  In this contribution we derive and analyze a new numerical method for kinetic
equations based on a variable transformation of the moment approximation.
Classical minimum-entropy moment closures are a class of reduced models for
kinetic equations that conserve many of the fundamental physical properties of
solutions. However, their practical use is limited by their high computational
cost, as an optimization problem has to be solved for every cell in the
space-time grid. In addition, implementation of numerical solvers for these
models is hampered by the fact that the optimization problems are only
well-defined if the moment vectors stay within the realizable set. For the same
reason, further reducing these models by, e.g., reduced-basis methods is not a
simple task. Our new method overcomes these disadvantages of classical
approaches. The transformation is performed on the semi-discretized level which
makes them applicable to a wide range of kinetic schemes and replaces the
nonlinear optimization problems by inversion of the positive-definite Hessian
matrix. As a result, the new scheme gets rid of the realizability-related
problems. Moreover, a discrete entropy law can be enforced by modifying the
time stepping scheme. Our numerical experiments demonstrate that our new method
is often several times faster than the standard optimization-based scheme.
