Many important groundwater transport applications require solving the Darcy flow in heterogeneous porous media. Flow simulations, especially in large, highly heterogeneous aquifers, require extensive computational resources, a multiresolution (multiscale) approach to resolve the different heterogeneity scales and an accurate calculation of the velocity field. Common methods, such as finite volumes and elements, assume a discontinuous conductivity field introducing velocity discontinuities along the cell or element interfaces due to using classic discrete operators or Lagrangian basis functions. Over the last decade, the development of isogeometric analysis (IGA) eliminates many of the aforementioned limitations bridging the gap between CAD and numerical analysis. Since classic IGA uses the Galerkin and collocation approach, in this paper, we present a third concept in the form of Control Volume IsoGeometric Analysis (CV-IGA) enabling local and global mass conservation as well as multiresolution description of all heterogeneity scales. Due to the approximation properties of spline basis functions, the velocity field and its derivatives are continuous and are obtained by an optimal convergence rate. The CV-IGA methodology is verified with 2-D numerical and stochastic benchmark flow simulations, including comparisons with classic methods and two other IGA formulations as well as the convergence analysis of the head and velocity fields for different orders of Fup and B-spline basis functions.

许多重要的地下水运输应用需要解决非均质多孔介质中的达西渗流问题。流动模拟，特别是在大型，高度非均质含水层中，需要大量的计算资源，多分辨率（多尺度）方法来解决不同的非均质尺度和速度场的精确计算。由于使用经典的离散算子或拉格朗日基函数，诸如有限体积和有限元之类的常见方法都采用不连续的电导率场，从而沿单元或单元界面引入速度不连续性。在过去的十年中，等几何分析（IGA）的发展消除了许多上述限制，弥合了CAD和数值分析之间的空白。由于经典的IGA使用Galerkin和搭配方法，因此在本文中，Ç ONTROL V olume我所以ģ eometric甲nalysis（CV-IGA），使局部和全局质量守恒，以及所有的异质性尺度多分辨率描述。由于样条基函数的近似性质，速度场及其导数是连续的，并且是通过最佳收敛速度获得的。在CV-IGA方法验证用2- d数值和随机基准流动模拟，包括经典方法和另外两个IGA制剂和不同阶的比较以及所述头部的收敛性分析速度场FUP和B样条基职能。