A multidimensional fluctuation splitting scheme for the three dimensional Euler equations

Bastin, 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 -