Control Volume Isogeometric Analysis for groundwater flow modeling in heterogeneous porous media

Abstract

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.