Parallel algorithms for solving the problem of coastal bottom relief dynamics

Предложена нестационарная 2D-модель транспорта донных отложений в прибрежной зоне мелководных водоемов, дополненная уравнениями Навье–Стокса, неразрывности и состояния водной среды. Дискретная модель транспорта наносов получена в результате аппроксимации соответствующей линеаризованной непрерывной модели. Поскольку задачи прогнозирования транспорта наносов требуют решения в реальном или ускоренном масштабах времени, на сетках, включающих 106–109 узлов, необходима разработка параллельных алгоритмов задач гидродинамики на системах с массовым параллелизмом. Представлены результаты работы созданного эффективного программного обеспечения для выполнения гидродинамических вычислительных экспериментов, позволяющие проводить численное моделирование деформации дна в прибрежной зоне водоема. Приведены результаты численных экспериментов. A nonstationary 2D model of bottom sediment transport in the coastal zones of shallow water reservoirs is supplemented with the Navier–Stokes equations, the continuity equation, and the state equation of the water environment. A discrete model of sediment transport is obtained by approximating the corresponding linearized continuous model. Since the problems of predicting sediment transport need to be solved in real or accelerated time scales, parallel algorithms for hydrodynamic problems on systems with mass parallelism should be developed on grids with 106–109 nodes. The paper contains the results obtained by an efficient software implemented to perform hydrodynamic computational experiments that allow the numerical modeling of bottom deformation in the coastal zones of reservoir. The results of numerical experiments are discussed.

Tsunami Observer: automatic system for estimate of tsunamigenicity of an earthquake

<p>In this talk the fully automatic system for estimate of tsunamigenicity of an earthquake is presented. The system is focused on simplicity and speed with usage of minimum of input data. The input dataset for the system includes (1) earthquake coordinates, (2) earthquake depth, (3) seismic moment, (4) focal mechanism. We use datasets provided by USGS and GEOFON. Upon receiving earthquake data the system performs the following consecutive actions. At first, the vector field of co-seismic bottom deformation is obtained using earthquake fault parameters and empirical relationships. Then the initial elevation in tsunami source is calculated and estimation of Soloviev-Imamura tsunami intensity is performed. Initial elevation is calculated taking into account vertical and horizontal components of bottom deformation, local bathymetry (GEBCO) and smoothing effect of water layer. An auxiliary study was conducted to obtain relationship between potential energy of initial elevation of water in tsunami source and intensity of resulting tsunami. More than 200 historical events from HTDB/WLD and NGDC/WDS databases was statistically processed. The obtained relationship is used to assess the intensity of tsunami generated by earthquake under consideration. Finally, if event is considered significant (energy > 10<sup>9</sup> J), the numerical simulation of propagation of tsunami waves is performed. As a result of numerical simulation, animations of wave propagation, distribution of maximum tsunami heights, and water surface time-histories in a number of given points are produced. Details of implementation, physical constraints, future development of system as well as 2-years experience of the system operation will be discussed during the talk.</p><p><strong>Acknowledgements</strong></p><p>This work was supported by the Russian Foundation for Basic Research, projects 20-07-01098, 20-35-70038, 19-05-00351.</p>

Determination of the bottom deformation from space- and time-resolved water wave measurements

In this paper we study both theoretically and experimentally the inverse problem of indirectly measuring the shape of a localized bottom deformation with a non-instantaneous time evolution, from either an instantaneous global state (space-based inversion) or a local time-history record (time-based inversion) of the free-surface evolution. Firstly, the mathematical inversion problem is explicitly defined and uniqueness of its solution is established. We then show that this problem is ill-posed in the sense of Hadamard, rendering its solution unstable. In order to overcome this difficulty, we introduce a regularization scheme as well as a strategy for choosing the optimal value of the associated regularization parameter. We then conduct a series of laboratory experiments in which an axisymmetric three-dimensional bottom deformation of controlled shape and time evolution is imposed on a layer of water of constant depth, initially at rest. The detailed evolution of the air–liquid interface is measured by means of a free-surface profilometry technique providing space- and time-resolved data. Based on these experimental data and employing our regularization scheme, we are able to show that it is indeed possible to reconstruct the seabed profile responsible for the linear free-surface dynamics either by space- or time-based inversions. Furthermore, we discuss the different relative advantages of each type of reconstruction, their associated errors and the limitations of the inverse determination.