(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models: Robust 2D approaches
(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models: Robust 2D approaches
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DOI：
10.1016/j.advwatres.2020.103693
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发表时间：
2020-07
影响因子：
4.7
通讯作者：
G. Kesserwani;M. Sharifian
中科院分区：
文献类型：
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作者：
G. Kesserwani;M. Sharifian
基于二阶不连续伽辽金（DG2）和一阶有限体积（FV1）方法的godunov型求解器中，多小波（MW）能够在多分辨率网格上压缩、分析和组装模型数据。利用一维（1D）水动力模型对多小波自适应进行了广泛研究（Kesserwani et al., 2019），发现MWDG2可以比均匀DG2快20倍，比均匀FV1快2倍，同时保持底层公式的准确性和鲁棒性。MWDG2方案在二维（2D）建模方面的潜力尚未得到研究，但这需要一种设计，能够稳健有效地解决具有复杂源项和干湿的二维浅水方程（SWE）。本文提出了一种二维MWDG2方案：(1)采用斜率解耦的DG2求解器作为参考方案，因为它能够提供由简化的三分量基形成的平衡良好的分段平面解；(2)采用多小波的多分辨率分析与斜率解耦的DG2基兼容。本文提出了斜率解耦DG2的缩放重新表述，以及两种多小波方法，产生具有相似性质的MWDG2格式，以及用于适应分段常数模型数据的Haar小波FV1 （HFV1）变体。研究了自适应HFV1和MWDG2求解器的性能，同时分析了它们的准确性、效率、网格粗化能力、处理陡峭床坡干湿锋的可靠性，以及捕捉与实际水力建模相关特征的能力。结果表明，一种特殊的多小波方法允许MWDG2方案利用其网格粗化能力，适用于最广泛的流类型。结果还表明，所提出的基于（多）小波的自适应方案在二维情况下更加有效。配套的模型软件在网上是公开的。
Multiwavelets (MW) enable the compression, analysis and assembly of model data on a multiresolution grid within Godunov-type solvers based on second-order discontinuous Galerkin (DG2) and first-order finite volume (FV1) methods. Multiwavelet adaptivity has been studied extensively with one-dimensional (1D) hydrodynamic models (Kesserwani et al., 2019), revealing that MWDG2 can be 20 times faster than uniform DG2 and 2 times faster than uniform FV1, while preserving the accuracy and robustness of the underlying formulation. The potential of the MWDG2 scheme has yet to be studied for two-dimensional (2D) modelling, but this requires a design that robustly and efficiently solves the 2D shallow water equations (SWE) with complex source terms and wetting and drying. This paper presents a two-dimensional MWDG2 scheme that: (1) adopts a slope-decoupled DG2 solver as a reference scheme, for its ability to deliver well-balanced piecewise-planar solutions shaped by a simplified 3-component basis; and, (2) adapts the multiresolution analysis of multiwavelets for compatibility with the slope-decoupled DG2 basis. A scaled reformulation of slope-decoupled DG2 is presented alongside two multiwavelet approaches that yield MWDG2 schemes with similar properties, and a Haar wavelet FV1 (HFV1) variant for adapting piecewise-constant model data. The performance of the adaptive HFV1 and MWDG2 solvers is explored alongside their uniform counterparts, while analysing their accuracy, efficiency, grid-coarsening ability, reliability in handling wet-dry fronts across steep bed-slopes, and ability to capture features relevant to practical hydraulic modelling. The results indicate a particular multiwavelet approach that allows the MWDG2 scheme to exploit its grid-coarsening ability for the widest range of flow types. Results also indicate that the proposed (multi)wavelet-based adaptive schemes are even more efficient for the 2D case. Accompanying model software is openly available online.