Viscous Compressible Slip Flows. Part 1: Kinetic Flux Vector Splitting and its Variance Reduction form

Mahendra, Ajit Kumar; Gouthaman, G.; Singh, R. K.
March 2011
International Journal of Emerging Multidisciplinary Fluid Scienc;Mar2011, Vol. 3 Issue 1, p21
Academic Journal
The work is in two parts: Part 1 deals with kinetic treatment of the slip flow and Part 2 deals with numerical modeling of the rarefied and rotating slip flow. The present paper containing Part 1 gives an overview of kinetic theory and its application to fluid flow, Bhatnagar-Gross-Krook (BGK) model and construction of Chapman-Enskog distribution. The paper describes the Kinetic Flux Vector Splitting (KFVS) scheme which performs upwinding in the Boltzmann level for viscous flows for three dimensional and axi-symmetric geometries. The paper also describes novel Variation Reduction Kinetic Flux Vector Splitting (VRKFVS) and kinetic treatment of the slip and far field boundary. Viscous split fluxes based on kinetic flux vector splitting satisfy the Onsager reciprocity relations and are treated in upwind manner for effective capture of slip phenomenon. Slip velocity not only depends on the velocity gradient in the normal direction but also on the fluid dynamic gradients in the tangential flow direction. Treatment of slip boundary using kinetic upwind fluxes based on diffuse reflection model considers these variations in the tangential flow direction.


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