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We review some geometrical properties of models of moment closures ofgas-kinetic equations, and consider a transport-projection splitting scheme forconstruction of solutions of such closures. The scheme, formulated in terms ofa dual kinetic density, defines the kinetic density in successive superpositionof transport in $x$--direction and projection to a finite dimensional linearspace in a weighted $L^2$ space, in the kinetic variable $v.$ Given smoothinitial data, we show that the approximate solutions converge to a uniqueclassical solution of a system of moment closure PDEs.

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