Rapidly emerging micro-electro-mechanical devices create new potential microfluidic applications. A simulation of an internal and external gas flows is important for their design. For small Knudsen number Kn < 0.1 (Kn = l0/L, where l0 is the mean free path of the gas molecules and L is the characteristic length), a continuum approach based on modified Navier-Stokes-Fourier or extended hydrodynamic continuum models with corresponding velocity-slip and temperature-jump boundary conditions is still applicable and, respectively, preferable. We restrict ourself to the use of Navier-Stokes-Fourier continuum model. A development of the algorithm to solve a specific class of problems is closely related to numerical schemes used for approximation of equations terms. Higher-order approximation schemes can reduce the number of mesh nodes and respectively computational time, but it is possible to obtain physical unrealistic results. In this paper we study influence of some approximation schemes for convective terms over the spatial steps. It is compared upwind, central difference and total variation diminishing (TVD) schemes Min-Mod, QUICK and SUPERBEE. A test case is gas flow past a square in a microchannel at subsonic speed (Mach number M = 0.1) and supersonic speed (M = 2.43), available in a literature.

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