Development of an Ideal Magnetohydrodynamics Flowsolver for High Speed Flow Control

  • Ramakrishnan BalasubramanianEmail author
  • Karupannasamy Anandhanarayanan
Original Contribution


This paper presents the baseline development of an ideal magnetohydrodynamics (MHD) solver towards enhancing the knowledge base on the numerical and flow physics complexities associated with MHD flows. The ideal MHD governing equations consisting of the coupled fluid flow equations and the Maxwell’s equations of electrodynamics are implemented in the three dimensional finite volume flowsolver, CERANS. Upwind flux functions such as AUSM-PW+, KFVS and the local Lax-Friedrichs schemes were used for solving the discretized form of governing equations. The solenoidal constraint which requires that the magnetic field to be divergence free all through the flow field evolution is ensured using the artificial compressibility analogy method or the Powell’s source term method. The code had been validated for standard MHD test cases involving complex flowfields such as the MHD shock tube, blast, vortex, cloud-shock interaction and cylinder shock interaction problems. The flow control effect of MHD interaction had been demonstrated for supersonic flow past a wedge and the results are compared with analytical results obtained by solving the MHD Rankine Hugoniot relations. Further, MHD flow control for high speed flows had been demonstrated for the hypersonic blunt body problem. Through rigorous testing and validation, it is observed that the CERANS-MHD code is able to mimic the complex flows due to MHD interactions and the comparison of results are found to be in good agreement with similar literature.


Ideal MHD CERANS Artificial compressibility analogy (ACA) Powell source Flow control 



Area of surface


jth component of magnetic field intensity


Characteristic speed


Specific energy


jth component of flux vector


Mach number


jth component of surface outward normal

p, \({\text{p}}_{\text{t}}\)

Static and total pressure


Time in seconds


Source term vector


Fluid temperature


Conserved variable vector


Contra-variant velocity


Velocity vector


Volume of cell element


Reference velocity for ACA method

u, v, w

Velocity components along x, y, z directions

x, y, z

Cartesian coordinate directions

L, R

Left, right states

Greek symbols


Ratio of specific heats


Divergence free variable for ACA method


Density of fluid




Magnetic permeability of free space (4π × 10−7 N/A2)


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Copyright information

© The Institution of Engineers (India) 2017

Authors and Affiliations

  • Ramakrishnan Balasubramanian
    • 1
    Email author
  • Karupannasamy Anandhanarayanan
    • 1
  1. 1.Computational Fluid Dynamics Division, Directorate of Computational DynamicsDefence Research and Development LaboratoryHyderabadIndia

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