The development of a versatile computational tool for the solution of turbulent magnetohydrodynamic flows is presented. The flow solver can simulate the full magnetohydrodynamic equations or simplified equations based on the low magnetic Reynolds number approximation. Both laminar and turbulent flows are investigated. The Baldwin‐Lomax turbulence model evaluates the eddy viscosity to represent turbulence. Modifications accounting for the presence of a magnetic field are presented to extend its range of application to magnetohydrodynamic flows. The modification of the turbulence model is performed based on the turbulent Hartmann flow. The numerical solutions are compared with existing analytical solutions and experimental data, for low- and high-speed magnetohydrodynamic flows.