parras Universidad de Malaga (2014)

dpivsoft.Postprocessing.vortex_profile(xo, yo, rmax, x, y, u, v, xv, yv, omega, nr, ntheta)

Vortex data

Inputs:

xo: float

x position of the vortex center

yo: float

y position of the vortex center

rmax: float

Radious of the polar grid to

x: 2d float array

x meshgrid

y: 2d float array

y meshgrid

omega: 2d float array

vorticty on the x,y meshgrid

nr: float

number of points to interpolate along the radious on the polar grid

n:theta

number of points to interpolate along the angle on the polar grid

Outputs:

R: float array

radious of the interpolated polar grid

utheta_mean: float array

mean azimuthal velocity along the radious of the interpolated polar grid

omega_mean: float array

mean azimuthal velocity along the radious of the interpolated polar grid

gamma_mean: float array

mean azimuthal velocity along the radious of the interpolated polar grid

dpivsoft.Postprocessing.walls_vorticity(xx, yy, pos_x, pos_y, x, y, u, v, omega)

Modify vorticy over the walls of an object. The derivatives to obtain the curl, are done in forward diferences following the surface normal vector direction.

Inputs:

xx: float array

x points along object surface

yy: float array

y points along object surface

pos_x: float array

x index of points on object surface

pos_y: float array

y index of points on object surface

x: 2d float array

x meshgrid

y: 2d float array

y meshgrid

u: 2d float array

velocity in x direction of the field

v: 2d float array

velocity in y direction of the field

omega: 2d float array

vorticity on the x,y meshgrid

Outputs:

omega: 2d float array

fixed vorticity on the x,y meshgrid

dpivsoft.Postprocessing.divergence(x, y, u, v)

Return divergence of the 2D flow, which for a incompressible flow should be zero

Inputs:

x: 2d float array

x meshgrid

y: 2d float array

y meshgrid

u: 2d float array

velocity in x direction of the field

v: 2d float array

velocity in y direction of the field

Inputs:

flow_divergence: 2d float array

divergence of the 2d flow

dpivsoft.Postprocessing.stream_lines(x, y, u, v)

Plot streamlines of the computed 2d flow

Inputs:

x: 2d float array

x meshgrid

y: 2d float array

y meshgrid

u: 2d float array

velocity in x direction of the field

v: 2d float array

velocity in y direction of the field

dpivsoft.Postprocessing.ImpulseMethod(x, y, u, v, omega, rho, Vsol, mu, solid_points, t, accel=0)

Obtain forces over an object using Vortical impulse method, described by J.-Z. Wu, X.-Y. Lu, and L.-X. Zhuang. Integral force acting on a body due to local flow structures. J. Fluid Mech., 576:265286, 2007. AIAA J., 19:432–441, 1981. This formulation is based on the one presented in Martín-Alcántara, A., & Fernandez-Feria, R. (2019). Assessment of two vortex formulations for computing forces of a flapping foil at high Reynolds numbers. Physical Review Fluids, 4(2), 024702. but written in dimensional version. The reference frame must be always centered in the object. In case of an accelerated reference frame, it is taken into account by accel.

Inputs:

x: 2D float array

X-coordinates of the mesh grid over the flow field.

y: 2D float array

Y-coordinates of the mesh grid over the flow field.

u: 2D float array

Velocity field in the x-direction, defined on the x, y grid.

v: 2D float array

Velocity field in the y-direction, defined on the x, y grid.

omega: 2D float array

Vorticity field on the same x, y grid.

rho: float

Fluid density. This is a constant value for the entire domain.

Vsol: float

Volume of the solid object immersed in the fluid. Used for calculating forces due to added mass, etc.

mu: float

Dynamic viscosity of the fluid. Also constant throughout the domain.

solid_points: list of coordinates tuples

Coordinates or mask identifying the solid object within the fluid as a list of (x, y) tuples

t: 1D float array

Time vector. Each element corresponds to a frame or timestep in the simulation or measurement.

accel: 2D float array

Instantaneous acceleration in x and y direction of the moving reference frame (centered on the object). Shape (N,2)

Outputs:

F_v: 2D foat array

Term of vortex force. Size (N,2), for x and y components.

F_i: 2D float array

Impulse term of the force. Size (N,2), for x and y components.

Fsol: 2D float array

Force integrated over the volume of the object. Size (N,2), for x and y components.

F_oe: 2D float array

Contribution to the total force of the vorticity leaving the control volume. Size (N,2), for x and y components.

F_mu: 2D float array

Viscous contribution to the force of vorticity leaving the control volume. Size (N,2), for x and y components.

dpivsoft.Postprocessing.ProjectionMethod(x, y, u, v, omega, grad_phi, rho, mu, solid_points, added_m=array([0., 0.]), accel=0)

Obtain forces over an object using projection method. The formulation used is from C.-C. Chang. Potential flow and forces for the incompressible viscous flow. Proc. R. Soc. A-Math. Phys. Engng Sci., 437:517–525, 1992. This formulation is based on the one presented in Martín-Alcántara, A., & Fernandez-Feria, R. (2019). Assessment of two vortex formulations for computing forces of a flapping foil at high Reynolds numbers. Physical Review Fluids, 4(2), 024702. but written in dimensional version. The reference frame must be centered in the object and accelerations on it are taken into account by accel.

Inputs:

x: 2D float array

X-coordinates of the mesh grid over the flow field.

y: 2D float array

Y-coordinates of the mesh grid over the flow field.

u: 2D float array

Velocity field in the x-direction, defined on the x, y grid.

v: 2D float array

Velocity field in the y-direction, defined on the x, y grid.

omega: 2D float array

Vorticity field on the same x, y grid.

grad_phi: 4D float array

Gradients of the two projection potentials, given by solving ∇2 ϕ = 0 , ns · ∇ϕ = −ns dimension of (2,2,y,x) with grad_phi[i,j] = dϕ_i/dx_j, arranged like:

[ϕ_xx, ϕ_xy] [ϕ_yx, ϕ_yy]

rho: float

Fluid density. This is a constant value for the entire domain.

mu: float

Dynamic viscosity of the fluid. Also constant throughout the domain.

solid_points: list of coordinates tuples

Coordinates or mask identifying the solid object within the fluid as a list of (x, y) tuples

t: 1D float array

Time vector. Each element corresponds to a frame or timestep in the simulation or measurement.

added_m: float list

added mass tensor obtained from integrating ϕ(∂ϕ/∂n)dS along the solid surface. Only needed if accelerated reference frame.

accel: 2D float array

Instantaneous acceleration in x and y direction of the moving reference frame (centered on the object). Shape (N,2)

Outputs:

F: 2D float array

Total force over the object. Size (N,2), for x and y components.

Fv: 2D float array

Vortical contribution to force. Size (N,2), for x and y components.

Fmu: 2D float array

Viscous contribution to force. Size (N,2), for x and y components.

dpivsoft.Postprocessing.Surface_projection(xx, yy, pos_x, pos_y, grad_phi, omega, mu)

Compute the viscous vortex-force contribution on a solid surface for the projection method.

The object boundary is defined by ordered points (xx, yy) and their corresponding mesh indices (pos_x, pos_y). Normal vectors are estimated along the path, and the viscous contribution is integrated using Simpson’s rule.

Inputs:

xx, yy: 1D float arrays

Ordered coordinates of the object boundary.

pos_x, pos_y: 1D int arrays

Mesh indices corresponding to the boundary coordinates.

x, y: 2D float arrays

Mesh grid coordinates (used only for consistency).

grad_phi: 4D float array

Hessian of the potential function, shape (2, 2, ny, nx).

omega: 3D float array

Vorticity field over time, shape (ny, nx, nt).

mu: float

Dynamic viscosity of the fluid.

Outputs:

Fx: 1D float array

x-component of the viscous surface force over time.

Fy: 1D float array

y-component of the viscous surface force over time.

dpivsoft.Postprocessing.Object(x, y, points, res=4)

Generate a binary mask and extract ordered boundary coordinates of a 2D object defined by a polygon within a structured mesh. The function identifies which mesh nodes lie inside the polygon, detects the boundary via dilation, and reorders the perimeter points to form a continuous path using a nearest-neighbor graph.

Inputs:

x: 2D float array

X-coordinates of the mesh grid.

y: 2D float array

Y-coordinates of the mesh grid.

points: array-like

(x, y) coordinates defining the polygonal shape of the object.

res: int, optional

Decimal precision for rounding mesh coordinates (default = 4).

Outputs:

x: 1D float array

Ordered x-coordinates of boundary points.

y: 1D float array

Ordered y-coordinates of boundary points.

posx: 1D int array

Mesh x-indices of boundary points.

posy: 1D int array

Mesh y-indices of boundary points.

mesh: 2D uint8 array

Binary mask of the domain (0 = solid, 1 = fluid).

dpivsoft.Postprocessing.ControlVolume(x, y, u, v, rho, mu, t, accel=0, p=0)

Compute hydrodynamic forces on a 2D body using the Control Volume method, based on the integral formulation of the momentum equation applied to a moving volume enclosing the body. This method follows the approach described in:

FERIA, Ramón Fernández; CASANOVA, J. Ortega. Mecánica de fluidos. Servicio de Publicaciones e Intercambio Científico de la Universidad de Málaga, 2001.

The implementation assumes a 2D incompressible flow over a domain defined by the (x, y) mesh, with velocity fields u and v. The control volume encloses the object and may be moving or accelerating. The total force is computed from several contributing terms: the unsteady and convective momentum flux, pressure contribution, viscous stresses, and added-mass effect if the reference frame is non-inertial.

The reference frame must always be centered on the object. In case of a moving or accelerated frame, the added-mass correction is applied using accel.

Inputs:

x: 2D float array

X-coordinates of the mesh grid over the flow field.

y: 2D float array

Y-coordinates of the mesh grid over the flow field.

u: 3D float array

X-component of the velocity field over time. Shape (nx, ny, nt).

v: 3D float array

Y-component of the velocity field over time. Shape (nx, ny, nt).

rho: float

Fluid density (assumed constant).

mu: float

Dynamic viscosity of the fluid (assumed constant).

t: 1D float array

Time vector. Each entry corresponds to a timestep.

accel: float or 2D float array, optional

Acceleration of the reference frame. If scalar, assumed zero contribution. If array of shape (nt, 2), it is used for added mass correction.

p: 2D float array or float, optional

Pressure field (same shape as u and v) or scalar zero if not used.

Outputs:

F_v: 2D float array

Convective momentum flux contribution to total force. Shape (nt, 2).

F_i: 2D float array

Local (unsteady) momentum contribution. Shape (nt, 2).

Fsol: 2D float array

Added-mass term due to acceleration of the control volume. Shape (nt, 2).

F_oe: 2D float array

Net outflow of momentum across control volume boundaries. Shape (nt, 2).

F_mu: 2D float array

Viscous stress contribution to the force. Shape (nt, 2).

dpivsoft.Postprocessing.FieldDerivatives(rho, dx, dy, u, v, accel, mu, dt)

Compute the spatial/temporal velocity derivatives and the pressure gradient field for the Control Volume method.

Spatial derivatives use central finite differences (which crops one node off each spatial border); time derivatives are central in the interior and one-sided at the first/last frame. The pressure gradient is obtained from the incompressible momentum equation ∇p = mu·∇²u - rho·(u·∇)u - rho·∂u/∂t on the cropped domain.

Inputs:

rho: float

Fluid density.

dx, dy: float

Grid spacing in x and y.

u, v: 3D float array

Velocity components over time, shape (ny, nx, nt).

accel: float or 2D float array

Reference-frame acceleration (unused here; kept for signature consistency with the caller).

mu: float

Dynamic viscosity.

dt: float

Time step between frames.

Outputs:

Gradx, Grady: 3D float array

x and y components of the pressure gradient on the cropped (interior) domain, shape (ny-2, nx-2, nt).

u, v: 3D float array

Velocity components cropped to the interior domain.

dudx, dudy, dvdx, dvdy: 3D float array

First spatial derivatives of the velocity on the interior domain.