Finitevolume flux reconstruction and semianalytical particle tracking on triangular prisms for finiteelementtype models of variablysaturated flow
Abstract
Consistent particle tracking relies on conforming velocity fields that ensure local mass conservation on elements. Cellcentered finitevolume and mixed finiteelement methods result in conforming velocity fields but this is not the case for continuous Galerkin methods, such as the standard finite element method (FEM). Nonetheless standard FEM is often used for subsurface flow modeling because it yields a continuous approximation of hydraulic heads, and it naturally handles unstructured grids and full material tensors. Acknowledging these advantages and the widespread use of finiteelementtype simulations, we present a postprocessing method that reconstructs a cellcentered finitevolume solution from a finiteelementtype solution of the variablysaturated subsurface flow equation to obtain conforming, massconservative fluxes. Using the linear average velocity field derived from these fluid fluxes, we employ elementwise analytical solutions for triangular prisms to compute particle trajectories and associated travel times. As a result, we can compute consistent particle trajectories for variablysaturated flow solutions generated by nodecentered methods, such as finite element or finite difference methods, that do not yield conforming velocity fields. Our flux reconstruction solves a linear elliptic problem whose size is on the order of the number of elements, which is computationally much faster than solving the initial, nonlinear transient variablysaturated flow equation. Compared to other postprocessing schemes, our flux reconstruction is numerically stable, fast to compute, and does not induce severe numerical artifacts when applied to heterogeneous domains with strongly varying velocities. However, these advantages come with a comparably high coding effort and the necessity of solving a global system of equations. We show that the results of our flux reconstruction are close to the nodecentered primal solution for variably saturated threedimensional flow with heterogeneous material properties.
 Publication:

Advances in Water Resources
 Pub Date:
 August 2021
 DOI:
 10.1016/j.advwatres.2021.103944
 Bibcode:
 2021AdWR..15403944S
 Keywords:

 Cellcentered finite volume method;
 Finite element method;
 Particle tracking;
 Local mass conservation;
 Triangular prisms;
 Variably saturated flow