This paper presents a numerical method for predicting 2-D and 3-D slightly compressible flow along microchannels, in which, one dimension is much smaller than the others (such as in ink jet printerheads). Both the configuration and the slightly compressible character of the fluid are very typical in practice and are amenable to simplification of the Navier-Stokes equations for more efficient calculation. Based on assumptions of these particular configurations and the fluid property, simplified systems of Navier-Stokes equations are obtained. Bicharacteristic based numerical calculations are developed to solve the systems of simplified, slightly compressible, viscous, Navier-Stokes equations. Two dimensional results are compared with analytical solutions. Three-dimensional results are compared with the results of commercial CFD code. Satisfactory agreements have been obtained and great efficiency has been achieved.

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