A hybrid finite element—finite volume method for incompressible flow through complex geometries using mixed grids

Abstract

A simple, robust, local divergence free, second-order accurate, stable solution procedure for incompressible flows using a finite element method for the evaluation of velocity components and a finite volume method for the evaluation of pressure is presented. In order to ensure pressure stability, the velocity components (at vertices) and pressure (at cell centres) are evaluated at different points of the elements. The finite element-finite volume combinations are taken from triangular and quadrilateral grids. These grids are used alone or together as mixed grids. A new element-cell configuration consisting of two adjacent triangular elements together as a finite volume quadrilateral cell for the evaluation of pressure is introduced. Predictions are found to be in good agreement with the available results for all types of grids used. The present method combines the pressure stability of the staggered grid finite volume method (FVM) and the flexibility of the finite element approach to analyse flow through complex geometries; it is easy to implement and locally divergence free.

Inference of Transmissivity in Crystalline Rock Using Flow Logs Under Steady‐State Pumping: Impact of Multiscale Heterogeneity

“…Note that the uniform‐sized mesh is essential for considering the fracture roughness in the present study. Although the dfnWorks suite (Hyman et al, 2015) contains flow solvers using the parallelized subsurface flow and reactive transport code PFLOTRAN (Lichtner et al, 2015) and FEHM (Zyvoloski et al, 1988), we implemented a hybrid finite volume and finite element (HYFVE for short) method to solve flow in 3‐D DFN models for convenience (Calgaro et al, 2008; Lal & Jabir, 2010).…”

“…The discretization scheme of this HYFVE method has been used in the field of computational fluid dynamics to solve the Navier‐Stokes systems. Detailed information on the dual mesh system and the numerical scheme can be found in the literature (e.g., Calgaro et al, 2008; Lal & Jabir, 2010). The implemented HYFVE method has been verified against known analytical solutions for flow in single fractures.…”