Simulation of extraction of velocity from passive scalar data in a two-dimensional diverging channel flow

A technique for determining n-dimensional (n =2,3) velocity fields from measurement of n-1 passive or reactive scalars has recently been developed [Phys. Fluids 7, 754 (1995)]. The method utilizes n linear, first-order, uncoupled hyperbolic equations for n velocity components, derived from transport equations for n-1 scalars and conservation of mass. The velocity is determined by integration along the characteristic curves defined by the hyperbolic equations. Here we present the results of a computational proof-of-concept study for a steady, two-dimensional, diverging channel flow. We consider the effects of the resolution of the grid (and the shape of its elements) on which the scalar is known and its derivatives are approximated, the integration step size used to calculate the velocity components along characteristic curves, and the effects of multiplicative noise introduced into the scalar field. The results show that extraction of the velocity by integration of the equations along characteristics is stable, and that the techniques proposed for removal of singularities are effective. For steady flows, we show that noise in the scalar field measurements can be dealt with by extracting the velocity from the mean of several noisy scalar fields.