Conservative hyperbolic droplet solver for aircraft icing

This paper joins two different methods from the literature to obtain a second-order finite volume convective scheme for computing the Eulerian two-phase flows composed of air and small water droplets. The work examines the numerical solution for the various numerical instabilities as well as zero and negative values met in several numerical application cases from the literature for the water to air volume fraction. The numerical problems are due to the non-strictly hyperbolic nature of the Eulerian droplet equations along with the scheme used. A term similar to the particle pressure is proposed to modify the problem from a weakly to a strictly hyperbolic one. A modified Harten-Lax-van Leer-Contact convective scheme is used on the modified hyperbolic equations. Results with the new scheme are presented on 2D and 2.5D test problems as a verification. The proposed HLLC scheme improves on a classical upwind scheme for the single and three-element airfoil cases examined