Multirate Timestepping Methods for Hyperbolic Conservation Laws

Abstract

This paper constructs multirate time discretizations for hyperbolic conservation laws that allow different time-steps to be used in different parts of the spatial domain. The discretization is second order accurate in time and preserves the conservation and stability properties under local CFL conditions. Multirate timestepping avoids the necessity to take small global time-steps (restricted by the largest value of the Courant number on the grid) and therefore results in more efficient algorithms.

On Extrapolated Multirate Methods

“…The reader can also examine more recent work presented in [Günther et al, 2001;Kvaernø and Rentrop, 1999;Kvaernø, 2000;Bartel and Günther, 2002]. Similar concepts for conservative solutions are found in [Constantinescu and Sandu, 2007;Dawson and Kirby, 2001;Kirby, 2002;Tang and Warnecke, 2006] and for parabolic equations using a locally self-adjusting multirate timestepping [Savcenco et al, 2005[Savcenco et al, , 2006.…”

Multirate Numerical Integration for Stiff ODEs

“…In [1,13,14] multirate methods have been applied to the modeling of electrical networks. Multirate methods for hyperbolic conservation laws were studied by Constantinescu and Sandu [2].…”

Error Analysis of Explicit Partitioned Runge–Kutta Schemes for Conservation Laws

“…Therefore, as noted in [3], the discrete conservation property h T u n+1 = h T u n will be satisfied provided that…”