On the behaviour of upwind schemes in the low Mach number limit
Guillard, Hervé ; Viozat, Cécile
HAL, hal-00871725 / Harvested from HAL
Text on HAL
This paper presents an asymptotic analysis in power of the Mach number of the flux difference splitting approximation of the compressible Euler equations in the low Mach number limit. We prove that the solutions of the discrete system contain pressure fluctuations of order of the Mach number while the continuous pressure scales with the square of the Mach number. This explains in a rigorous manner why this approximation of the compressible equations fails to compute very subsonic flow. We then show that a preconditioning of the numerical dissipation tensor allows to recover a correct scaling of the pressure. These theoretical results are totally confirmed by numerical experiments.
Publié le : 1999-07-05
Classification:  Low Mach number,  flux difference splitting upwind schemes,  Roe scheme,  preconditioning,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],  [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph],  [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph],  [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph] 
@article{hal-00871725,
     author = {Guillard, Herv\'e and Viozat, C\'ecile},
     title = {On the behaviour of upwind schemes in the low Mach number limit},
     journal = {HAL},
     volume = {1999},
     number = {0},
     year = {1999},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00871725}
}

Guillard, Hervé; Viozat, Cécile. On the behaviour of upwind schemes in the low Mach number limit. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00871725/