Construction of two dimensional temperature field from first derivative fields

Schlieren and its variants such as differential interferometry and schlieren microscopy, have been used extensively for flow visualization where first derivative fields are captured. The derivative fields obtained from the schlieren like methods can be further processed to estimate the temperature field when the first derivative fields relate to those of temperature. Temperature construction from first derivative field is an ill-posed problem owing to the experimental noise and a few discrete points where measured temperatures may be available. A new approach has been proposed where the domain is discretized into a large number of triangular elements and least-squares based finite-element analysis is performed over the discretized domain. The domain and boundaries are identified manually based on prior knowledge. Temperature fields have been constructed for experimentally obtained first derivative fields from a Differential Interferometer (DI) for different cases. The performance of the new methodology is found to be good.