Finite element or finite difference methods for the two-dimensional shallow water equations?

1976 ◽  
Vol 7 (3) ◽  
pp. 351-357 ◽  
Author(s):  
T.J. Weare
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Difference Methods ◽  
Two Dimensional ◽  
Difference Methods

Finite difference methods for 2D shallow water equations with dispersion

2019 ◽  
Vol 34 (2) ◽  
pp. 105-117 ◽  
Author(s):  
Gayaz S. Khakimzyanov ◽  
Zinaida I. Fedotova ◽  
Oleg I. Gusev ◽  
Nina Yu. Shokina
Keyword(s):  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Difference Methods ◽  
Original System ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Elliptic Type ◽  
Two Dimensional ◽  
Nonlinear Hyperbolic System

Abstract Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively different in the cases the dispersion is taken into account, or not. The difference in the behavior of phase errors in one- and two-dimensional cases is pointed out. Special attention is paid to the numerical algorithm based on the splitting of the original system of equations into a nonlinear hyperbolic system and a scalar linear equation of elliptic type.

Characteristics of finite difference methods for dispersive shallow water equations

2016 ◽  
Vol 31 (3) ◽  
Author(s):  
Zinaida I. Fedotova ◽  
Gayaz S. Khakimzyanov
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Difference Methods ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Hydrodynamic Equations ◽  
Difference Methods

AbstractThe paper contains a description of the most important properties of numerical methods for solving nonlinear dispersive hydrodynamic equations and their distinctions from similar properties of finite difference schemes approximating classic dispersion-free shallow water equations.

RECENT DEVELOPMENTS IN THE NUMERICAL SIMULATION OF SHALLOW WATER EQUATIONS II: TEMPORAL DISCRETIZATION

1994 ◽  
Vol 04 (04) ◽  
pp. 533-556 ◽  
Author(s):  
V. AGOSHKOV ◽  
E. OVCHINNIKOV ◽  
A. QUARTERONI ◽  
F. SALERI
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Results ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Recent Developments ◽  
Numerical Approaches

This paper deals with time-advancing schemes for shallow water equations. We review some of the existing numerical approaches, propose new schemes and investigate their stability. We present numerical results obtained using the time-advancing schemes proposed, with finite element and finite difference approximation in space variables.

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