A comparison of finite element and hybrid ray-tracing propagation models for shallow water environments

2016 ◽  
Vol 140 (4) ◽  
pp. 3014-3014 ◽  
Author(s):  
Marcia J. Isakson ◽  
Jacob George ◽  
David Harvey
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Ray Tracing ◽  
Propagation Models

Ray tracing in a finite-element domain using nodal basis functions

2014 ◽  
Vol 53 (24) ◽  
pp. F10 ◽  
Author(s):  
Karl N. Schrader ◽  
Samuel R. Subia ◽  
John W. Myre ◽  
Kenneth L. Summers
Keyword(s):  
Finite Element ◽  
Ray Tracing ◽  
Basis Functions ◽  
Nodal Basis

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 conservative fully-discrete numerical method for the regularised shallow water wave equations

2021 ◽  
Author(s):  
Dimitrios Mitsotakis ◽  
Hendrik Ranocha ◽  
David I Ketcheson ◽  
Endre Süli
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Numerical Method ◽  
Solitary Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Mixed Finite Element ◽  
Boussinesq System ◽  
Fully Discrete ◽  
Long Time

The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and reflective boundary conditions. The particular system is one of a class of equations derived recently and can be used in practical simulations to describe the propagation of weakly nonlinear and weakly dispersive long water waves, such as tsunamis. Studies of small-amplitude long waves usually require long-time simulations in order to investigate scenarios such as the overtaking collision of two solitary waves or the propagation of transoceanic tsunamis. For long-time simulations of non-dissipative waves such as solitary waves, the preservation of the total energy by the numerical method can be crucial in the quality of the approximation. The new conservative fully-discrete method consists of a Galerkin finite element method for spatial semidiscretisation and an explicit relaxation Runge--Kutta scheme for integration in time. The Galerkin method is expressed and implemented in the framework of mixed finite element methods. The paper provides an extended experimental study of the accuracy and convergence properties of the new numerical method. The experiments reveal a new convergence pattern compared to standard Galerkin methods.

Application of finite‐element models to backscatter from shallow water internal waves

1992 ◽  
Vol 92 (4) ◽  
pp. 2467-2467
Author(s):  
Stanley A. Chin‐Bing ◽  
David B. King ◽  
Joseph E. Murphy ◽  
Gongqin Li
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Internal Waves ◽  
Finite Element Models
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