Simulation of the Effect of Far Field Tsunami Through an Open Boundary Condition in a Boundary-Fitted Curvilinear Grid System (original) (raw)
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2012
A new approach is developed to simulate the effect of far field tsunami in a limited area model domain where the coastal and Island boundaries are curvilinear in nature and the bending is high. The model is designed in a boundary fitted curvilinear grid system. To simulate the effect of far field tsunami, it is considered that the tsunami source is located far away from the model domain. The coastal and island boundaries and the other open boundaries of the model domain are represented by some functions so as to generate the boundary fitted grids. To use the regular finite difference scheme a transformation is used so that the physical domain is transformed into a rectangular one. The transformed shallow water equations are then solved in the transformed domain. The response of the tsunami source due to 26 December 2004 Indonesian tsunami is computed along the western open boundary of the model domain. Based on the response of the tsunami source, an appropriate boundary condition is...
Global Journal of Science Frontier Research, 2012
The 26 December 2004 Indonesian tsunami was the third known global tsunami and reached every distant corner of the globe. An effort has been made here to evaluate the effect of this distant tsunami in a limited area model domain. The effect of distant tsunami has been simulated through an open boundary condition in a Cartesian coordinate shallow water linear model. The open boundary condition is applied to simulate the tsunami propagation when it is assumed that the tsunami is generated far away from the region of interest. The computational domain covers the region so that the 26 December 2004 Indonesian tsunami source is well within the model domain. First, the initial disturbance of the tsunami source are examined along the western open boundary of the model domain and then the boundary condition is formulated and adjusted in such a manner that the effects of tsunami due to the source along the coasts are same as the effects due to the formulated boundary condition. The response ...
Int. J. Tsunami Soc, 2007
The west coast of Peninsular Malaysia and Thailand is curvilinear in nature and the bending is especially high along the coast of South Thailand. In hydrodynamic models for coastal seas, bays and estuaries, the use of boundary-fitted curvilinear grids not only makes the model grids fit well with the coastline and bathymetry, but also makes the finite difference scheme simple. In this study, a shallow water model is developed using boundary fitted curvilinear mesh. The west coast of Peninsular Malaysia and Thailand and the western open boundary are represented by two curves, which are defined by two functions. The other two boundaries are considered as straight lines along the open sea. Appropriate transformations of independent coordinates are applied so that the curvilinear physical domain transforms to a rectangular domain and the curvilinear grid system transforms to a rectangular system. The depth averaged shallow water equations and the boundary conditions are transformed to the new space domain and these are solved in the rectangular mesh of the transformed space. The model is applied to compute some aspects of the tsunami associated with the 26 December 2004 Indonesian tsunami along the coastal belts of Penang in Malaysia and Phuket in Thailand. The computed results along the coastal belts are in excellent agreement with the observe data available in the USGS website.
2017
A numerical technique in a boundary-fitted curvilinear grid model is developed to simulate the extent of inland inundation along the coastal belts of Peninsular Malaysia and Southern Thailand due to 2004 Indian ocean tsunami. Tsunami propagation and run-up are also studied in this paper. The vertically integrated shallow water equations are solved by using the method of lines (MOL). For this purpose the boundary-fitted grids are generated along the coastal and island boundaries and the other open boundaries of the model domain. A transformation is used to the governing equations so that the transformed physical domain is converted into a rectangular one. The MOL technique is applied to the transformed shallow water equations and the boundary conditions so that the equations are converted into ordinary differential equations initial value problem. Finally the 4<sup>th</sup> order Runge-Kutta method is used to solve these ordinary differential equations. The moving boundar...
Numerical Modelling of 2004 Indonesian Tsunami along the coast of Phuket
IOSR Journal of Mathematics, 2015
In coastline, the boundary-fitted curvilinear grids are appropriate to make the grid model and build up the simple boundary conditions, which are more mathematic. The method of lines (MOL) is a general procedure for the solution of time dependent partial differential equations (PDEs. The methods of lines (MOL) are more feasible and comparable to the regular finite difference method in terms of computational time, accuracy and numerical stability. Thus, we have tried to present the new numerical solution technique to simulate the 2004 Indonesian tsunami. At first, this numerical solution technique set up on a curvilinear grid model where the vertically integrated shallow water equations are solved by using MOL. The boundary fitted curvilinear grids are presented along the coastal and island boundaries. Thereafter, we have applied the method of lines (MOL) technique to transform the shallow water equations and boundary conditions. These equations transfigure into ordinary differential equations with the initial value problem. At last, we have used Runge-Kutta 4 th order method to solve these ordinary differential equations. To simulate the 2004 Indonesian tsunami along the Puket coast, we have compared our results with the authentic research papers and USGS, where this simulation shows excellent agreement with observing data.
Applied Numerical …, 2011
Tsunami waves (long waves) are effectively modelled by the nonlinear shallow water equations. These are often solved numerically by appropriate finite difference or finite volume techniques. For the applications presented herein, a dispersive, splitting direction based, finite difference method is applied for the construction of an approximate solution. All three phases of the evolution of the tsunami wave, the generation, propagation and runup are reproduced, providing a complete simulation capability of the tsunami wave. A case study considering an earthquake generated tsunami that strikes Crete island is considered. Seismic fault parameters are reconstructed from historical description of the specific earthquake and related geological and seismological references. Thus realistic initial and boundary conditions were generated, for the numerical simulation of the wave field of the induced tsunami. Actual bathymetric and topographic data of the coastal area considered are used for the description of the complex computational domain and grid generation. Inundation maps for the wave field and plots of damage metrics of the tsunami, like the flow depth and current speed, are also shown.
2015
This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. We develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons of water surface elevation obtained from numerical simulations and field measurements are made.
2008
After the destructive event of December 26, 2004, many attempts have been made to accurately simulate the generation and propagation of tsunami waves in the Indian Ocean. In support of the Tsunami Early Warning System for the Indian Ocean, a very high-resolution finite element model (TsunAWI) has been developed for simulations of the wave propagation. It offers geometrical flexibility by working on unstructured triangular grids and is based on finite-element 1 1 P P NC ! discretization. The paper offers a brief description of the model, with a focus on its verification and validation. The key issue in modelling the tsunami is wetting and drying. The original algorithm to solve this problem is discussed. Full and reduced formulation of the momentum advection for 1 1 P P NC ! elements and parameterization of horizontal diffusion are presented. Using the wellknown Okushiri test case, the influence of nonlinearity on the wave propagation is demonstrated. Numerical experiments simulating...
Applied Numerical Mathematics, 2013
Tsunamis are long waves and commonly modeled with the shallow-water wave approximation of the equations of motion. The calculation of tsunami inundation remains after two decades of progress a vexing and temperamental computation exquisitely dependent on ad-hoc algorithms. We present computed results using, a splitting method in space to reduce this hyperbolic system in two successive hyperbolic systems, one for each primitive variable. Then, we use dispersive, Godunov type finite difference method and solve the equations in characteristic form. We use the methodology implemented in the code MOST to calculate inundation from four different earthquake scenarios for Heraklion, Greece. MOST has been repeatedly benchmarked. The scenarios are geophysical estimates of the source mechanisms of the 365 AD event, the largest known earthquake in the Eastern Mediterranean in the last two millenia. The earthquake scenarios used allow for defining the seafloor deformation resulting from the parent seismic motions and, after translating them to the water surface, they constitute the initial conditions for computations. We use high resolution bathymetric and topographic data to generate fine resolution grids used in the computations. Our practice allows for a precise identification of the onland inundation and the overland flow depths and currents during tsunami flooding in Heraklion. This is the first time such a quantitative study has been undertaken for Eastern Crete. We conclude that there is substantial hazard, and there is little difference among the four different seismic interpretations of the 365 AD earthquake.
Finite element method for tsunami wave propagation analysis considering the open boundary condition
Computers & Mathematics with Applications, 1988
A method for the treatment of the open boundary condition in the shallow-water equation to analyze the propagation of tsunami waves using a finite element method is proposed. The key feature of this method is that the analytical solutions of the linear shallow-water equation can be linked with the inner values of the velocity and the water elevation on the open boundary. The two-step explicit method is used to discretize the time function, which has an advantage in problems treating large numbers of elements and unsteady state. Two test examples have been carried out. The numerical results are in good agreement with the analytical solutions. The Tokachi-oki Earthquake tsunami has been computed. The computed results have been compared with the observed tide gauge records. From these comparative studies, it can be concluded that the present method is a useful and effective tool in predicting tsunami generation and propagation.