Computation of a distance field by means of combined geometry representation in fluid dynamics simulations with embedded boundaries

We present a method for calculating the signed distance field to three-dimensional geometric models by representing them as a result of Boolean operations on elementary objects for each of which the signed distance is known. Two versions of the algorithm are proposed. The first is a simplified version for quick calculation of the rough distance approximation (with an exact zero isosurface and correct separation of domains inside and outside the model). The second version includes calculation of the distance to the intersection contours between elements, allowing the distance to be reconstructed with a greater accuracy without considerable additional computational costs. Both methods are much faster than the computation of distance based on the triangulation of the surfaces. The proposed approach also allows for interactively changing relative positions and orientation of the geometry parts; this makes it possible to perform calculations with moving boundaries. The approach has been tested in fluid dynamics simulation with an interphase boundary and adaptive multilevel grid refinement in Basilisk open source code for simulation of multiphase flows.