article

High Order Multi-dimensional Characteristics Tracing for the Incompressible Euler Equation and the Guiding-Center Vlasov Equation

Authors:

Giovanni Russo,

Jing-Mei QiuAuthors Info & Claims

Journal of Scientific Computing, Volume 77, Issue 1

Pages 263 - 282

https://doi.org/10.1007/s10915-018-0705-y

Published: 01 October 2018 Publication History

Abstract

In this paper, we propose a high order characteristics tracing scheme for the two-dimensional nonlinear incompressible Euler system in vorticity stream function formulation and the guiding center Vlasov model. Such a scheme is incorporated into a semi-Lagrangian finite difference WENO framework for simulating the aforementioned model equations. This is an extension of our earlier work on high order characteristics tracing scheme for the 1D nonlinear Vlasov---Poisson system (Qiu and Russo in J Sci Comput 71:414---434, 2017). The effectiveness of the proposed scheme is demonstrated numerically by an extensive set of test cases.

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Cited By

Boscheri WTavelli MPareschi L(2022)On the Construction of Conservative Semi-Lagrangian IMEX Advection Schemes for Multiscale Time Dependent PDEsJournal of Scientific Computing10.1007/s10915-022-01768-090:3Online publication date: 11-Feb-2022
https://dl.acm.org/doi/10.1007/s10915-022-01768-0
Zoni EGüçlü Y(2019)Solving hyperbolic-elliptic problems on singular mapped disk-like domains with the method of characteristics and spline finite elementsJournal of Computational Physics10.1016/j.jcp.2019.108889398:COnline publication date: 1-Dec-2019
https://dl.acm.org/doi/10.1016/j.jcp.2019.108889
Xiong TRusso GQiu J(2019)Conservative Multi-dimensional Semi-Lagrangian Finite Difference SchemeJournal of Scientific Computing10.1007/s10915-018-0892-679:2(1241-1270)Online publication date: 17-May-2019
https://dl.acm.org/doi/10.1007/s10915-018-0892-6
Show More Cited By

High Order Multi-dimensional Characteristics Tracing for the Incompressible Euler Equation and the Guiding-Center Vlasov Equation
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
    2. Numerical analysis
2. Theory of computation

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Published In

cover image Journal of Scientific Computing

Journal of Scientific Computing Volume 77, Issue 1

October 2018

688 pages

ISSN:0885-7474

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Copyright © Copyright © 2018 Springer Science+Business Media, LLC, part of Springer Nature.

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Plenum Press

United States

Publication History

Published: 01 October 2018

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Cited By

Boscheri WTavelli MPareschi L(2022)On the Construction of Conservative Semi-Lagrangian IMEX Advection Schemes for Multiscale Time Dependent PDEsJournal of Scientific Computing10.1007/s10915-022-01768-090:3Online publication date: 11-Feb-2022
https://dl.acm.org/doi/10.1007/s10915-022-01768-0
Zoni EGüçlü Y(2019)Solving hyperbolic-elliptic problems on singular mapped disk-like domains with the method of characteristics and spline finite elementsJournal of Computational Physics10.1016/j.jcp.2019.108889398:COnline publication date: 1-Dec-2019
https://dl.acm.org/doi/10.1016/j.jcp.2019.108889
Xiong TRusso GQiu J(2019)Conservative Multi-dimensional Semi-Lagrangian Finite Difference SchemeJournal of Scientific Computing10.1007/s10915-018-0892-679:2(1241-1270)Online publication date: 17-May-2019
https://dl.acm.org/doi/10.1007/s10915-018-0892-6
Cai XGuo WQiu J(2019)A High Order Semi-Lagrangian Discontinuous Galerkin Method for the Two-Dimensional Incompressible Euler Equations and the Guiding Center Vlasov Model Without Operator SplittingJournal of Scientific Computing10.1007/s10915-018-0889-179:2(1111-1134)Online publication date: 17-May-2019
https://dl.acm.org/doi/10.1007/s10915-018-0889-1

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