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The applicability of the Parareal parallel-in-time integration scheme for thesolution of a linear, two-dimensional hyperbolic acoustic-advection system,which is often used as a test case for integration schemes for numericalweather prediction (NWP), is addressed. Parallel-in-time schemes are a possibleway to increase, on the algorithmic level, the amount of parallelism, arequirement arising from the rapidly growing number of CPUs in high performancecomputer systems. A recently introduced modification of the "parallel implicittime-integration algorithm" could successfully solve hyperbolic problemsarising in structural dynamics. It has later been cast into the framework ofParareal. The present paper adapts this modified Parareal and employs it forthe solution of a hyperbolic flow problem, where the initial value problemsolved in parallel arises from the spatial discretization of a partialdifferential equation by a finite difference method. It is demonstrated thatthe modified Parareal is stable and can produce reasonably accurate solutionswhile allowing for a noticeable reduction of the time-to-solution. Theimplementation relies on integration schemes already widely used in NWP (RK-3,partially split forward Euler, forward-backward). It is demonstrated that usingan explicit partially split scheme for the coarse integrator allows to avoidthe use of an implicit scheme while still achieving speedup.

Explicit Parallel-in-time Integration of a Linear Acoustic-Advection System