Asymptotic Preserving and Multiscale Methods for Kinetic and Hyperbolic Problems

Semi-implicit IMEX schemes for evolutionary partial differential equations

Giovanni Russo

Università di Catania
[SLIDES]

new formulation of implicit-explicit (IMEX) Runge-Kutta (R-K) methods for the numerical discretization of time dependent partial differential equations. The approach is based on identifying the (linear) dependence on the unknown of the system which generates the stiffness. Only the stiff dependence is treated implicitly, then making the whole method much simpler than fully implicit ones. This approach generalizes classical IMEX methods based on additive and partitioned R-K, and allows a novel application of semi-implicit schemes. Several applications will be presented to a variety of systems. In particular, application to a class of degenerate convection-diffusion problems, for which the new semi-implicit approach allows is more cost-effective when compared to IMEX schemes with fully implicit treatment. There are cases which require fully-implicit treatment of the stiff term, such as the case of low Mach-number flow for Euler equations of gas dynamics.