显式与IMEX MRI多速率方法在现代并行自适应结构化网格框架下复杂反应流问题中的性能
Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks
AI总结：
针对多物理场模拟的多时间尺度耦合难题，对比了SUNDIALS中不同MRI多速率方法在两类反应流问题上的性能，验证了其结合AMReX高级空间离散特性的显著效率优势。
摘要：
大规模多物理场模拟因多个时间尺度差异极大的过程相互耦合，在计算层面极具挑战性。百亿亿次（exascale）计算系统的出现进一步加剧了这些挑战，因为这类系统支持规模更大、复杂度更高的模拟。近年来，学界重新燃起了开发多速率方法以应对大范围时间尺度问题的兴趣，因为与使用IMEX（隐式-显式）和低阶算子分裂格式的传统方法相比，这类方法有望实现更高的精度与效率。然而，目前鲜有针对复杂应用问题对比不同类别多速率积分器的性能研究。我们研究了在SUNDIALS求解器包中实现的几种最新开发的多速率无穷小（MRI，multirate infinitesimal）方法，在两个基于结构化网格框架构建的反应流模型问题上的性能。第一个模型重温了Emmet等人（2014年）关于含复杂化学反应的可压缩反应流问题的工作，该问题使用BoxLib实现，但我们新增了一种新型显式MRI格式与原论文中多速率谱延迟校正（SDC，spectral deferred correction）方法的对比。第二个问题采用与第一个问题相同的复杂化学反应机制，结合简化的流动模型，但在大空间尺度下运行，此时显式方法因稳定性约束而变得不可行。我们测试了两种最新开发的隐式-显式MRI多速率方法，这些方法依赖于模型所基于的AMReX框架的高级特性，例如多层网格和多层预处理器。这两个问题的结果表明，MRI多速率方法能够在复杂多物理场应用问题上带来显著的性能收益，并且这类方法可与高级空间离散化方法结合，进一步叠加二者的优势。
英文摘要：
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.
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