Benchmark for numerical solutions of flow in heterogeneous groundwater formations

by   Cristian D. Alecsa, et al.

This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin, spectral, and random walk methods are tested on one- and two-dimensional benchmark flow problems. Realizations of log-normal hydraulic conductivity fields are generated by Kraichnan algorithms in closed form as finite sums of random periodic modes, which allow direct code verification by comparisons with manufactured reference solutions. The quality of the methods is assessed for increasing number of random modes and for increasing variance of the log-hydraulic conductivity fields with Gaussian and exponential correlation. Experimental orders of convergence are calculated from successive refinements of the grid. The numerical methods are further validated by comparisons between statistical inferences obtained from Monte Carlo ensembles of numerical solutions and theoretical first-order perturbation results. It is found that while for Gaussian correlation of the log-conductivity field all the methods perform well, in the exponential case their accuracy deteriorates and, for large variance and number of modes, the benchmark problems are practically not tractable with reasonably large computing resources, for all the methods considered in this study.



There are no comments yet.


page 1

page 2

page 3

page 4


Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media (extended version)

In this article, we present new random walk methods to solve flow and tr...

Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media

Flow and multicomponent reactive transport in saturated/unsaturated poro...

Stabilized finite element methods for a fully-implicit logarithmic reformulation of the Oldroyd-B constitutive law

Logarithmic conformation reformulations for viscoelastic constitutive la...

Finite volume methods for the computation of statistical solutions of the incompressible Euler equations

We present an efficient numerical scheme based on Monte Carlo integratio...

A Moving Discontinuous Galerkin Finite Element Method with Interface Conservation Enforcement for Compressible Flows

A moving discontinuous Galerkin finite element method with interface con...

A time-spectral Stokes solver for simulation of time-periodic flows in complex geometries

Simulation of unsteady creeping flows in complex geometries has traditio...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.