RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 8, ES5004, doi:10.2205/2006ES000213, 2006
A software complex for the numerical simulation of generation and propagation of tsunami waves in various marine areas from dynamic seismic sourcesL. Yu. Kataeva, A. V. Romanov, R. Kh. Mazova, and I. V. Kozhevnikov Nizhny Novgorod State Technical University, Nizhny Novgorod, RussiaContentsAbstract[1] A software complex is designed for the simulation of tsunami generation by a dynamic seismic source consisting of several vertically moving blocks of a preset configuration. The program interface allows the user to change the source kinematics of the blocks as a function of the seismic source under consideration. The software makes it possible to display the tsunami wave propagation in a water area (unconstrained by concrete conditions), perform its monitoring, interrupt and resume computations, depict the tsunami wave propagation front, display the distribution of maximum wave heights in a marine area, construct histograms of maximum wave heights along a coastline, and construct the velocity fields of particles in the traveling wave, wave front velocities, and mareograms at any given points of the area under consideration. Using the software capabilities, current data and their variation in time can be obtained at any point of the calculation domain, and all results (both final and intermediate) can be saved in the form of both numerical data and plots or diagrams. Introduction[2] At present, many numerical schemes exist together with the related interfaces designed in such a way that a user insufficiently skilled in programming can work with the program. Developed software complexes are not always conformable to the algorithm used by its author for implementing the concept of a given physical process. Our software complex is based on the original concept of a dynamic seismic source of various configurations moving in various times intervals and at various velocities, and its interface enables the most comprehensive implementation of this idea. As a mathematical model, we used the well-known nonlinear equations of shallow water [Garagash et al., 2003; Lobkovsky et al., 2005], and both the well-known numerical schemes [Bakhvalov, 1975; Marchuk et al., 1983] and efficient difference schemes based on the iterative interpolation method were used for numerical implementation of the model, which significantly reduced the computation time, without invoking methods of concurrent programming. Main Equations[3] To describe the generation and propagation of a wave, we use the nonlinear system of equations of shallow water
Here grad(s) = sxi + syj, div(s) = (s1)x + (s2)y, i and j are unit vectors directed along the x and y axes,
[4] The inferred values are then corrected for the Earth's curvature. The time step was chosen from the stability condition of the difference scheme in use.
[5] For an adequate implementation, we introduced a model grid with spatial intervals (in degrees)
Dx and
Dy and with a time step
Dt. The spatial intervals were corrected
for the Earth's curvature:
Dxp = (Dx [6] To describe free boundaries in the problem of tsunami wave propagation, we chose the well-known Sommerfeld condition, according to which the part of the wave field beyond the boundary is transferred along the outer normal with a constant velocity defined by the basin depth near the boundary and without changing the waveform. The normal component of the velocity at the free boundary is calculated from the known relation un = c h/(H + h), and the tangential velocity component vanishes, ut = 0. Program Interface and Its Description[7] The developed software complex can be easily used for modeling the generation and propagation of tsunami waves from a dynamic source in various water areas. Below we describe the possibilities of this complex.
[9] 1. Transformation of initial data; [10] 2. Module loading the transformed file and initializing the required data arrays; [11] 3. Module specifying calculation parameters and display parameters of results; [12] 4. Module specifying dynamic sources and their characteristics; [13] 5. Module displaying and saving results; [14] 6. Computation module. [15] Below we illustrate the operation of these modules in more detail. [16] The module of transformation of initial data reads the initial data file, corrects the data, and converts them into the binary format. In addition, the module allows the user to choose a part of the given water area that will be used for calculations. [17] Module 2 loads the data file into memory; the data are used for calculations and for the initialization of arrays required for the calculations and saving of their results.
[20] Module displaying and saving results enables the following functions.
[22] (ii) The Show Terr tool enables the display of the bottom topography and the dynamics of block motion. The result can be saved in the bmp format (Figure 6). [23] In addition, the following functions of automatic saving of pictures in the process of computations are implemented. [24] (iii) The Show max H and Show min H tools display the current maximum and minimum values of wave heights in the water area. These tools are active only if the process of computations is in progress or interrupted. The result can be saved in the bmp format. [25] (iv) The Show Eta tool displays current values of wave heights in the water area. The tool is active only if the process of computations is in progress or interrupted. The result can be saved in the bmp format. If the auto option is inactive, results are not saved.
[27] (vi) Show data window can be active only during the computation process. If active, this tool displays a floating popup window showing the following values: h, ocean depth at a given point; u and v, velocities of wave particles at the given point along the X and Y axes, respectively; vis, current wave height at the given point; max vis and min vis, maximum and minimum ocean surface heights at the given point over the entire time of computations; C, wave front velocity (Figure 8). [28] Thus, we have complete information on the water area throughout the computation process.
[31] Computation module provides for the possibility of a new run, its saving, its interruption and renewal, and the test run, i.e., the computation in the same water area with a fixed depth value. ReferencesBakhvalov, N. S. (1975), Numerical Methods (Analysis, Algebra, and Ordinary Differential Equations) (in Russian), 632 pp., Nauka, Moscow. Garagash, I. A., L. I. Lobkovsky, O. R. Kozyrev, and R. Kh. Mazova (2003), Tsunami wave generation and runup caused by a submarine landslide, Okeanologiya (in Russian), 43, (2), 185. Lobkovsky, L. I., R. Kh. Mazova, L. A. Garagash, L. Kataeva, and N. S. Petrukhin (2005), Analysis of the 26 December 2004 earthquake and tsunami in the Indian Ocean on the basis of the subduction keyboard model, EGU General Assembly, EGU, Vienna, Austria, 24-30 April 2005. Marchuk, A. G., L. B. Chubarov, and Yu. I. Shokin (1983), Numerical Simulation of Tsunami Waves (in Russian), 175 pp., Nauka, Novosibirsk. Received 21 October 2006; accepted 30 October 2006; published 20 December 2006. Keywords: program interface, mathematical model, shallow water equations, software product. Index Terms: 3285 Mathematical Geophysics: Wave propagation; 4255 Oceanography: General: Numerical modeling; 4594 Oceanography: Physical: Instruments and techniques. ![]() Citation: 2006), A software complex for the numerical simulation of generation and propagation of tsunami waves in various marine areas from dynamic seismic sources, Russ. J. Earth Sci., 8, ES5004, doi:10.2205/2006ES000213. (Copyright 2006 by the Russian Journal of Earth SciencesPowered by TeXWeb (Win32, v.2.0). |