# On a hybrid finite-volume-particle method

• Volume: 38, Issue: 6, page 1071-1091
• ISSN: 0764-583X

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## Abstract

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We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the finite-volume-particle method is to use different schemes for the flow and pollution computations: the shallow water equations are numerically integrated using a finite-volume scheme, while the transport equation is solved by a particle method. This way the specific advantages of each scheme are utilized at the right place. A special attention is given to the recovery of the point values of the numerical solution from its particle distribution. The reconstruction is obtained using a dual equation for the pollutant concentration. This results in a significantly enhanced resolution of the computed solution and also makes it much easier to extend the finite-volume-particle method to the two-dimensional case.

## How to cite

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Chertock, Alina, and Kurganov, Alexander. "On a hybrid finite-volume-particle method." ESAIM: Mathematical Modelling and Numerical Analysis 38.6 (2010): 1071-1091. <http://eudml.org/doc/194248>.

@article{Chertock2010,
abstract = { We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the finite-volume-particle method is to use different schemes for the flow and pollution computations: the shallow water equations are numerically integrated using a finite-volume scheme, while the transport equation is solved by a particle method. This way the specific advantages of each scheme are utilized at the right place. A special attention is given to the recovery of the point values of the numerical solution from its particle distribution. The reconstruction is obtained using a dual equation for the pollutant concentration. This results in a significantly enhanced resolution of the computed solution and also makes it much easier to extend the finite-volume-particle method to the two-dimensional case. },
author = {Chertock, Alina, Kurganov, Alexander},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Shallow water equations; transport of passive pollutant; finite-volume schemes; particle method.; numerical examples; transport of pollutant},
language = {eng},
month = {3},
number = {6},
pages = {1071-1091},
publisher = {EDP Sciences},
title = {On a hybrid finite-volume-particle method},
url = {http://eudml.org/doc/194248},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Chertock, Alina
AU - Kurganov, Alexander
TI - On a hybrid finite-volume-particle method
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 6
SP - 1071
EP - 1091
AB - We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the finite-volume-particle method is to use different schemes for the flow and pollution computations: the shallow water equations are numerically integrated using a finite-volume scheme, while the transport equation is solved by a particle method. This way the specific advantages of each scheme are utilized at the right place. A special attention is given to the recovery of the point values of the numerical solution from its particle distribution. The reconstruction is obtained using a dual equation for the pollutant concentration. This results in a significantly enhanced resolution of the computed solution and also makes it much easier to extend the finite-volume-particle method to the two-dimensional case.
LA - eng
KW - Shallow water equations; transport of passive pollutant; finite-volume schemes; particle method.; numerical examples; transport of pollutant
UR - http://eudml.org/doc/194248
ER -

## References

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