VCG - ABC Flow

Description

The Arnold-Beltrami-Childress flow is an incompressible 3D flow, which represents an exact solution of the Euler's equation.

Details

The Arnold–Beltrami–Childress [Haller] flow is an incompressible three dimensional flow which is an exact solution to the Euler's equation. Its equation in cartesian coordinates is as follows:
$v(x,y,z)= \begin{pmatrix}A*\sin(z) + C*\cos(y)\\ B*\sin(x) + A*\cos(z)\\ C*\sin(y) + B*\cos(x)\end{pmatrix} $

Input

Output

vtkImageData

Parameters

Name
Description
Values/Default
A Parameter A of the ABC-Flow. 1.73205080757
B Parameter B of the ABC-Flow. 1.41421356237
C Parameter C of the ABC-Flow. 1.0
OutputSpaceTime Add time dimension to output dimenstions. 0
TimeRange Time range of samples. 0.0 0.0
TimeSteps Number of time steps for the samples. 1
Samples Number of samples in each dimension. 100 100 100
Origin Point of origin for the samples window. 0.0 0.0 0.0
Scale Scale of sample distance in each dimension. 6.283185307179586 6.283185307179586 6.283185307179586

Installation Instructions

Authors

Lutz Hofmann

References

G. Haller:
Distinguished material surfaces and coherent structures in three-dimensional fluid flows
Physica D: Nonlinear Phenomena, vol. 149, no. 4, pp. 248 - 277, 2001.

Acknowledgements