scholarly journals Adaptive Numerical Modelling of Tsunami Wave Generation and Propagation with FreeFem++

2020 ◽  
Author(s):  
Georges Sadaka ◽  
Denys Dutykh
Keyword(s):  
Finite Element Method ◽  
Water Waves ◽  
Tsunami Wave ◽  
Boussinesq Approximation ◽  
The Finite Element Method ◽  
Flat Bottom ◽  
Variable Bottom ◽  
Dispersive System ◽  
Surface Water Waves ◽  
Tsunami Event

A simplified nonlinear dispersive system of BBM-type, initially derived by D. Mitsotakis, is employed here in order to model the generation and propagation of surface water waves over variable bottom. The simplification consists in applying the so-called Boussinesq approximation. Using the finite element method and the FreeFem++ software, we solve numerically this system for three different complexities for the bathymetry function: a flat bottom case, a variable bottom in space, and a variable bottom both in space and in time. The last case is illustrated with the Java 2006 tsunami event. This article is designed rather as a tutorial paper even if it contains the description of completely new adaptation techniques.

scholarly journals Adaptive Numerical Modeling of Tsunami Wave Generation and Propagation with FreeFem++

Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 351
Author(s):  
Georges Sadaka ◽  
Denys Dutykh
Keyword(s):  
Water Waves ◽  
Tsunami Wave ◽  
New Technology ◽  
Boussinesq Approximation ◽  
Boussinesq System ◽  
The Finite Element Method ◽  
Flat Bottom ◽  
Source Codes ◽  
Variable Bottom ◽  
Surface Water Waves

A simplified nonlinear dispersive Boussinesq system of the Benjamin–Bona–Mahony (BBM)-type, initially derived by Mitsotakis (2009), is employed here in order to model the generation and propagation of surface water waves over variable bottom. The simplification consists in prolongating the so-called Boussinesq approximation to bathymetry terms, as well. Using the finite element method and the FreeFem++ software, we solve this system numerically for three different complexities for the bathymetry function: a flat bottom case, a variable bottom in space, and a variable bottom both in space and in time. The last case is illustrated with the Java 2006 tsunami event. This article is designed to be a pedagogical paper presenting to tsunami wave community a new technology and a novel adaptivity technique, along with all source codes necessary to implement it.

Water waves over a variable bottom: a non-local formulation and conformal mappings

2012 ◽  
Vol 695 ◽  
pp. 288-309 ◽  
Author(s):  
A. S. Fokas ◽  
A. Nachbin
Keyword(s):  
Water Waves ◽  
Conformal Mappings ◽  
The Novel ◽  
Local Equation ◽  
Flat Bottom ◽  
Weakly Nonlinear ◽  
Variable Bottom ◽  
Non Local ◽  
Three Space ◽  
Non Local Equations

AbstractIn Ablowitz, Fokas & Musslimani (J. Fluid Mech., vol. 562, 2006, pp. 313–343) a novel formulation was proposed for water waves in three space dimensions. In the flat-bottom case, this formulation consists of the Bernoulli equation, as well as of a non-local equation. The variable-bottom case, which now involves two non-local equations, was outlined but not explored in the above paper. Here, the variable-bottom formulation is addressed in more detail. First, it is shown that in the weakly nonlinear, weakly dispersive regime, the above system of three equations can be reduced to a system of two equations. Second, by combining the novel non-local formulation of the above authors with conformal mappings, it is shown that in the two-dimensional case, it is possible to obtain a system of two equations without any asymptotic approximations. Furthermore, for the weakly nonlinear, weakly dispersive regime, the nonlinear equations are simpler than the equations obtained without conformal mappings, since they contain lower order derivatives for the terms involving the bottom variable.

Simulation of the Conjugate Heat Trasfer on the Process Incipient State in a Bridgman Method

2012 ◽  
Vol 7 (4) ◽  
pp. 127-135
Author(s):  
Vladimir Berdnikov ◽  
Mariya Kudryavtseva
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Graphite Crucible ◽  
Boussinesq Approximation ◽  
Bridgman Method ◽  
The Finite Element Method ◽  
Rectangular Mesh ◽  
Silicon Melt ◽  
Self Consistent ◽  
Region Evolution

Numerically the conjugate convective heat transfer in a flat-bottomed graphite crucible at a stage previous an onset of solidification of a silicon melt in a vertical variant of a Bridgman method is researched. The finite element method on rectangular mesh solves set of equations of thermogravitational convection in Boussinesq approximation in variables temperature, a stream function and a vorticity in cylindrical co-ordinates. At the fixed geometry of calculation region evolution of the space configuration of melt flow of silicon of the thermogravitational nature in a range of Grashof numbers Gr from 1 to 1,3 × 107 is studied. Self-consistent fields of temperature in a melt, walls of a crucible and in a gas interlayer are calculated at stationary boundary conditions

scholarly journals A COMBINED FE-BIE METHOD FOR WATER WAVES

1978 ◽  
Vol 1 (16) ◽  
pp. 40
Author(s):  
A. Hauguel
Keyword(s):  
Finite Element Method ◽  
Integral Equation ◽  
Water Waves ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
The Finite Element Method ◽  
Combined Method ◽  
Engineering Problems ◽  
Oscillations And Waves ◽  
Harbour Oscillations

The finite element method and boundary integral equation method are general approximation processes applicable to a wide variety of engineering problems. After a brief description of the combined method, several examples are given for water waves problems : tides, harbour oscillations and waves diffraction and refraction.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

Sign in / Sign up

Export Citation Format

Share Document