# On a hybrid finite-volume-particle method

Alina Chertock; Alexander Kurganov

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topChertock, 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 -

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