224 research outputs found
The GeoClaw software for depth-averaged flows with adaptive refinement
Many geophysical flow or wave propagation problems can be modeled with
two-dimensional depth-averaged 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 high-resolution shock-capturing 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
large-scale geophysical problems. Examples are given illustrating its use for
modeling tsunamis, dam break problems, and storm surge. Documentation and
download information is available at www.clawpack.org/geoclawComment: 18 pages, 11 figures, Animations and source code for some examples at
http://www.clawpack.org/links/awr10 Significantly modified from original
posting to incorporate suggestions of referee
Equal-area method for scalar conservation laws
We study one-dimensional conservation law. We develop a simple numerical
method for computing the unique entropy admissible weak solution to the initial
problem. The method basis on the equal-area principle and gives the solution
for given time directly.Comment: 10 pages, 7 figure
A moving mesh method for one-dimensional hyperbolic conservation laws
We develop an adaptive method for solving one-dimensional systems of hyperbolic conservation laws that employs a high resolution Godunov-type scheme for the physical equations, in conjunction with a moving mesh PDE governing the motion of the spatial grid points. Many other moving mesh methods developed to solve hyperbolic problems use a fully implicit discretization for the coupled solution-mesh equations, and so suffer from a significant degree of numerical stiffness. We employ a semi-implicit approach that couples the moving mesh equation to an efficient, explicit solver for the physical PDE, with the resulting scheme behaving in practice as a two-step predictor-corrector method. In comparison with computations on a fixed, uniform mesh, our method exhibits more accurate resolution of discontinuities for a similar level of computational work
- …