A novel numerical method of high‐order accuracy for flow in unsaturated porous media

[1]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[2]  E. Toro,et al.  Solution of the generalized Riemann problem for advection–reaction equations , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  Michael Dumbser,et al.  Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems , 2007, J. Comput. Phys..

[4]  Karsten Pruess,et al.  Robust numerical methods for saturated-unsaturated flow with dry initial conditions in heterogeneous media , 1995 .

[5]  Gordon E. Grant,et al.  Comment on A Distributed Hydrology-Vegetation Model for Complex Terrain by Mark S. Wigmosta, Lance , 1996 .

[6]  C. Fassino,et al.  Fast‐secant algorithms for the non‐linear Richards equation , 1998 .

[7]  R. G. Hills,et al.  Algorithms for solving Richards' equation for variably saturated soils , 1992 .

[8]  Michael Dumbser,et al.  Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws , 2008, J. Comput. Phys..

[9]  Michael Dumbser,et al.  Building Blocks for Arbitrary High Order Discontinuous Galerkin Schemes , 2006, J. Sci. Comput..

[10]  Jaap J. W. van der Vegt,et al.  Space-Time Discontinuous Galerkin Method for the Compressible Navier-Stokes , 2006 .

[11]  Michael Dumbser,et al.  A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes , 2008, J. Comput. Phys..

[12]  Y. Mualem.  A New Model for Predicting the Hydraulic Conductivity , 1976 .

[13]  P. Roe,et al.  On Godunov-type methods near low densities , 1991 .

[14]  H. D. Scott,et al.  Some Analytical and Approximate Darcian Means , 1999 .

[15]  Eleuterio F. Toro,et al.  ADER schemes for three-dimensional non-linear hyperbolic systems , 2005 .

[16]  Matthew W. Farthing,et al.  Adaptive local discontinuous Galerkin approximation to Richards’ equation , 2007 .

[17]  Bernardo Cockburn,et al.  Discontinuous Galerkin Methods for Convection-Dominated Problems , 1999 .

[18]  S. Sloan,et al.  Adaptive backward Euler time stepping with truncation error control for numerical modelling of unsaturated fluid flow , 2002 .

[19]  P. Milly,et al.  A mass-conservative procedure for time-stepping in models of unsaturated flow , 1985 .

[20]  T. Vogel,et al.  On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve , 1988 .

[21]  Matthew W. Farthing,et al.  Local discontinuous Galerkin approximations to Richards’ equation , 2007 .

[22]  W. Durner.  Hydraulic conductivity estimation for soils with heterogeneous pore structure , 1994 .

[23]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[24]  Michael Dumbser,et al.  Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems , 2007, J. Comput. Phys..

[25]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .

[26]  Luca Bergamaschi,et al.  MIXED FINITE ELEMENTS AND NEWTON-TYPE LINEARIZATIONS FOR THE SOLUTION OF RICHARDS' EQUATION , 1999 .

[27]  K. Abbaspour,et al.  A sequential uncertainty domain inverse procedure for estimating subsurface flow and transport parameters , 1997 .

[28]  M. Th. van Genuchten,et al.  Effect of the shape of the soil hydraulic functions near saturation on variably-saturated flow predictions , 2000 .

[29]  H. Vanderven.  Space?time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flowsII. Efficient flux quadrature , 2002 .

[30]  M. Celia,et al.  A General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation , 1990 .

[31]  Liwang Ma,et al.  Adaptive Grid Refinement in Numerical Models for Water Flow and Chemical Transport in Soil: A Review , 2002 .

[32]  Bernd Einfeld.  On Godunov-type methods for gas dynamics , 1988 .

[33]  Lehua Pan,et al.  A Transformed Pressure Head‐Based Approach to Solve Richards' Equation for Variably Saturated Soils , 1995 .

[34]  S. Osher,et al.  One-sided difference approximations for nonlinear conservation laws , 1981 .

[35]  Gianmarco Manzini,et al.  Mass-conservative finite volume methods on 2-D unstructured grids for the Richards’ equation , 2004 .

[36]  Michael Dumbser,et al.  Arbitrary high order PNPM schemes on unstructured meshes for the compressible Navier–Stokes equations , 2010 .

[37]  H. van der Ven,et al.  Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature , 2002 .

[38]  L. A. Richards.  Capillary conduction of liquids through porous mediums , 1931 .

[39]  Bernardo Cockburn.  Discontinuous Galerkin methods , 2003 .

[40]  R. G. Hills,et al.  Modeling one‐dimensional infiltration into very dry soils: 1. Model development and evaluation , 1989 .

[41]  J. V. D. Vegt,et al.  Space--time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. general formulation , 2002 .

[42]  Vincenzo Casulli,et al.  A high‐resolution wetting and drying algorithm for free‐surface hydrodynamics , 2009 .

[43]  Nick Croft,et al.  Computational modelling of variably saturated flow in porous media with complex three‐dimensional geometries , 2006 .

[44]  Yan Xu,et al.  Space-time discontinuous Galerkin method for nonlinear water waves , 2007, J. Comput. Phys..

[45]  Shen-Haw Ju,et al.  Mass types, element orders and solution schemes for the Richards equation , 1997 .

[46]  Douglas N. Arnold,et al.  Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems , 2001, SIAM J. Numer. Anal..

[47]  Dmitri Kavetski,et al.  Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards equation | NOVA. The University of Newcastle's Digital Repository , 2001 .

[48]  E. Toro,et al.  Restoration of the contact surface in the HLL-Riemann solver , 1994 .

[49]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

[50]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .