Calculation of Internodal Transmissivities in Finite Difference Models of Flow in Heterogeneous Porous Media
Régis Kruel Romeu, B. Nœtinger · Water Resources Research · 1995
We present an analytical and numerical investigation of the finite difference computation of the equivalent conductivity of heterogeneous porous media. The customary harmonic scheme to evaluate finite difference internodal transmissivities produces a systematic bias in the numerical results unless an extremely fine grid is used. In order to quantify such effects, we have developed an analytical approach in the form of a series expansion of the equivalent numerical conductivity in powers of the conductivity variance. This leads to an expression of the numerical answer as a function of the grid block size. The calculation confirms the existence of a strong bias and of a very slow convergence. We propose a simple method to correct it, which is well suited for upscaling. Numerical experiments performed with more contrasting heterogeneous media show similar results. This allows the use of coarser gridding and consequently an appreciable speedup in the numerical simulation approach.