A one-dimensional local discontinuous Galerkin Richards' equation solution with dual-time stepping

We present a compact, high-order Richards' equation solver using a local discontinuous Galerkin finite element method in space and a dual-time stepping method in time. Dual-time stepping methods convert a transient problem to a steady state problem, enabling direct evaluation of residual terms and resolve implicit equations in a step-wise manner keeping the method compact and amenable to parallel computing. Verification of our solver against an analytical solution shows high-order error convergence and demonstrates the solvers ability to maintain high accuracy using low spatial resolution; the method is robust and accurately resolves numerical solutions with time steps that are much larger than what is normally required for lower-order implicit schemes. Resilience of our solver (in terms of nonlinear convergence) is demonstrated in ponded infiltration into homogeneous and layered soils, for which HYDRUS-1D solutions are used as qualitative references to gauge performance of two slope limiting schemes.