  We describe a new theoretical and numerical framework of the
magnetohydrodynamic simulation incorporated with an anisotropic pressure
tensor, which can play an important role in a collisionless plasma. A classical
approach to handle the anisotropy is based on the double adiabatic
approximation assuming that a pressure tensor is well described only by the
components parallel and perpendicular to the local magnetic field. This
gyrotropic assumption, however, fails around a magnetically neutral region,
where the cyclotron period may get comparable to or even longer than a
dynamical time in a system, and causes a singularity in the mathematical
expression. In this paper, we demonstrate that this singularity can be
completely removed away by the combination of direct use of the 2nd-moment of
the Vlasov equation and an ingenious gyrotropization model. Numerical tests
also verify that the present model properly reduces to the standard MHD or the
double adiabatic formulation in an asymptotic manner under an appropriate
limit.
