MHD flow control is a relevant topic in today’s aerospace engineering. An OpenFOAM density-based solver that is capable of handling MHD supersonic flow problems with constant magnetic field is developed. The proposed solver is based on Balbas-Tadmor central difference schemes. This solver can be applied to studying the potential of MHD flow control systems for atmospheric entry vehicles. A supersonic flow around a spherically blunt cone both with and without MHD interaction is studied. Gases with thermodynamic parameters characteristic for Earth’s and Martian atmospheres are considered. The results show visible effect of magnetic field on surface temperature of the body. The differences between shock standoff distances and general shockwave configurations of MHD and non-MHD flow are also apparent. The solution is stable for Stuart number below 0.2. Conditional instability of the solver can be attributed to the MHD term’s contribution to the local speed of sound and can be avoided by taking it into account. The developed application has proven the suitability of the used schemes for resolving steep gradients in MHD supersonic flow problems. The study itself has shown theoretical possibility of studying the MHD flow control using OpenFOAM. Further research may include an effort to stabilize the solver and to enhance the mathematical model of the flow.