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Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction
Published in Journal of Computational Physics, 2018
This paper is about Tsunami simulations using a Discontinuous Galerkin method for the Spherical Shallow Water Equations. We present a method that is well-balanced even when wetting-drying and dynamically adaptive meshing is considered. We demonstrate this using large-scale tsunami simulations such as the 2011 Tohoku tsunami. Results are compared to real-world measurements.
Recommended citation: Bonev, Boris; Hesthaven, Jan S.; Giraldo, Francis X.; Kopera, Michal A. (2018). "Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction." Journal of Computational Physics. 362, 425-448. http://dx.doi.org/10.1016/j.jcp.2018.02.008
Published in International Conference on Learning Representations, 2018
This publication proposes a method of using neural networks to generate liquid simulations on the fly. Space-time datasets are used to learn deformation networks which can reconstruct a new space-time dataset that the network is fed. We demonstrate the effectiveness of the method, by doing this on a smartphone in real-time.
Recommended citation: Prantl, Lukas; Bonev, Boris; Thuerey Nils. (2019). "Generating Liquid Simulations with Deformation-aware Neural Networks." International Conference on Learning Representations 2019. https://openreview.net/pdf?id=HyeGBj09Fm
Published in Ocean Modelling, 2019
This paper is about different tsunami source models. We study the impact of dynamic and static source models on the numerical results obtained with them. This is done using our discontinuous Galerkin method. Numerical results are comnpared to real-world data such as satellite and buoy measurements.
Recommended citation: Hajihassanpour, Mahya; Bonev, Boris; Hesthaven, Jan S. (2019). "A comparative study of earthquake source models in high-order accurate tsunami simulations." Ocean Modelling. 141. http://dx.doi.org/10.1016/j.ocemod.2019.101429
Discontinuous Galerkin methods have desirable properties, which make them suitable for the com- putation of wave problems. Being parallelizable and hp-adaptive makes them attractive for the simulation of large-scale tsunami propagation. In order to retrieve such a scheme, we formulate the shallow water equations on the spherical shell and apply the discontinuous Galerkin discretiza- tion to construct a numerical method which is able to handle the effects of curvature and Coriolis forces naturally. Common challenges in solving the shallow water equations numerically are well- balancedness and wetting/drying. To overcome this, we utilize a method based on a timestep restriction, which guarantees the positivity of the numerical solution. Moreover, we show that our discretization yields a well-balanced numerical scheme. In this talk we will present our method as well as the numerical results, that we have obtained with our implementation.
We present a novel method for the simulation of large scale tsunami events using a high-order discontinuous Galerkin discretization of the spherical shallow water equations. This requires a well-balanced discretization, which cannot rely on exact quadrature, due to the curved mesh. We achieve this by splitting the well-balanced condition into individual problems for the flux and volume terms. As it turns out, this approach has significant advantages: It allows the construction of non-conforming, well-balanced flux discretizations. Thus we can perform non-conforming mesh refinement, all while preserving the well-balanced property of the scheme. More importantly, we are able to develop a new method for handling wet/dry transitions. In contrast to other wetting/drying methods, this method is well-balanced and able to handle wetting/drying at any order - all without the introduction of further model assumptions such as artificial viscosity, porosity or cancellation of gravity. We demonstrate our new method for both the one-dimensional and spherical shallow water equa- tions. In the latter case, we perform a simulation of the 2011 Tohoku tsunami and validate our results with real-world buoy data.
While physics aims to describe nature in terms of mathematics, numerical mathematics aims to represent nature on a computer. This talk will show how we develop a computational model with the example of large-scale tsunami simulations. Finally, we will see how we can use these models to gain a better understanding of our world. Numerical mathematics brings together physics, computer science, engineering and of course, mathematics.
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.
Undergraduate course, EPFL, Math department, 2019
Principal assistant for the course “Probabilité et Statistique”, teaching engineering students the fundamentals of probability theory and statistics.