  Weakly ionised plasmas, formed in high enthalpy hypersonic flows, can be
actively manipulated via imposed magnetic fields - a concept termed
magnetohydrodynamic (MHD) flow control. Imposed MHD effects, within flows which
exhibit multiple shock interactions, are consequential for emerging aerospace
technologies: including aerodynamic control via magnetic actuation. However,
numerical modelling of this flow type remains challenging due to the
sensitivity of feature formation and the real gas modelling of weakly ionised,
electrically conductive, air plasma. In this work, numerical simulation
capabilities have been developed for the study of MHD affected, hypersonic
flows, around 2D axisymmetric non-simple geometries. The validated numerical
methodology, combined with an advanced 19 species equation of state for air
plasma, achieves quantitative agreement between simulation and experiment for a
Mach 5.6 double cone geometry with applied magnetic field. Numerical studies
are conducted for varied conical surface angle and magnetic field
configuration. This paper demonstrates how, for hypersonic flows with complex
shock interactions, the MHD affected flow is not only augmented in terms of
shock position, but may exhibit topological adaptations in the fundamental flow
structure. A classification system is introduced for the emergent flow
topologies. The applied numerical studies examine the mechanisms by which the
magnetic field configuration influences the MHD augmented shock structure,
leading to: (1) differences in magnitude of MHD enhancement effect, and (2)
structural adaptations of the flow topology. Most critically, classes of
conditions are identified which produce topological equivalence between the
magnetic interaction effects and a generalised mechanical control surface.
