Bound-Preserving Flux-Corrected Transport Methods for Solving Richards' Equation
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arXiv
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| Format: | Preprint |
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2026
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| author | Barua, Arnob Kees, Christopher E. Kuzmin, Dmitri |
| author_facet | Barua, Arnob Kees, Christopher E. Kuzmin, Dmitri |
| contents | Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been applied over the past several decades, basic higher-order numerical methods often fail to preserve physical bounds on water pressure and saturation, leading to spurious oscillations and poor iterative solver convergence. Instead, low-order, bound-preserving methods have been preferred. The combination of mass lumping and relative permeability upwinding preserves bounds but degrades accuracy to first order in space. Flux-corrected transport is a high-resolution numerical technique designed for combining the bound-preserving property of low-order schemes with the accuracy of high-order methods, by blending the two methods through limited anti-diffusive fluxes. In this work, we extend flux-corrected transport schemes to the nonlinear, degenerate parabolic structure of Richards' equation, verify attainment of second-order convergence on unstructured meshes, and demonstrate applications to stormwater management infrastructure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14107 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bound-Preserving Flux-Corrected Transport Methods for Solving Richards' Equation Barua, Arnob Kees, Christopher E. Kuzmin, Dmitri Numerical Analysis Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been applied over the past several decades, basic higher-order numerical methods often fail to preserve physical bounds on water pressure and saturation, leading to spurious oscillations and poor iterative solver convergence. Instead, low-order, bound-preserving methods have been preferred. The combination of mass lumping and relative permeability upwinding preserves bounds but degrades accuracy to first order in space. Flux-corrected transport is a high-resolution numerical technique designed for combining the bound-preserving property of low-order schemes with the accuracy of high-order methods, by blending the two methods through limited anti-diffusive fluxes. In this work, we extend flux-corrected transport schemes to the nonlinear, degenerate parabolic structure of Richards' equation, verify attainment of second-order convergence on unstructured meshes, and demonstrate applications to stormwater management infrastructure. |
| title | Bound-Preserving Flux-Corrected Transport Methods for Solving Richards' Equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.14107 |