This paper presents a study for solving unsaturated flow in heterogeneous porous media using the meshless method with radial basis function (RBF). For modeling nonlinear hydrological process zone, an exponential model is introduced Richards equation such that we may obtain linearized equation. We adopt multiquadric as RBF simulating problems layered soils, flux and head must satisfy continuity ...

We present a novel hp-adaptive space-time discontinuous Galerkin (hp-STDG) method for the numerical solution of nonstationary Richards equation equipped with Dirichlet, Neumann and seepage face boundary conditions. The hp-STDG presented in this paper is generalization which was developed time dependent non-linear convective-diffusive problems. describe single ring experiment, then we experiment...

In this paper, we present a class of solvers developed for the parallel solution of Richards' equation, a model used in variably saturated ow simulations. These solvers take advantage of the fast, robust convergence of globalized Newton methods as well as the parallel scalability of multigrid preconditioners. We compare two multigrid methods. The methods di er primarily in their handling of dis...

Sharp fronts with rapid changes in uid saturations over short distance and time scales often exist in multiphase ow in subsurface systems. Such highly nonlinear problems are notoriously diicult to solve, and standard solution approaches are often ineecient and unreliable. We summarize four existing and one new transformation method (IT2) for solving Richards' equation within a common framework ...

A mathematical macroscopic traffic flow model known as Lighthill, Whitham and Richards (LWR) model appended with a closure nonlinear velocity-density relationship yielding a quasilinear first order (hyperbolic) partial differential equation as an initial boundary value problem (IBVP) was considered. The traffic model IBVP by finite difference method which leads to a first order explicit upwind ...

The gradient scheme family, which includes the conforming and mixed finite elements as well as the mimetic mixed hybrid family, is used for the approximation of Richards equation and the two-phase flow problem in heterogeneous porous media. We prove the convergence of the approximate saturation and of the approximate pressures and approximate pressure gradients thanks to monotony and compactnes...

Richards’ equation and the two-phase flow equations are well-known degenerate parabolic models of air/water flow in porous media. Poor iterative solver performance and small time steps during transient simulations are often reported in field-scale simulations. In this work we study Newton-multigrid and nonlinear multigrid methods applied to discrete air/water flow models. The models are discret...