Minimization of discrete errors in two-phase flow modeling with unequal densities

Particle-based methods, like the lattice Boltzmann method, solve a unified incompressible fluid dynamical formulation along with interface tracking to solve fluid dynamical equations. This approach requires a correction term to account for the unequal densities in the two-phase system. Surprisingly, these correction terms reduce the error associated with external forces (gravity or surface tension). The project aims to explain these observations in terms of the coupling of the discretization errors in the momentum balance equations. The work requires familiarity with C++.