Multirate integration methods for hyperbolic PDEs
Adrian Sandu (Virginia Tech, Blacksburg, VA, U.S.A) and Emil Constantinescu (Virginia Tech, Blacksburg, VA, U.S.A)
Two families of explicit multirate time discretization methods based on Adams-Bashforth and partitioned Runge-Kutta are presented for hyperbolic conservation laws. They allow different timesteps to be used in different parts of the spatial domain, while being second order accurate in time and conservative. Linear and nonlinear stability are guaranteed only under local CFL conditions. The necessity to take small global timesteps restricted by the largest CFL number is thus avoided. Numerical results obtained for the advection and Burgers equations confirm the theoretical findings.