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Large-scale multiphysics simulations are computationally challenging due tothe coupling of multiple processes with widely disparate time scales. Theadvent of exascale computing systems exacerbates these challenges, since theseenable ever increasing size and complexity. Recently, there has been renewedinterest in developing multirate methods as a means to handle the large rangeof time scales, as these methods may afford greater accuracy and efficiencythan more traditional approaches of using IMEX and low-order operator splittingschemes. However, there have been few performance studies that comparedifferent classes of multirate integrators on complex application problems. Westudy the performance of several newly developed multirate infinitesimal (MRI)methods, implemented in the SUNDIALS solver package, on two reacting flow modelproblems built on structured mesh frameworks. The first model revisits the workof Emmet et al. (2014) on a compressible reacting flow problem with complexchemistry that is implemented using BoxLib but where we now include comparisonsbetween a new explicit MRI scheme with the multirate spectral deferredcorrection (SDC) methods in the original paper. The second problem uses thesame complex chemistry as the first problem, combined with a simplified flowmodel, but run at a large spatial scale where explicit methods becomeinfeasible due to stability constraints. Two recently developedimplicit-explicit MRI multirate methods are tested. These methods rely onadvanced features of the AMReX framework on which the model is built, such asmultilevel grids and multilevel preconditioners. The results from these twoproblems show that MRI multirate methods can offer significant performancebenefits on complex multiphysics application problems and that these methodsmay be combined with advanced spatial discretization to compound the advantagesof both.

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks