Benchmarking a multiresolution discontinuous Galerkin shallow water model: Implications for computational hydraulics
Benchmarking a multiresolution discontinuous Galerkin shallow water model: Implications for computational hydraulics
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DOI：
10.1016/j.advwatres.2015.09.016
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发表时间：
2015-12
影响因子：
4.7
通讯作者：
Daniel Caviedes‐Voullième;G. Kesserwani
中科院分区：
文献类型：
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作者：
Daniel Caviedes‐Voullième;G. Kesserwani
浅水问题中涉及的各种不同物理尺度的数值模拟一直是计算水力学的一个关键挑战。自适应网格技术通常与数值方法相结合，试图解决这一挑战。MultiWavelength（MW）与Runge-Kutta间断Galerkin（RKDG）方法的结合提供了一种新的理念，可以轻松实现由数值解的局部变化驱动的网格自适应性，并且不需要用户设置多个阈值。然而，妇女权利、知识和发展部在多大程度上有助于应对上述关键挑战方面的实际优点和影响尚待探讨。这项工作系统地探讨了这一点，通过选定的稳态和瞬态基准测试，其中涉及的功能真实的SW问题的MWRKDG的验证和确认。我们的研究结果揭示了SW-MWRKDG求解器在高效和准确的网格自适应方面的实用前景，但也建议进一步改进SW-RKDG参考方案，以更好地与基于MW的自适应性交织并利用其威力。
Numerical modelling of wide ranges of different physical scales, which are involved in Shallow Water (SW) problems, has been a key challenge in computational hydraulics. Adaptive meshing techniques have been commonly coupled with numerical methods in an attempt to address this challenge. The combination of MultiWavelets (MW) with the Runge–Kutta Discontinuous Galerkin (RKDG) method offers a new philosophy to readily achieve mesh adaptivity driven by the local variability of the numerical solution, and without requiring more than one threshold value set by the user. However, the practical merits and implications of the MWRKDG, in terms of how far it contributes to address the key challenge above, are yet to be explored. This work systematically explores this, through the verification and validation of the MWRKDG for selected steady and transient benchmark tests, which involves the features of real SW problems. Our findings reveal a practical promise of the SW-MWRKDG solver, in terms of efficient and accurate mesh-adaptivity, but also suggest further improvement in the SW-RKDGreference schemeto better intertwine with, and harness the prowess of, the MW-based adaptivity.