157 research outputs found
Parallel-in-time integration of the shallow water equations on the rotating sphere using Parareal and MGRIT
Despite the growing interest in parallel-in-time methods as an approach to
accelerate numerical simulations in atmospheric modelling, improving their
stability and convergence remains a substantial challenge for their application
to operational models. In this work, we study the temporal parallelization of
the shallow water equations on the rotating sphere combined with time-stepping
schemes commonly used in atmospheric modelling due to their stability
properties, namely an Eulerian implicit-explicit (IMEX) method and a
semi-Lagrangian semi-implicit method (SL-SI-SETTLS). The main goal is to
investigate the performance of parallel-in-time methods, namely Parareal and
Multigrid Reduction in Time (MGRIT), when these well-established schemes are
used on the coarse discretization levels and provide insights on how they can
be improved for better performance. We begin by performing an analytical
stability study of Parareal and MGRIT applied to a linearized ordinary
differential equation depending on the choice of a coarse scheme. Next, we
perform numerical simulations of two standard tests to evaluate the stability,
convergence and speedup provided by the parallel-in-time methods compared to a
fine reference solution computed serially. We also conduct a detailed
investigation on the influence of artificial viscosity and hyperviscosity
approaches, applied on the coarse discretization levels, on the performance of
the temporal parallelization. Both the analytical stability study and the
numerical simulations indicate a poorer stability behaviour when SL-SI-SETTLS
is used on the coarse levels, compared to the IMEX scheme. With the IMEX
scheme, a better trade-off between convergence, stability and speedup compared
to serial simulations can be obtained under proper parameters and artificial
viscosity choices, opening the perspective of the potential competitiveness for
realistic models.Comment: 35 pages, 23 figure
Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization
We propose an extension of the discretization approaches for multilayer
shallow water models, aimed at making them more flexible and efficient for
realistic applications to coastal flows. A novel discretization approach is
proposed, in which the number of vertical layers and their distribution are
allowed to change in different regions of the computational domain.
Furthermore, semi-implicit schemes are employed for the time discretization,
leading to a significant efficiency improvement for subcritical regimes. We
show that, in the typical regimes in which the application of multilayer
shallow water models is justified, the resulting discretization does not
introduce any major spurious feature and allows again to reduce substantially
the computational cost in areas with complex bathymetry. As an example of the
potential of the proposed technique, an application to a sediment transport
problem is presented, showing a remarkable improvement with respect to standard
discretization approaches
Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks
Large-scale multiphysics simulations are computationally challenging due to
the coupling of multiple processes with widely disparate time scales. The
advent of exascale computing systems exacerbates these challenges, since these
enable ever increasing size and complexity. Recently, there has been renewed
interest in developing multirate methods as a means to handle the large range
of time scales, as these methods may afford greater accuracy and efficiency
than more traditional approaches of using IMEX and low-order operator splitting
schemes. However, there have been few performance studies that compare
different classes of multirate integrators on complex application problems. We
study the performance of several newly developed multirate infinitesimal (MRI)
methods, implemented in the SUNDIALS solver package, on two reacting flow model
problems built on structured mesh frameworks. The first model revisits the work
of Emmet et al. (2014) on a compressible reacting flow problem with complex
chemistry that is implemented using BoxLib but where we now include comparisons
between a new explicit MRI scheme with the multirate spectral deferred
correction (SDC) methods in the original paper. The second problem uses the
same complex chemistry as the first problem, combined with a simplified flow
model, but run at a large spatial scale where explicit methods become
infeasible due to stability constraints. Two recently developed
implicit-explicit MRI multirate methods are tested. These methods rely on
advanced features of the AMReX framework on which the model is built, such as
multilevel grids and multilevel preconditioners. The results from these two
problems show that MRI multirate methods can offer significant performance
benefits on complex multiphysics application problems and that these methods
may be combined with advanced spatial discretization to compound the advantages
of both
IMplicit-EXplicit Formulations for Discontinuous Galerkin Non-Hydrostatic Atmospheric Models
This work presents IMplicit-EXplicit (IMEX) formulations for discontinuous
Galerkin (DG) discretizations of the compressible Euler equations governing
non-hydrostatic atmospheric flows. In particular, we show two different IMEX
formulations that not only treat the stiffness due to the governing dynamics
but also the domain discretization. We present these formulations for two
different equation sets typically employed in atmospheric modeling. For both
equation sets, efficient Schur complements are derived and the challenges and
remedies for deriving them are discussed. The performance of these IMEX
formulations of different orders are investigated on both 2D (box) and 3D
(sphere) test problems and shown to achieve their theoretical rates of
convergence and their efficiency with respect to both mesoscale and global
applications are presented
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