Results 1  10
of
15
Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation
 J. Comput. Phys
, 2008
"... We present a class of augmented approximate Riemann solvers for the shallow water equations in the presence of a variable bottom surface. These belong to the class of simple approximate solvers that use a set of propagating jump discontinuities, or waves, to approximate the true Riemann solution. Ty ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
(Show Context)
We present a class of augmented approximate Riemann solvers for the shallow water equations in the presence of a variable bottom surface. These belong to the class of simple approximate solvers that use a set of propagating jump discontinuities, or waves, to approximate the true Riemann solution. Typically, a simple solver for a system of m conservation laws uses m such discontinuities. We present a four wave solver for use with the the shallow water equations—a system of two equations in one dimension. The solver is based on a decomposition of an augmented solution vector—the depth, momentum as well as momentum flux and bottom surface. By decomposing these four variables into four waves the solver is endowed with several desirable properties simultaneously. This solver is wellbalanced: it maintains a large class of steady states by the use of a properly defined steady state wave—a stationary jump discontinuity in the Riemann solution that acts as a source term. The form of this wave is introduced and described in detail. The solver also maintains depth nonnegativity and extends naturally to Riemann problems with an initial dry state. These are important properties for applications with steady states and inundation, such as tsunami and flood modeling. Implementing the solver with LeVeque’s wave propagation algorithm [25] is also described. Several numerical simulations are shown, including a test problem for tsunami modeling. Key words: shallow water equations, hyperbolic conservation laws, finite volume methods, Godunov methods, Riemann solvers, wave propagation, shock capturing methods, tsunami modeling
The VOLNA code for the numerical modeling of tsunami waves: Generation, propagation and inundation
 Eur. J. Mech. B/Fluids
"... To cite this version: ..."
FINITE VOLUME METHODS AND ADAPTIVE REFINEMENT FOR GLOBAL TSUNAMI PROPAGATION AND LOCAL INUNDATION.
"... The shallow water equations are a commonly accepted approximation governing tsunami propagation. Numerically capturing certain features of local tsunami inundation requires solving these equations in their physically relevant conservative form, as integral conservation laws for depth and momentum. T ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
(Show Context)
The shallow water equations are a commonly accepted approximation governing tsunami propagation. Numerically capturing certain features of local tsunami inundation requires solving these equations in their physically relevant conservative form, as integral conservation laws for depth and momentum. This form of the equations presents challenges when trying to numerically model global tsunami propagation, so often the best numerical methods for the local inundation regime are not suitable for the global propagation regime. The different regimes of tsunami flow belong to different spatial scales as well, and require correspondingly different grid resolutions. The long wavelength of deep ocean tsunamis requires a large global scale computing domain, yet near the shore the propagating energy is compressed and focused by bathymetry in unpredictable ways. This can lead to large variations in energy and runup even over small localized regions. We have developed a finite volume method to deal with the diverse flow regimes of tsunamis. These methods are well suited for the inundation regime—they are robust in the presence of bores and steep gradients, or drying regions, and can capture the inundating shoreline and runup features. Additionally, these methods are wellbalanced, meaning that they can appropriately model global propagation. To deal with the disparate spatial scales, we have used adaptive refinement algorithms originally developed for gas dynamics, where often steep variation is highly localized at a given time, but moves throughout the domain. These algorithms allow evolving Cartesian subgrids that can move with the propagating waves and highly resolve local inundation of impacted areas in a single global scale computation. Because the dry regions are part of the computing domain, simple rectangular cartesian grids eliminate the need for complex shorelinefitted mesh generation. Science of Tsunami Hazards, Vol. 24, No. 5, page 319 (2006)
The GeoClaw software for depthaveraged flows with adaptive refinement
 Adv. Water Resour
"... Many geophysical flow or wave propagation problems can be modeled with twodimensional depthaveraged equations, of which the shallow water equations are the simplest example. We describe the GeoClaw software that has been designed to solve problems of this nature, consisting of open source Fortran ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
(Show Context)
Many geophysical flow or wave propagation problems can be modeled with twodimensional depthaveraged equations, of which the shallow water equations are the simplest example. We describe the GeoClaw software that has been designed to solve problems of this nature, consisting of open source Fortran programs together with Python tools for the user interface and flow visualization. This software uses highresolution shockcapturing finite volume methods on logically rectangular grids, including latitude–longitude grids on the sphere. Dry states are handled automatically to model inundation. The code incorporates adaptive mesh refinement to allow the efficient solution of largescale geophysical problems. Examples are given illustrating its use for modeling tsunamis and dambreak flooding problems. Documentation and download information is available at www.clawpack.org/geoclaw. 1.
High Resolution Methods and Adaptive Refinement for Tsunami Propagation and Inundation.
"... We describe the extension of high resolution finite volume methods and adaptive refinement for the shallow water equations in the context of tsunami modeling. Godunovtype methods have been used extensively for modeling the shallow water equations in many contexts, however, tsunami modeling presents ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
We describe the extension of high resolution finite volume methods and adaptive refinement for the shallow water equations in the context of tsunami modeling. Godunovtype methods have been used extensively for modeling the shallow water equations in many contexts, however, tsunami modeling presents some unique challenges that must be overcome. We describe some of the specific difficulties associated with tsunami modeling, and summarize some numerical approaches that we have used to overcome these challenges. For instance, we have developed a wellbalanced Riemann solver that is appropriate in the deep ocean regime as well as robust in nearshore and dry regions. Additionally, we have extended adaptive refinement algorithms to this application. We briefly describe some of the modifications necessary for using these adaptive methods for tsunami modeling.
Dynamic coupling between horizontal vessel motion and twolayer shallowwater sloshing
, 2014
"... Abstract. Numerical and analytical results are presented for fluid sloshing, of a twolayer inviscid, incompressible and immiscible fluid with thin layers and a rigid lid, coupled to a vessel which is free to undergo horizontal motion governed by a nonlinear spring. Exact analytical results are ob ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Numerical and analytical results are presented for fluid sloshing, of a twolayer inviscid, incompressible and immiscible fluid with thin layers and a rigid lid, coupled to a vessel which is free to undergo horizontal motion governed by a nonlinear spring. Exact analytical results are obtained for the linear problem, giving the natural frequencies and the resonance structure, particularly between the fluid and vessel. A numerical method for the linear and nonlinear equations is developed based on the highresolution fwavepropagation finite volume methods
FullSWOF Paral: Comparison of two parallelization strategies (MPI and SKELGIS) on a software designed for hydrology applications∗
, 2013
"... In this paper, we perform a comparison of two approaches for the parallelization of an existing, free software, FullSWOF 2D ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper, we perform a comparison of two approaches for the parallelization of an existing, free software, FullSWOF 2D
GeoClaw User’s Guide
, 2008
"... GeoClaw is a subset of the Clawpack software [4], a set of fortran routines for solving hyperbolic systems of PDE. This document contains information specific to GeoClaw. More general documentation for Clawpack is available at the Clawpack website, and should be consulted if you are new to Clawpack. ..."
Abstract
 Add to MetaCart
(Show Context)
GeoClaw is a subset of the Clawpack software [4], a set of fortran routines for solving hyperbolic systems of PDE. This document contains information specific to GeoClaw. More general documentation for Clawpack is available at the Clawpack website, and should be consulted if you are new to Clawpack. GeoClaw is available for download at www.geoclaw.org, and is included with the more general Clawpack
in
"... Adaptation of fwave finite volume methods to the twolayer shallowwater equations ..."
Abstract
 Add to MetaCart
(Show Context)
Adaptation of fwave finite volume methods to the twolayer shallowwater equations
arbitrary bed in the presence
"... finitevolume scheme for modeling shallow water flows over an ..."
(Show Context)