14-17 May 2018
New Orleans
US/Central timezone

Nonlinear finite-volume schemes for complex flow processes and challenging grids

15 May 2018, 18:15
New Orleans

New Orleans

Poster MS 2.10: Advanced finite-volume methods for flow and transport in porous media Poster 2


Mr Martin Schneider (University of Stuttgart)


The numerical simulation of subsurface processes requires efficient and robust methods due to the large scales and the complex geometries involved. To resolve such complex geometries, corner-point grids are the industry standard to spatially discretize geological formations. Such grids include non-planar, non-matching and degenerated faces. The standard scheme used in industrial codes is the cell-centered finite-volume scheme with two-point flux (TPFA) approximation, an efficient scheme that produces unconditionally monotone solutions. However, large errors in face fluxes are introduced on unstructured grids. The authors present a nonlinear finite-volume scheme applicable to corner-point grids, which maintains the monotonicity property, but has superior qualities with respect to face-flux accuracy. The scheme is compared to linear ones for complex flow simulations in realistic geological formations [1,2]. In addition, we present recent developments regarding convergence analysis for a family of nonlinear finite-volume schemes [3].


[1] Schneider, M., Flemisch, B., & Helmig, R. (2017). Monotone nonlinear finite‐volume method for nonisothermal two‐phase two‐component flow in porous media. International Journal for Numerical Methods in Fluids, 84(6), 352-381.

[2] Schneider, M., Gläser, D., Flemisch, B., & Helmig, R. (2017). Nonlinear Finite-Volume Scheme for Complex Flow Processes on Corner-Point Grids. In International Conference on Finite Volumes for Complex Applications (pp. 417-425). Springer, Cham.

[3] Schneider, M., Agélas, L., Enchéry, G., & Flemisch, B. (2017). Convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes. Journal of Computational Physics, 351, 80-107.

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Primary authors

Prof. Bernd Flemisch (University of Stuttgart) Prof. Rainer Helmig (University of Stuttgart) Mr Martin Schneider (University of Stuttgart)

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