  In this paper, we contribute operator-splitting methods improved by the
Zassenhaus product for the numerical solution of linear partial differential
equations. We address iterative splitting methods, that can be improved by
means of the Zassenhaus product formula, which is a sequnential splitting
scheme. The coupling of iterative and sequential splitting techniques are
discussed and can be combined with respect to their compuational time. While
the iterative splitting schemes are cheap to compute, the Zassenhaus product
formula is more expensive, based on the commutators but achieves higher order
accuracy. Iterative splitting schemes and also Zassenhaus products are applied
in physics and physical chemistry are important and are predestinated to their
combinations of each benefits. Here we consider phase models in CFD
(computational fluid dynamics). We present an underlying analysis for obtaining
higher order operator-splitting methods based on the Zassenhaus product.
  Computational benefits are given with sparse matrices, which arose of spatial
discretization of the underlying partial differential equations. While
Zassenhaus formula allows higher accuracy, due to the fact that we obtain
higher order commutators, we combine such an improved initialization process to
cheap computable to linear convergent iterative splitting schemes.
  Theoretical discussion about convergence and application examples are
discussed with CFD problems.
