BOLTZMANN SCHEMES FOR CONTINUUM GAS-DYNAMICS

Many problems arising in the aerodynamic design of aerospace vehicles require the numerical solution of the Euler equations of gas dynamics. These are nonlinear partial differential equations admitting weak sol utions such as shock waves and constructing robust numerical schemes f or these equations is a challenging task. A new line of research calle d Boltzmann or kinetic schemes discussed in the present paper exploits the connection between the Boltzmann equation of the kinetic theory o f gases and the Euler equations for inviscid compressible flows. Becau se of this connection, a suitable moment of a numerical scheme for the Boltzmann equation yields a numerical scheme for the Euler equations. This idea called the ''moment method strategy'' turns out to be an ex tremely rich methodology for developing robust numerical schemes for t he Euler equations. The richness is demonstrated by developing a varie ty of kinetic schemes such as kinetic numerical method, kinetic flux v ector splitting method, thermal velocity based splitting, multidirecti onal upwind method and least squares weak upwind Scheme. A 3-D time-ma rching Euler code called BHEEMA based on the kinetic flux vector split ting method and its variants involving equilibrium chemistry have been developed for computing hypersonic reentry flows. The results obtaine d from the code BHEEMA, demonstrate the robustness and the utility of the kinetic flux vector splitting method as a design tool in aerodynam ics.