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Some background: the Front-Tracking method uses a triangular surface mesh to describe the boundary between two immiscible fluids. To deal with the breakup and coalescence of the fluid interface, direct topological operations are executed on the surface mesh. Since in this case, there exists a history of topological operations between the old and the new mesh, it is possible to conservatively map a field stored on the surface mesh before and after topological operations. This is used e.g. to solve transport equations for a surfactant (a field that describes surface-active agents whose concentration on the fluid interface changes the surface tension).

What I would like to know if there is an established algorithm that can logically connect two completely topologically disconnected surface meshes that could serve as a mapping basis?

E.g. something like the nearest element search algorithm: for each triangle of surface mesh A, find the nearest triangle of surface mesh B.

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