Fully coupled methods for multiphase morphodynamics

[1]  Ethan J. Kubatko,et al.  A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations , 2009 .

[2]  V. Nikora,et al.  Exner equation: A continuum approximation of a discrete granular system , 2009 .

[3]  Enrique D. Fernández-Nieto,et al.  Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods , 2008 .

[4]  Tuomas Kärnä,et al.  A finite-element, multi-scale model of the Scheldt tributaries, river, estuary and ROFI , 2010 .

[5]  Carlos Parés Madroñal,et al.  On the Convergence and Well-Balanced Property of Path-Conservative Numerical Schemes for Systems of Balance Laws , 2011, J. Sci. Comput..

[6]  James R. Anderson,et al.  A land use and land cover classification system for use with remote sensor data , 1976 .

[7]  Rémi Abgrall,et al.  A comment on the computation of non-conservative products , 2010, J. Comput. Phys..

[8]  E. Oelkers,et al.  The rainbow vent fluids (36°14′N, MAR): the influence of ultramafic rocks and phase separation on trace metal content in Mid-Atlantic Ridge hydrothermal fluids , 2002 .

[9]  H.-P. Cheng,et al.  A numerical model simulating reactive transport in shallow water domains: model development and demonstrative applications , 2000 .

[10]  P. Ackers,et al.  SEDIMENT TRANSPORT THEORIES. , 1975 .

[11]  Michael Dumbser,et al.  Well-Balanced High-Order Centred Schemes for Non-Conservative Hyperbolic Systems. Applications to Shallow Water Equations with Fixed and Mobile Bed , 2009 .

[12]  Clint Dawson,et al.  Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations , 2010, J. Comput. Phys..

[13]  G. D. Maso,et al.  Definition and weak stability of nonconservative products , 1995 .

[14]  A. J. Roberts,et al.  A centre manifold description of containment dispersion in channels with varying flow properties , 1990 .

[15]  J. Westerink,et al.  Dynamic p-enrichment schemes for multicomponent reactive flows , 2011, 1104.3834.

[16]  R. Iverson,et al.  U. S. Geological Survey , 1967, Radiocarbon.

[17]  J. Miller Numerical Analysis , 1966, Nature.

[18]  J. Nédélec,et al.  First order quasilinear equations with boundary conditions , 1979 .

[19]  H. Möhwald,et al.  Sonochemical nanosynthesis at the engineered interface of a cavitation microbubble. , 2006, Physical chemistry chemical physics : PCCP.

[20]  Ethan J. Kubatko,et al.  An unstructured grid morphodynamic model with a discontinuous Galerkin method for bed evolution , 2006 .

[21]  W. Seyfried,et al.  Hydrothermal serpentinization of peridotite within the oceanic crust: Experimental investigations of mineralogy and major element chemistry , 1986 .

[22]  Craig Michoski,et al.  A discontinuous Galerkin method for viscous compressible multifluids , 2009, J. Comput. Phys..

[23]  Denys Dutykh,et al.  Modified Shallow Water Equations for significantly varying seabeds , 2012, 1202.6542.

[24]  Shu-Qing Yang,et al.  Formula for Sediment Transport in Rivers, Estuaries, and Coastal Waters , 2005 .

[25]  P. Nielsen Coastal Bottom Boundary Layers and Sediment Transport , 1992 .

[26]  Clint Dawson,et al.  A Performance Comparison of Continuous and Discontinuous Finite Element Shallow Water Models , 2009, J. Sci. Comput..

[27]  J. Damgaard,et al.  BED-LOAD SEDIMENT TRANSPORT ON STEEP LONGITUDINAL SLOPES , 1997 .

[28]  D. Arnold,et al.  Discontinuous Galerkin Methods for Elliptic Problems , 2000 .

[29]  Manuel Torrilhon,et al.  Essentially optimal explicit Runge–Kutta methods with application to hyperbolic–parabolic equations , 2007, Numerische Mathematik.

[30]  Ethan J. Kubatko,et al.  hp Discontinuous Galerkin methods for advection dominated problems in shallow water flow , 2006 .

[31]  Didier Bresch,et al.  Recent mathematical results and open problems about shallow water equations. Analysis and simulation of fluid dynamic , 2006 .

[32]  Clint Dawson,et al.  Semi discrete discontinuous Galerkin methods and stage-exceeding-order, strong-stability-preserving Runge-Kutta time discretizations , 2007, J. Comput. Phys..

[33]  J. Restrepo Behavior of a sand ridge model , 1997 .

[34]  J. Bona,et al.  Discretization of a model for the formation of longshore sand ridges , 1994 .

[35]  D. Dutykh,et al.  MODIFIED SHALLOW WATER EQUATIONS FOR SIGNIFICANTLY VARYING BOTTOMS , 2012 .

[36]  D. Dutykh,et al.  Modified 'irrotational' Shallow Water Equations for significantly varying bottoms , 2012 .

[37]  Michael Dumbser,et al.  A p-Adaptive Discontinuous Galerkin Method with Local Time Steps for Computational Seismology , 2009 .

[38]  Dmitri Kuzmin,et al.  A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods , 2010, J. Comput. Appl. Math..

[39]  M. Yücel,et al.  Hydrothermal vents as a kinetically stable source of iron-sulphide-bearing nanoparticles to the ocean , 2011 .

[40]  C. Dawson,et al.  Local time-stepping in Runge–Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations , 2012 .

[41]  J. C. Dietrich,et al.  A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi. Part I: Model Development and Validation , 2010 .

[42]  Craig Michoski,et al.  Discontinuous Galerkin hp-adaptive methods for multiscale chemical reactors: Quiescent reactors , 2014 .

[43]  Yulong Xing,et al.  Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations , 2010 .

[44]  V. Voller,et al.  A generalized Exner equation for sediment mass balance , 2005 .

[45]  Joannes J. Westerink,et al.  Continuous, discontinuous and coupled discontinuous–continuous Galerkin finite element methods for the shallow water equations , 2006 .

[46]  V. Legat,et al.  A fully implicit wetting-drying method for DG-FEM shallow water models, with an application to the Scheldt Estuary , 2011 .

[47]  N. Chien Closure of "The Present Status of Research on Sediment Transport" , 1954 .

[48]  Magnus Larson,et al.  A general formula for non-cohesive bed load sediment transport , 2005 .

[49]  L. Rijn Unified view of sediment transport by currents and waves. I: Initiation of motion, bed roughness, and bed-load transport , 2007 .

[50]  Ethan J. Kubatko,et al.  Implementation of a discontinuous Galerkin morphological model on two-dimensional unstructured meshes , 2011 .

[51]  C. F. Curtiss,et al.  Molecular Theory Of Gases And Liquids , 1954 .

[52]  L. Rijn Sediment Transport, Part II: Suspended Load Transport , 1984 .

[53]  Steven J. Ruuth Global optimization of explicit strong-stability-preserving Runge-Kutta methods , 2005, Math. Comput..

[54]  Sander Rhebergen,et al.  A discontinuous Galerkin finite element model for river bed evolution under shallow flows , 2007 .

[55]  William J. Rider,et al.  On sub-linear convergence for linearly degenerate waves in capturing schemes , 2008, J. Comput. Phys..

[56]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[57]  Clint Dawson,et al.  Discontinuous Galerkin Methods for Modeling Hurricane Storm Surge , 2011 .

[58]  Siddhartha Mishra,et al.  Accurate numerical discretizations of non-conservative hyperbolic systems , 2012 .

[59]  Van Rijn,et al.  Closure of "Sediment Transport, Part III: Bed Forms and Alluvial Roughness" , 1984 .

[60]  T. Hou,et al.  Why nonconservative schemes converge to wrong solutions: error analysis , 1994 .

[61]  C. Parés Numerical methods for nonconservative hyperbolic systems: a theoretical framework. , 2006 .

[62]  Chi-Wang Shu,et al.  High-order finite volume WENO schemes for the shallow water equations with dry states , 2011 .

[63]  Jan G. Verwer,et al.  An Implicit-Explicit Runge-Kutta-Chebyshev Scheme for Diffusion-Reaction Equations , 2004, SIAM J. Sci. Comput..

[64]  Clint Dawson,et al.  Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids , 2008, J. Comput. Phys..

[65]  D. Walstra,et al.  Unified View of Sediment Transport by Currents and Waves. IV: Application of Morphodynamic Model , 2007 .

[66]  I. Babuska,et al.  GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE , 2004 .

[67]  Van Rijn,et al.  Sediment transport; Part I, Bed load transport , 1984 .

[68]  Michael Westdickenberg,et al.  Gravity driven shallow water models for arbitrary topography , 2004 .

[69]  P. Roe Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[70]  V. Giovangigli Multicomponent flow modeling , 1999 .

[71]  J. Breidt,et al.  A Measure-Theoretic Computational Method for Inverse Sensitivity Problems I: Method and Analysis , 2011, SIAM J. Numer. Anal..