Scalable Riemann Solvers with the Discontinuous Galerkin Method for Hyperbolic Network Simulation
Scalable Riemann Solvers with the Discontinuous Galerkin Method for Hyperbolic Network Simulation
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DOI：
10.1145/3592979.3593421
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
Aidan Hamilton;Jing-Mei Qiu;Hong Zhang
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作者：
Aidan Hamilton;Jing-Mei Qiu;Hong Zhang
我们开发了一套高效且有效的计算算法和模拟工具，用于网络上的流体模拟。数学模型是网络边缘上的一组双曲守恒定律，以及网络结点上的耦合条件。例如，浅水系统以及河流交叉口的通量平衡和连续性条件可以对河网中的水流进行建模。计算准确且鲁棒的不连续伽辽金方法与显式强稳定性保持龙格库塔方法相结合，用于网络边缘的模拟。与此同时，线性和非线性可扩展黎曼求解器正在网络顶点开发和实现。这些网络模拟产生的工具被添加到现有的 PETSc 和 DMNetwork 软件库中，供整个科学界使用。密西西比河网络上具有超过 10 亿网络变量的浅水系统的仿真结果是在使用多达 8,192 个处理器的超大规模计算机上执行的，具有最佳的并行效率。进一步的潜在应用包括高速公路网络上的交通流模拟和动脉网络上的血流模拟等。
We develop a set of highly efficient and effective computational algorithms and simulation tools for fluid simulations on a network. The mathematical models are a set of hyperbolic conservation laws on edges of a network, as well as coupling conditions on junctions of a network. For example, the shallow water system, together with flux balance and continuity conditions at river intersections, model water flows on a river network. The computationally accurate and robust discontinuous Galerkin methods, coupled with explicit strong stability preserving Runge-Kutta methods, are implemented for simulations on network edges. Meanwhile, linear and nonlinear scalable Riemann solvers are being developed and implemented at network vertices. These network simulations result in tools that are added to the existing PETSc and DMNetwork software libraries for the scientific community in general. Simulation results of a shallow water system on a Mississippi river network with over one billion network variables are performed on an extreme-scale computer using up to 8,192 processor with an optimal parallel efficiency. Further potential applications include traffic flow simulations on a highway network and blood flow simulations on a arterial network, among many others.