  Composite supernova remnants consist of a pulsar wind nebula located inside a
shell-type remnant. The presence of a shell has implications on the evolution
of the nebula, although the converse is generally not true. The purpose of this
paper is two-fold. The first aim is to determine the effect of the pulsar's
initial luminosity and spin-down rate, the supernova ejecta mass, and density
of the interstellar medium on the evolution of a spherically-symmetric,
composite supernova remnant expanding into a homogeneous medium. The second aim
is to investigate the evolution of the magnetic field in the pulsar wind nebula
when the the composite remnant expands into a non-uniform interstellar medium.
The Euler conservation equations for inviscid flow, together with the
magnetohydrodynamic induction law in the kinematic limit, are solved
numerically for a number of scenarios where the ratio of magnetic to particle
energy is $\sigma < 0.01$. The simulations in the first part of the paper is
solved in a one-dimensional configuration. In the second part of the paper, the
effect of an inhomogeneous medium on the evolution is studied using a
two-dimensional, axis-symmetric configuration.
