Scalable Adaptive PDE Solvers in Arbitrary Domains
Scalable Adaptive PDE Solvers in Arbitrary Domains
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DOI：
10.1145/3458817.3476220
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发表时间：
2021-08
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影响因子：
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通讯作者：
K. Saurabh;Masado Ishii;Milinda Fernando;Boshun Gao;Kendrick Tan;M. Hsu;A. Krishnamurthy;H. Sundar;B. Ganapathysubramanian
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作者：
K. Saurabh;Masado Ishii;Milinda Fernando;Boshun Gao;Kendrick Tan;M. Hsu;A. Krishnamurthy;H. Sundar;B. Ganapathysubramanian
高效准确地模拟任意定义的几何中及其周围的偏微分方程（PDE），特别是具有高水平的自适应性，对不同的应用领域具有重要意义。上述过程中的一个关键瓶颈是快速构建一个“好”的自适应细化网格。在这项工作中，我们提出了一种有效的新的基于八叉树的自适应离散化方法，能够雕刻出任意形状的空白区域从父域：复杂物体周围的流体模拟的基本要求。分割对象会产生不完整的八叉树。我们开发了有效的自上而下和自下而上的遍历方法来执行有限元计算不完整的八叉树。我们验证的框架（a）显示适当的收敛分析和（B）计算阻力系数的流动通过一个球体的雷诺数范围（0（1-106））包括阻力危机制度。最后，我们将该框架部署在当前项目的现实几何图形上，以评估COVID-19在教室中的传播风险。
Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a ‘good’ adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of carving out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects. Carving out objects produces an incomplete octree. We develop efficient top-down and bottom-up traversal methods to perform finite element computations on incomplete octrees. We validate the framework by (a) showing appropriate convergence analysis and (b) computing the drag coefficient for flow past a sphere for a wide range of Reynolds numbers (0(1-106)) encompassing the drag crisis regime. Finally, we deploy the framework on a realistic geometry on a current project to evaluate COVID-19 transmission risk in classrooms.