Adaptive POD model reduction for solute transport in heterogeneous porous media
Adaptive POD model reduction for solute transport in heterogeneous porous media
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DOI：
10.1007/s10596-017-9693-5
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发表时间：
2018-02
影响因子：
2.5
通讯作者：
Calogero B. Rizzo;F. D. de Barros;S. Perotto;Luca Oldani;A. Guadagnini
中科院分区：
文献类型：
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作者：
Calogero B. Rizzo;F. D. de Barros;S. Perotto;Luca Oldani;A. Guadagnini
研究了一种模型降阶技术在求解均匀和非均匀多孔介质中被动标量输运问题中的适用性。输运动力学通过对流-弥散方程(ADE)来模拟，并且我们使用适当的正交分解(POD)作为策略来减少与ADE数值解相关的计算负担。我们的POD应用依赖于解决选定时间的管理ADE，称为快照。然后使用后者来实现所需的模型降阶。我们引入了一种新的技术，称为快照分裂技术(SST)，它可以丰富POD子空间的维度，并抑制建模误差的时间增长。将SST与基于在不同时间尺度上交替的建模策略相结合，将全数值输送模式的解扩展到其简化的对应物，允许在延长的时间窗口上扩展POD的好处，从而可以在降低计算成本的情况下捕获过程的显著特征。整个模式和简化模式的解交替使用的时间尺度的选择与代表系统中发生的平流和弥散过程之间的相互作用的Péclet数(Pe)相联系。因此，该方法通过POD和SST的组合使用，并通过交替求解完整模型和简化模型的方式，在空间和时间上跨越区域的异质结构。我们发现，基于POD的简化模型解提供精确结果的时间尺度的宽度随着Pe的减小而增加。这表明局地尺度弥散过程的影响有助于POD方法捕捉嵌入在所选快照中的系统动力学的显著特征。由于简化模型的维度远低于全数值模型的维度，因此我们提出的方法能够以显著降低的计算代价精确地模拟输运。
We study the applicability of a model order reduction technique to the solution of transport of passive scalars in homogeneous and heterogeneous porous media. Transport dynamics are modeled through the advection-dispersion equation (ADE) and we employ Proper Orthogonal Decomposition (POD) as a strategy to reduce the computational burden associated with the numerical solution of the ADE. Our application of POD relies on solving the governing ADE for selected times, termed snapshots. The latter are then employed to achieve the desired model order reduction. We introduce a new technique, termed Snapshot Splitting Technique (SST), which allows enriching the dimension of the POD subspace and damping the temporal increase of the modeling error. Coupling SST with a modeling strategy based on alternating over diverse time scales the solution of the full numerical transport model to its reduced counterpart allows extending the benefit of POD over a prolonged temporal window so that the salient features of the process can be captured at a reduced computational cost. The selection of the time scales across which the solution of the full and reduced model are alternated is linked to the Péclet number (Pe), representing the interplay between advective and dispersive processes taking place in the system. Thus, the method is adaptive in space and time across the heterogenous structure of the domain through the combined use of POD and SST and by way of alternating the solution of the full and reduced models. We find that the width of the time scale within which the POD-based reduced model solution provides accurate results tends to increase with decreasingPe. This suggests that the effects of local-scale dispersive processes facilitate the POD method to capture the salient features of the system dynamics embedded in the selected snapshots. Since the dimension of the reduced model is much lower than that of the full numerical model, the methodology we propose enables one to accurately simulate transport at a markedly reduced computational cost.