Comparison of 3D Flow Fields Arising in Mixed and Standard Unstructured Finite Elements

Abstract

Abstract. Computing 3D velocity fields is an important task in subsurface water flow analysis. While Finite Element (FE) simulations generally yields accurate estimates of the head, the numerical velocity may display errors and even unphysical behavior in some parts of the domain. Theoretically, the Mixed Hybrid FE (MHFE) approach provide a more accurate approximation to the velocities. In this communication we analyze a number of 3D-flow test cases, and compare the results obtained using FE and MHFE on tetrahedral meshes. Theoretical convergence estimates are numerically verified for a few simple problems. A more complex heterogeneous test case is used to show that, even for very fine meshes, the results obtained using the two discretization approaches may differ.

On the performance of the variational multiscale formulation for subsurface flow and transport in heterogeneous porous media

“…in the mathematical statements (10) and ( 13) and subsequent steps. In such cases, the function spaces for the velocity and corresponding weighting function will be modified as follows: the weighting function corresponding to the concentration as w c (x).…”

“…The pursuit of stable, locally conservative finite element formulations has received substantial attention (for examples see [7,8,9] among many others). In addition, a number of comparisons have been made between various formulations (for example, see [10,11,12]), Of particular interest is the work presented in [12] that showed a computational efficiency advantage for control volume approaches vs. mixed methods for problems with only moderate heterogeneity.…”