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-dimensionalgeometric models by representing them as a result of Boolean operations on elementary objects foreach of which the signed distance is known. Two versions of the algorithm are proposed. The firstis a simplified version for quick calculation of the rough distance approximation (with an exactzero isosurface and correct separation of domains inside and outside the model). The secondversion includes calculation of the distance to the intersection contours between elements, allowingthe distance to be reconstructed with a greater accuracy without considerable additionalcomputational costs. Both methods are much faster than the computation of distance based onthe triangulation of the surfaces. The proposed approach also allows for interactively changingrelative positions and orientation of the geometry parts; this makes it possible to performcalculations with moving boundaries. The approach has been tested in fluid dynamics simulationwith an interphase boundary and adaptive multilevel grid refinement in Basilisk open source code for simulation ofmultiphase flows.