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.

scholarly journals A FINITE ELEMENT METHOD FOR STORM SURGE AND TIDAL COMPUTATION

1984 ◽  
Vol 1 (19) ◽  
pp. 82 ◽  
Author(s):  
Y. Coeffe ◽  
S. Dal Secco ◽  
P. Esposito ◽  
B. Latteux
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shallow Water ◽  
Storm Surge ◽  
Incident Wave ◽  
Shallow Water Equations ◽  
Implicit Scheme ◽  
Wave Condition ◽  
Recent Developments ◽  
Element Method

The paper reports the current progress in developing a finite element method for the shallow water equations. Some recent developments as the implementation of a semi implicit scheme or the use of an incident wave condition are described. Different realistic applications are presented concerning tidal and storm surge simulations.

scholarly journals A FINITE ELEMENT METHOD FOR THE SHALLOW WATER EQUATIONS

1982 ◽  
Vol 1 (18) ◽  
pp. 40
Author(s):  
A. Hauguel ◽  
G. Labadie ◽  
B. Latteux
Keyword(s):  
Boundary Layer ◽  
Finite Element Method ◽  
Finite Element ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Solution Procedure ◽  
Numerical Results ◽  
Characteristic Curves ◽  
Element Method

The paper reports the current progress in developing a finite element method for the shallow water equations. The main feature of the method is the special care given to the advective and diffusive parts of the equations, so that it can be of interest to use it when dealing with flows strongly influenced by convective and boundary layer effects. The solution procedure has been chosen so as to allow a calculation with a big number of nodes. Section 3 of the paper outlines the method. In section 4, is detailed the procedure for the advective terms, involving the determination of the characteristic curves. Section 5 is devoted to the diffusion and propagation terms. Finally numerical results are presented in section 6.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

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