Journal
ADVANCES IN WATER RESOURCES
Volume 143, Issue -, Pages -Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.advwatres.2020.103673
Keywords
Multi-point flux approximation (MPFA); Multi-point upstream weighting (MPUPS); Variably saturated flow; Unstructured mesh; Piecewise gradient reconstruction
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Funding
- Nuclear Waste Management Organization (NWMO), Canada
- Mitacs-Accelerate fellowship [IT07518]
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Richards equation for variably saturated flow can exhibit stability problems due to its nonlinearity. The challenge is to resolve sharp wetting fronts without introducing spurious oscillations, especially for simulations with very dry initial conditions. Flow instabilities at sharp wetting fronts may arise particularly in anisotropic and heterogeneous media, leading to oscillations or convergence problems. The focus of this work is to evaluate and minimize instability problems for simulations with unstructured meshes. To this end, numerical experiments were performed to investigate the accuracy, monotonicity and convergence behavior of numerical solutions for variably saturated flow based on different control volume methods, piecewise gradient reconstruction methods, and flux approximation methods. In particular, nonphysical oscillations at the wetting front were investigated. novel multi-point flux approximation with multi-point upstream weighting based on piecewise gradient reconstruction was developed. Numerical simulations in both homogeneous and heterogeneous domains with isotropic and anisotropic conductivity tensors demonstrate that the proposed multi-point flux approximation with multi point upstream weighting avoids spurious oscillations and improves the results for challenging sharp wetting front problems using general unstructured meshes as well as meshes with distortion. The revised Voronoi-dual control volume method has also been found to provide more flexibility than commonly used center-dual and median-dual control volume methods.
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