# A multidimensional fluctuation splitting scheme for the three dimensional Euler equations

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 6, page 1241-1259
- ISSN: 0764-583X

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topBastin, Jérôme, and Rogé, Gilbert. "A multidimensional fluctuation splitting scheme for the three dimensional Euler equations." ESAIM: Mathematical Modelling and Numerical Analysis 33.6 (2010): 1241-1259. <http://eudml.org/doc/197433>.

@article{Bastin2010,

abstract = {
The fluctuation splitting schemes were introduced by Roe in the beginning of the
80's and have been then developed since then, essentially thanks to Deconinck.
In this paper, the fluctuation splitting
schemes formalism is recalled. Then, the hyperbolic/elliptic decomposition of the
three dimensional Euler equations is presented. This decomposition leads to an acoustic
subsystem and two scalar advection equations, one of them being the entropy advection.
Thanks to this decomposition, the two scalar equations are treated with the well known
PSI scalar fluctuation splitting scheme, and the acoustic subsystem is treated
with the Lax Wendroff matrix fluctuation splitting scheme. An
additional viscous term is introduced in order to reduce the oscillatory behavior of the
Lax Wendroff scheme. An implicit form leads
to a robust scheme which enables computations over a large range
of Mach number. This fluctuation splitting scheme, called the Lax Wendroff - PSI scheme, produces
little
spurious entropy, thus leading to accurate drag predictions.
Numerical results obtained with this Lax Wendroff PSI scheme are presented and compared to a
reference Euler code, based on a Lax Wendroff scheme.
},

author = {Bastin, Jérôme, Rogé, Gilbert},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {3D Euler equations; robust fluctuation splitting scheme;
large range of Mach number; accurate flow computations.; fluctuation splitting scheme; hyperbolic/elliptic decomposition; three-dimensional Euler equations; acoustic subsystem; two scalar advection equations; entropy advection; Lax-Wendroff matrix fluctuation splitting scheme; Lax-Wendroff-PSI scheme},

language = {eng},

month = {3},

number = {6},

pages = {1241-1259},

publisher = {EDP Sciences},

title = {A multidimensional fluctuation splitting scheme for the three dimensional Euler equations},

url = {http://eudml.org/doc/197433},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Bastin, Jérôme

AU - Rogé, Gilbert

TI - A multidimensional fluctuation splitting scheme for the three dimensional Euler equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 6

SP - 1241

EP - 1259

AB -
The fluctuation splitting schemes were introduced by Roe in the beginning of the
80's and have been then developed since then, essentially thanks to Deconinck.
In this paper, the fluctuation splitting
schemes formalism is recalled. Then, the hyperbolic/elliptic decomposition of the
three dimensional Euler equations is presented. This decomposition leads to an acoustic
subsystem and two scalar advection equations, one of them being the entropy advection.
Thanks to this decomposition, the two scalar equations are treated with the well known
PSI scalar fluctuation splitting scheme, and the acoustic subsystem is treated
with the Lax Wendroff matrix fluctuation splitting scheme. An
additional viscous term is introduced in order to reduce the oscillatory behavior of the
Lax Wendroff scheme. An implicit form leads
to a robust scheme which enables computations over a large range
of Mach number. This fluctuation splitting scheme, called the Lax Wendroff - PSI scheme, produces
little
spurious entropy, thus leading to accurate drag predictions.
Numerical results obtained with this Lax Wendroff PSI scheme are presented and compared to a
reference Euler code, based on a Lax Wendroff scheme.

LA - eng

KW - 3D Euler equations; robust fluctuation splitting scheme;
large range of Mach number; accurate flow computations.; fluctuation splitting scheme; hyperbolic/elliptic decomposition; three-dimensional Euler equations; acoustic subsystem; two scalar advection equations; entropy advection; Lax-Wendroff matrix fluctuation splitting scheme; Lax-Wendroff-PSI scheme

UR - http://eudml.org/doc/197433

ER -

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