Volume determination for bulk materials in bunkers

A simple model for the determination of the shape of large granular piles in complicated geometries is discussed. An eikonal formulation of the problem is proposed. Two distinct cases arise. In cylindrical geometries, i.e., if both container and possible obstacles have vertical walls, the problem is equivalent to a two-dimensional travel time problem with obstacles, while in general geometries, this analogy breaks down. In the first case, classical one-sided discretizations are generalized to handle obstacles without loss in accuracy. In the second case, a fast and efficient numerical method is proposed, implemented and tested. The discrete problems are solved through fast marching