Numerical simulations are a highly valuable tool to evaluate the impact of the uncertainties of various modelparameters, and to optimize e.g. injection-production scenarios in the context of underground storage (of CO2typically). Finite volume approximations of Darcy's parabolic model for flows in porous media are typically runmany times, for many values of parameters like permeability and porosity, at costly computational efforts.We study the relevance of reduced basis methods as a way to lower the overall simulation cost of finite volumeapproximations to Darcy's parabolic model for flows in porous media for different values of the parameters suchas permeability. In the context of underground gas storage (of CO2 typically) in saline aquifers, our aim isto evaluate quickly, for many parameter values, the flux along some interior boundaries near the well injectionarea-regarded as a quantity of interest-. To this end, we construct reduced bases by a standard POD-Greedyalgorithm. Our POD-Greedy algorithm uses a new goal-oriented error estimator designed from a discrete space-time energy norm independent of the parameter. We provide some numerical experiments that validate theefficiency of the proposed estimator.

翻译：数值模拟是评估各类模型参数不确定性影响及优化（如CO₂地下封存背景下）注采方案的高价值工具。多孔介质流动达西抛物型模型的有限体积近似通常需针对渗透率、孔隙度等参数的大量取值进行多次运算，计算成本高昂。本文研究降基方法在降低多孔介质流动达西抛物型模型有限体积近似计算成本方面的适用性，该方法适用于渗透率等参数的不同取值。在咸水层（典型如CO₂）地下储气库背景下，我们的目标是对井注区域附近内部边界的通量（视为关注量）实现多参数取值的快速评估。为此，我们采用标准POD-Greedy算法构建降基空间。该POD-Greedy算法采用新型目标导向误差估计器，该估计器基于与参数无关的离散时空能量范数设计。我们通过数值实验验证了所提估计器的有效性。