Journal ArticleDOI
Semi-implicit finite difference methods for the two-dimensional shallow water equation
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TLDR
It is shown that the stability restriction is eliminated and the artificial viscosity is reduced when an Eulerian-Lagrangian approach with large time steps is used to discretize the convective terms.About:
This article is published in Journal of Computational Physics.The article was published on 1990-01-03. It has received 411 citations till now. The article focuses on the topics: Finite difference method & Discretization.read more
Citations
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Semi-implicit finite difference methods for three-dimensional shallow water flow
Vincenzo Casulli,Ralph T. Cheng +1 more
TL;DR: The resulting two- and three- dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows and is fully vectorizable for an efficient implementation on modern vector computers.
Journal ArticleDOI
A staggered conservative scheme for every Froude number in rapidly varied shallow water flows
TL;DR: In this paper, the authors proposed a numerical technique based on the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied flows as well.
Journal ArticleDOI
An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator
TL;DR: In this paper, a finite-volume formulation is presented that solves the three-dimensional, non-hydrostatic Navier-Stokes equations with the Boussinesq approximation on an unstructured, staggered, z-level grid.
Journal ArticleDOI
Stability, accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow☆
Vincenzo Casulli,E. Cattani +1 more
TL;DR: In this paper, a semi-implicit finite difference scheme for the numerical solution of a three-dimensional shallow water model is presented and discussed, in which pressure is assumed to be hydrostatic and the velocity gradient in the momentum equations and the velocities in the vertically integrated continuity equation are discretized with the θ-method, with θ being an implicitness parameter.
Journal ArticleDOI
An unstructured grid, three-dimensional model based on the shallow water equations
Vincenzo Casulli,Roy A. Walters +1 more
TL;DR: A semi-implicit finite difference model based on the three-dimensional shallow water equations is modified to use unstructured grids, which is relatively simple, conserves mass, can fit complicated boundaries and yet is sufficiently flexible to permit local mesh refinements in areas of interest.
References
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Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures*
Jim Douglas,Thomas F. Russell +1 more
TL;DR: Finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form $cu_t + bu_x - (au_x )_x = f as mentioned in this paper.
Journal ArticleDOI
Finite-Difference Methods for Partial Differential Equations.
Journal ArticleDOI
An Efficient Two‐Time‐Level Semi‐Lagrangian Semi‐Implicit Integration Scheme
TL;DR: This paper presents a two-time-level version of the semi-implicit semi-Lagrangian integration technique, which yields the same level of accuracy for half the computational effort and does not rely on operator splitting.
Related Papers (5)
Semi-implicit finite difference methods for three-dimensional shallow water flow
Vincenzo Casulli,Ralph T. Cheng +1 more
Stability, accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow☆
Vincenzo Casulli,E. Cattani +1 more
An unstructured grid, three-dimensional model based on the shallow water equations
Vincenzo Casulli,Roy A. Walters +1 more