Projective and Telescopic Projective Integration for Kinetic Mixtures

We propose fully explicit projective integration schemes for non-linear collisional kinetic equations for mixtures. The methods employ a sequence of small forward-Euler steps, intercalated with extrapolation steps. The telescopic approach repeats said extrapolations as the basis for an even larger step. This hierarchy renders the computational complexity of the method essentially independent of the stiffness of the problem, which permits the efficient solution of equations in the hyperbolic scaling with very small Knudsen numbers. We validate the scheme against standard test cases, and we demonstrate its prowess in dealing with large mass ratios, fluid instabilities and other complex phenomena. This is joint work with Thomas Rey.