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Its behavior is examined in the nearly incompressible limit and in the fully compressible limit.
The occurring shear reduces with the drift ratio and is ascribed to the compressible limit of the underlying LBM.
Thus, in the compressible limit, the governing equations are hyperbolic but can not be written as conservation laws, i.e. in divergence form.
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The quasineutral limit of the compressible Navier-Stokes-Poisson system was studied in [13 15].
The incompressible limit of the compressible fluid equations is a significant issue in the mathematical theory of fluid dynamics.
We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M≪1.
Based on the work of Rossow and Swanson we are going to present a further modification for the extension of a compressible code towards the incompressible limit.
This paper is concerned with the incompressible limit of the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions in RN (N= 2,3).
The physical model is described by the low Mach number equations, which are obtained as a limit of the compressible Navier Stokes equations in the small Mach number regime.
Analysis of the dissipation terms in this form for both the Roe scheme and the basic (current) scheme leads to the incorporation of certain terms into the basic scheme to establish the transition from compressible flow toward the incompressible limit.
It is found necessary to use preconditioning with this blending technique to account for a remaining "compressible" contribution in the incompressible limit, and a suitable matrix directly applicable to conservative residuals is derived.
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