Boundary-independent shortest path integration algorithm for planar pressure reconstruction

The reconstruction of the conserved scalar from gradient field like pressure is important in many applications. Most current direct integration algorithms initiate the integration at the domain boundaries, where gradient measurement is often unreliable. This study proposes the Boundary-Independent Shortest Path (BISP) integration method, which initiates at an internal node and grows outwards towards the boundaries, thereby eliminating any dependency on the boundaries. This integration algorithm can be directly applied to pressure gradient fields containing inner voids of arbitrary shapes and sizes without compromising the accuracy.