Abstract
We study a linear model for the propagation of hydro-acoustic waves and tsunami in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. The new formulation is obtained by studying the functional spaces and operators associated to the model. The mathematical study of this new formulation is easier and the discretization is also more efficient than for the previous formulation. We prove that both formulations are well posed and show that the solution to the first formulation can be obtained from the solution to the second. Finally, the formulations are discretized using a spectral element method, and we simulate tsunamis generation from submarine earthquakes and landslides.
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Abstract
We address an optimization problem where the cost function is the expectation of a random mapping. To tackle the problem two approaches based on the approximation of the objective function by consensus-based particle optimization methods on the search space are developed. The resulting methods are mathematically analyzed using a mean-field approximation and their connection is established. Several numerical experiments show the validity of the proposed algorithms and investigate their rates of convergence.
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Abstract
The interest in boundary feedback control of multi-dimensional hyperbolic systems is increasing. In the present work we want to compare some of the recent results available in the literature.
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Abstract
Recently the barotropic two fluid model belonging to the class of symmetric hyperbolic thermodynamically compatible (SHTC) systems was studied in detail in [13]. There the question was raised whether the dissipative structure introduced by the source terms satisfies the Shizuta - Kawashima condition. This well-known condition is a sufficient criterion for the existence of global smooth solutions of the studied system. In this work we exploit the dissipative structure of the system under consideration and verify that the Shizuta-Kawashima condition holds.
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Abstract
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure, the spatial part of the dimensionless four-velocity and the particle density. Radially symmetric solutions of these equations are studied in two and three space dimensions. Of particular interest in the solutions are the formation of shock waves and a pressure blow up. For the investigation of these phenomena we develop a one-dimensional scheme using radial symmetry and integral conservation laws. We compare the numerical results with solutions of multi-dimensional high-order numerical schemes for general initial data in two space dimensions. The presented test cases and results may serve as interesting benchmark tests for multi-dimensional solvers.