Oberseminar Angewandte Mathematik

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mohlb_01

Hendrik Ranocha (Mathematics Münster) via Zoom: Combining Analysis and Data: Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics.

Wednesday, 07.07.2021 14:00

Mathematik und Informatik

We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime, focusing on discontinuous spectral element semidiscretizations. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice by combining analysis with a data-driven approach, which we apply to design design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We compare a wide range of error-control-based methods, along with the common approach in which step size control is based on the Courant-Friedrichs-Lewy (CFL) number. The new optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances, while additionally providing control of the temporal error at tighter tolerances. The numerical examples include challenging industrial CFD applications.

A preprint of this joint work with Lisandro Dalcin, Matteo Parsani, and David Ketcheson is available at http://arxiv.org/abs/2104.06836.



Angelegt am Tuesday, 15.06.2021 16:16 von mohlb_01
Geändert am Tuesday, 15.06.2021 16:16 von mohlb_01
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Konferenzen+Kolloquien
Angewandte Mathematik Münster
Kolloquium der angewandten Mathematik
Oberseminar Angewandte Mathematik
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giesbec

Hendrik Ranocha (WWU Münster) via ZOOM: Combining Analysis and Data: Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

Wednesday, 07.07.2021 14:00

Mathematik und Informatik

Abstract: We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime, focusing on discontinuous spectral element semidiscretizations. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice by combining analysis with a data-driven approach, which we apply to design design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We compare a wide range of error-control-based methods, along with the common approach in which step size control is based on the Courant-Friedrichs-Lewy (CFL) number. The new optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances, while additionally providing control of the temporal error at tighter tolerances. The numerical examples include challenging industrial CFD applications. A preprint of this joint work with Lisandro Dalcin, Matteo Parsani, and David Ketcheson is available at http://arxiv.org/abs/2104.06836.



Angelegt am Tuesday, 15.06.2021 17:22 von giesbec
Geändert am Tuesday, 15.06.2021 17:22 von giesbec
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Angewandte Mathematik Münster
Kolloquium der angewandten Mathematik
Oberseminar Angewandte Mathematik
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giesbec

Sara Merino Aceituno (Universität Wien, Österreich) via ZOOM: Applying kinetic theory to the study of collective dynamics

Wednesday, 14.07.2021 14:00

Mathematik und Informatik

Abstract: The aim of this introductory talk is to illustrate how kinetic theory is used to investigate collective behaviour. Particularly, I will introduce the Vicsek model and Vicsek-related models. In the Vicsek model agents have a constant speed while trying to move in the same direction as their neighbors. The goal is to derive continuum/fluid-like equations from the discrete dynamics of the system. This derivation corresponds to linking microscopic and macroscopic phenomena.



Angelegt am Tuesday, 20.04.2021 10:56 von giesbec
Geändert am Tuesday, 04.05.2021 12:09 von giesbec
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Oberseminar Angewandte Mathematik
Kolloquium der angewandten Mathematik
Angewandte Mathematik Münster