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A kinetic transport-projection splitting algorithm for an hierarchy of moment closures of gas-kinetic equations

We review some geometrical properties of models of moment closures of gas-kinetic equations, and consider a transport-projection splitting scheme for construction of solutions of such closures. The scheme, formulated in terms of a dual kinetic density, defines the kinetic density in successive superposition of transport in $x$--direction and projection to a finite dimensional linear space in a weighted $L^2$ space, in the kinetic variable $v.$ Given smooth initial data, we show that the approximate solutions converge to a unique classical solution of a system of moment closure PDEs.