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Authors: Anton Ponomarev 1 ; Julian Hofmann 2 and Lutz Gröll 2

Affiliations: 1 Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia ; 2 Karlsruhe Institute of Technology, Institute for Automation and Applied Informatics, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

Keyword(s): Partial Differential Equations, Simulink, Transport, Convection, Method of Characteristics.

Abstract: The paper deals with solving first-order quasilinear partial differential equations in an online simulation environment, such as Simulink, utilizing the well-known and well-recommended method of characteristics. Compared to the commonly applied space discretization methods on static grids, the characteristics-based approach provides better numerical stability. Simulink subsystem implementing the method of characteristics is developed. It employs Simulink’s built-in solver and its zero-crossing detection algorithm to perform simultaneous integration of a pool of characteristics as well as to create new characteristics dynamically and discard the old ones. Numerical accuracy of the solution thus obtained is established. The subsystem has been tested on a full-state feedback example and produced better results than the space discretization-based “method of lines”. The implementation is available for download and can be used in a wide range of models.

CC BY-NC-ND 4.0

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Paper citation in several formats:
Ponomarev, A.; Hofmann, J. and Gröll, L. (2020). Characteristics-based Simulink Implementation of First-order Quasilinear Partial Differential Equations. In Proceedings of the 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - SIMULTECH; ISBN 978-989-758-444-2; ISSN 2184-2841, SciTePress, pages 139-146. DOI: 10.5220/0009569001390146

@conference{simultech20,
author={Anton Ponomarev. and Julian Hofmann. and Lutz Gröll.},
title={Characteristics-based Simulink Implementation of First-order Quasilinear Partial Differential Equations},
booktitle={Proceedings of the 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - SIMULTECH},
year={2020},
pages={139-146},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0009569001390146},
isbn={978-989-758-444-2},
issn={2184-2841},
}

TY - CONF

JO - Proceedings of the 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - SIMULTECH
TI - Characteristics-based Simulink Implementation of First-order Quasilinear Partial Differential Equations
SN - 978-989-758-444-2
IS - 2184-2841
AU - Ponomarev, A.
AU - Hofmann, J.
AU - Gröll, L.
PY - 2020
SP - 139
EP - 146
DO - 10.5220/0009569001390146
PB - SciTePress

- Science and Technology Publications, Lda.
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