Constrained Field Construction Using Bernstein Polynomial Derived Operators

This method recasts the mass-conservation equation as a Sylvester equation employing high-order derivative operators derived from modified Bernstein polynomial expansions. Given prescribed velocity fields, the algorithm yields a constrained, least-squared solution for the associated density field. To demonstrate the practical utility of this methodology, it is applied to a computationally-derived two-dimensional isolator dataset. This reconstruction method is envisioned to be used in conjunction with diagnostic techniques to aid in the quantification of isolator flow fields, since obtaining highly characterized datasets within this engine component is exceedingly difficult.