Interplanetary coronal mass ejections (ICMEs) have complex magnetic and
density structures, which is the result of their interaction with the
structured solar wind and with previous eruptions. ICMEs are revealed by in
situ measurements and in the past five years, through remote-sensing
observations by heliospheric imagers. However, to understand and analyze these
observations often requires the use of numerical modeling. It is because no
instruments can yet provide a simple view of ICMEs in two or three dimensions.
Numerical simulations can be used to determine the origin of a complex ejecta
observed near Earth, or to analyze the origin, speed and extent of density
structures observed remotely. Here, we review and discuss recent efforts to use
numerical simulations of ICMEs to investigate the magnetic topology, density
structure, energetics and kinematics of ICMEs in the interplanetary space.
After reviewing existing numerical models of ICMEs, we first focus on
numerical modeling in support of the SMEI and STEREO observations. 3-D
simulations can help determining the origins of the fronts observed by SECCHI
and SMEI, especially for complex events such as the January 24-25, 2007 CMEs.
They can also be used to test different methods to derive ICME properties from
remote observations, to predict and explain observational effects, and to
understand the deceleration and deformation of ICMEs. In the last part, we
focus on the numerical investigation of non-magnetic cloud ejecta. We discuss
how simulations are crucial to understand the formation of non-twisted ejecta
and the formation of complex ejecta due to the interaction of multiple ICMEs.