Discontinuous Galerkin method for a nonlocal hydrodynamic model of flocking dynamics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10382255" target="_blank" >RIV/00216208:11320/18:10382255 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jcp.2018.06.055" target="_blank" >https://doi.org/10.1016/j.jcp.2018.06.055</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jcp.2018.06.055" target="_blank" >10.1016/j.jcp.2018.06.055</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Discontinuous Galerkin method for a nonlocal hydrodynamic model of flocking dynamics

Popis výsledku v původním jazyce

In this paper we devise an efficient and robust numerical method for a nonlocal nonlinear model of flocking dynamics. The governing equations are a hydrodynamic limit of the model of Cucker and Smale which consists of the compressible Euler equations with added nonlinear nonlocal interaction terms. The numerical scheme is based on the discontinuous Galerkin method. A semi-implicit scheme is used in the time discretization which requires only the solution of one linear system per time level while retaining the stability of an implicit scheme. A crucial point is the construction of a suitable linearization of the nonlocal terms which does not result in fill-in of the system matrices. Element-wise and inter-element artificial diffusion is added to the scheme along with a postprocessing procedure to deal with near-vacuum states that typically arise in the solution. We demonstrate the efficiency and robustness of the scheme on numerical experiments in 1D and 2D. (C) 2018 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Discontinuous Galerkin method for a nonlocal hydrodynamic model of flocking dynamics

Popis výsledku anglicky

In this paper we devise an efficient and robust numerical method for a nonlocal nonlinear model of flocking dynamics. The governing equations are a hydrodynamic limit of the model of Cucker and Smale which consists of the compressible Euler equations with added nonlinear nonlocal interaction terms. The numerical scheme is based on the discontinuous Galerkin method. A semi-implicit scheme is used in the time discretization which requires only the solution of one linear system per time level while retaining the stability of an implicit scheme. A crucial point is the construction of a suitable linearization of the nonlocal terms which does not result in fill-in of the system matrices. Element-wise and inter-element artificial diffusion is added to the scheme along with a postprocessing procedure to deal with near-vacuum states that typically arise in the solution. We demonstrate the efficiency and robustness of the scheme on numerical experiments in 1D and 2D. (C) 2018 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA17-01747S" target="_blank" >GA17-01747S: Teorie a numerická analýza sdružených problémů dynamiky tekutin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Computational Physics

ISSN

0021-9991

e-ISSN

—

Svazek periodika

372

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

500-523

Kód UT WoS článku

000443284400024

EID výsledku v databázi Scopus

2-s2.0-85049088335