Abstract
It is known that the Navier-Stokes equations do not adequately predict gasdynamic shock profiles and thicknesses for Mach numbers exceeding about 1.4. The Burnett equations, second-order in the Knudsen number, improve agreement with experiment but at a critical Mach number of 1.8 the inclusion of these terms causes pathological oscillations to develop in the solution. It appears that this failure arises in the initial formulation of the kinetic equation, not in its method of solution. Spurious terms in the Burnett equations arise because standard theories do not properly distinguish between convection and diffusion. Such theories are valid only to first-order.
By incorporating fluid acceleration, Woods (1993) eliminates the frame-dependence from the second-order transport equations. A novel solution method is developed to solve the steady shock wave equations, including the modified second-order terms, in one dimension. This Finite Difference Global Scheme (FDGS) makes use of a global Newton iterative procedure. The scheme is applied to obtain shock thicknesses in a monatomic gas up to Mach 30. Comparison with experimental data for argon gas shows good agreement, well within the data point spread and a significant improvement over Navier-Stokes predictions. The method of solution is straightforward, needs no higher-order terms for stabilization, and is efficient in computational time.
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© 1995 Springer-Verlag Berlin Heidelberg
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Reese, J.M., Woods, L.C., Thivet, F.J.P., Candel, S.M. (1995). The Inner Shock Structure Determined From a Modified Frame-Independent Second-Order Kinetic Theory. In: Brun, R., Dumitrescu, L.Z. (eds) Shock Waves @ Marseille IV. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79532-9_7
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DOI: https://doi.org/10.1007/978-3-642-79532-9_7
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