Simulating water infiltration from a strip source with radial basis functions methods

Richards' equation governs water infiltration in unsaturated soils but poses numerical challenges due to its nonlinearity and soil heterogeneity. This study investigates two meshless numerical methods – the radial basis function partition of unity method with QR factorisation (RBF-PU-QR) and the radial basis function-generated finite-difference method with Gaussian radial basis functions (RBF-GA) – to solve bidimensional infiltration problems under a strip source. RBF-PU-QR improves efficiency and stability through localised approximations and QR factorisation, while RBF-GA enhances accuracy via Gaussian kernels and finite-difference stencils. Numerical experiments on homogeneous and heterogeneous soil domains show that both methods accurately capture infiltration dynamics, and with relative errors below 1% and 2%, respectively, with refined discretisation while maintaining reasonable execution times. These results highlight the stability, accuracy, and adaptability of RBF-based methods for simulating nonlinear flow in hydrological and environmental applications.