1 research outputs found
A consistent analytical formulation for volume-estimation of geometries enclosed by implicitly defined surfaces
We have derived an analytical formulation for estimating the volume of
geometries enclosed by implicitly defined surfaces. The novelty of this work is
due to two aspects. First we provide a general analytical formulation for all
two-dimensional cases, and for elementary three three-dimensional cases by
which the volume of general three-dimensional cases can be computed. Second,
our method addresses the inconsistency issue due to mesh refinement. It is
demonstrated by several two-dimensional and three-dimensional cases that this
analytical formulation exhibits 2nd-order accuracy