Variational method for determining pressure from velocity in two dimensions

This paper proposes a variational formulation with a smoothness constraint for extraction of pressure from two-dimensional velocity field. The method of characteristics is first described as a reduced case to obtain pressure data by a line integral along a given line. Then, a global optimization method is developed, and the Euler-Lagrange equation is obtained to determine a pressure field from velocity data in a domain with suitable boundary conditions. Numerical algorithms are developed to solve the Euler-Lagrange equation with suitable boundary conditions. The accuracy of the developed methods and the effects of the relevant parameters on extraction of pressure are evaluated on a simulated two-dimensional oblique Hiemenz flow. Subsequently, in an experimental case, pressure fields near a freely flying hawkmoth are estimated from high-resolution velocity fields that are obtained by applying the optical flow method to high-speed Schlieren photography images. [GRAPHICS] .