Animation of chaotic mixing by a backward Poincare cell-map method

A Backward Poincare cell-mapping (BPCM) method has been developed for anima ting chaotic fluid mixing. The chaotic mixing field considered is induced b y periodically rotating tile secondary flow of incompressible fluids in a c urved pipe. The pipe's cross-section is transformed into a cell space where each cell is initially assigned with a color code and mapped by integratin g the velocity field forward in time. The mixing process is thus animated e fficiently with each cell being painted with its color on a computer screen . We propose the backward Poincare cell-mapping instead of direct Poincare cell-mapping as a useful tool for probing the chaotic fluid mixing and for animating the phase deformation of nonlinear dynamical systems.