A scalable and implicit meshless RBF method for the 3D unsteady nonlinear Richards equation with single and multi‐zone domains

The Local Hermitian Interpolation (LHI) method is a strong‐form meshless numerical technique which uses Radial Basis Function (RBF) interpolants to satisfy linear and nonlinear governing equations and boundary operators. Recent developments have shown that, for linear transport problems, applying the PDE governing equation directly to the basis functions can greatly improve the accuracy and stability of the resulting solutions. In this work, the LHI formulation with local PDE‐interpolation is extended to the nonlinear gravity‐driven Richards equation, in order to solve unsteady problems involving flow in unsaturated porous media.

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