An interface reconstruction method based on analytical formulae for 2D planar and axisymmetric arbitrary convex cells

In this paper, we propose a non-iterative interface reconstruction method for 2D planar and axisymmetric geometries that is valid for arbitrary convex cells and intended to be used in multi-material simulation codes with sharp interface treatment for instance. Assuming that the normal vector to the interface is known, we focus on the computation of the line constant so that the polygon resulting from the cell-interface intersection has the requested volume. To this end, we first decompose the cell in trapezoidal elements and then propose a new approach to derive an exact formula for the trapezoids volumes. This formula, derived for both the planar and axisymmetric cases, is used to first bracket and then find the line constant that exactly matches the prescribed volume. The computational efficiency of the proposed method is demonstrated over a large number of reproducible conditions and against two existing methods.