Multidimensional aware subfaced-based Finite Volume scheme for the Eulerian droplet system of equation

In clouds and under cold weather, water droplets impact and freeze on aircraft structures. The Eulerian model for the droplet flow predicts the impinging water mass. The model equations are close to the Euler equations but without the pressure term, known as pressureless Euler model. Consequently, the resulting system is only weakly hyperbolic and standard Riemann solvers strongly relying on the eigenstructure of the system cannot solve the Eulerian model. To circumvent this problem, the model is supplemented with an extra-term mimicking the divergence of a particle pressure. The main purpose of this work is to implement a multidimensional aware Riemann solver for a Finite Volume simulation code for the modified formulation of the Eulerian droplet model. The numerical method should preserve physical properties such as the positivity of the liquid water content, and must produce accurate results without sacrificing the general robustness. The flow around a cylinder assess the numerical method in 2D on radial meshes. •New multidimensional Riemann solver for the modified formulation of the Eulerian droplet model.•This model is only weakly hyperbolic. An additional term is added.•The multidimensional Riemann solver is derived and adapted to the Eulerian droplet model.•The proposed method, preserves physical properties such as positivity, is accurate and robust.