Parallel local time stepping for rigid bodies represented by triangulated meshes
Parallel local time stepping for rigid bodies represented by triangulated meshes
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DOI：
10.48550/arxiv.2309.15417
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发表时间：
2023-09
期刊：
影响因子：
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通讯作者：
Peter Noble;Tobias Weinzierl
中科院分区：
文献类型：
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作者：
Peter Noble;Tobias Weinzierl
离散元方法(DEM)，即许多刚性粒子的模拟，在空间和时间上受到非常严格的微分方程组和多尺度挑战的困扰。粒子在空间中平稳移动，直到由于碰撞而几乎瞬间相互作用。因此，密集的颗粒堆积需要很小的时间步长，而自由颗粒可以随着大的时间步长前进。允许的时间步长可以跨越多个数量级。我们提出了一种自适应局部时间步长算法，该算法识别可独立更新的粒子簇，乐观地独立地在时间上推进它们，确定时空中的碰撞时间戳以最大化所用的时间步长，并隐式地解决动量交换问题。它与利用多尺度几何表示和时间上的多尺度行为的各种加速技术相结合。时空中的碰撞时间戳检测与实际碰撞方程的隐式求解相结合，避免了粒子被锁定在微小的时间步长，聚类产生高并发水平，加速技术加上局部时间步长避免了不必要的计算。这为DEM带来了可伸缩的、自适应的时间步长，以应对现实世界的挑战。
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost instantaneously due to collisions. Dense particle packings hence require tiny time step sizes, while free particles can advance with large time steps. Admissible time step sizes can span multiple orders of magnitudes. We propose an adaptive local time stepping algorithm which identifies clusters of particles that can be updated independently, advances them optimistically and independently in time, determines collision time stamps in space-time such that we maximise the time step sizes used, and resolves the momentum exchange implicitly. It is combined with various acceleration techniques which exploit multiscale geometry representations and multiscale behaviour in time. The collision time stamp detection in space-time in combination with the implicit solve of the actual collision equations avoids that particles get locked into tiny time step sizes, the clustering yields a high concurrency level, and the acceleration techniques plus local time stepping avoid unnecessary computations. This brings a scaling, adaptive time stepping for DEM for real-world challenges into reach.