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Center for Nonlinear Studies |
Multi-physics problems are typically characterized by multiple simultaneous physical processes, each with different dynamics and stability properties. A plethora of time integration schemes have been proposed in the past 50 years aimed at efficiently addressing the challenges posed by such problems. We discuss the classical Runge-Kutta and linear multistep schemes, as well as the advent of such special time stepping methods as semi-implicit, implicit-explicit (IMEX), multi-rate, partitioned methods, and their numerical properties. We also present error control, predictors, and parallelization aspects of these algorithms.
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