Fluid dynamics simulations using grid-based methods, such as the lattice Boltzmann equation, can benefit from parallel-in-space computation. However, for a fixed-size simulation of this type, the efficiency of larger ...
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Fluid dynamics simulations using grid-based methods, such as the lattice Boltzmann equation, can benefit from parallel-in-space computation. However, for a fixed-size simulation of this type, the efficiency of larger processor counts will saturate when the number of grid points per core becomes too small. To overcome this fundamental strong scaling limit in space-parallel approaches, we present a novel time-parallel version of the lattice Boltzmann method using the parareal algorithm. This method is based on a predictor-corrector scheme combined with mesh refinement to enable the simulation of larger number of time steps. We present results of up to a 32x increase in speed for a model system consisting of a cylinder with conditions for laminar flow. The parallel gain obtainable is predicted with strong accuracy, providing a quantitative understanding of the potential impact of this method. (C) 2014 Elsevier Inc. All rights reserved.
We present a novel class of integrators for differential equations that are suitable for parallel in time computation, whose structure can be considered as a generalization of the extrapolation methods. Starting with ...
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We present a novel class of integrators for differential equations that are suitable for parallel in time computation, whose structure can be considered as a generalization of the extrapolation methods. Starting with a low order integrator (preferably a symmetric second order one) we can build a set of second order schemes by few compositions of this basic scheme that can be computed in parallel. Then, a proper linear combination of the results (obtained from the order conditions associated to the corresponding Lie algebra) allows us to obtain new higher order methods. In this letter we present the structure of the methods, how to obtain several methods, we notice some order barriers that depend on the structure of the compositions used and finally, we show how this analysis can be further carried to obtain new and higher order schemes. (C) 2021 Elsevier Ltd. All rights reserved.
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