A decoupled Crank-Nicolson time-stepping scheme for thermally coupled magneto-hydrodynamic system

S. S. Ravindran

doi:10.11121/ijocta.01.2018.00325

Authors

S. S. Ravindran University of Alabama in Huntsville

DOI:

https://doi.org/10.11121/ijocta.01.2018.00325

Keywords:

thermally coupled MHD, Crank-Nicolson, mixed finite element, error estimates, non-homogeneous boundary condition, partitioned method

Abstract

Thermally coupled magneto-hydrodynamics (MHD) studies the dynamics of electro-magnetically and thermally driven flows,
involving MHD equations coupled with heat equation. We introduce a partitioned method that allows one to decouple
the MHD equations from the heat equation at each time step and solve them separately. The extrapolated
Crank-Nicolson time-stepping scheme is used for time discretization
while mixed finite element method is used for spatial discretization.
We derive optimal order error estimates in suitable norms without assuming any stability condition or restrictions on the time step
size. We prove the unconditional stability of the scheme. Numerical experiments are used to illustrate the theoretical results.

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Author Biography

S. S. Ravindran, University of Alabama in Huntsville

Dr. Ravindran is currently a professor at the University of Alabama in Huntsville, which he joined in 1999. Prior to this appointment, he was an NRC research fellow in the Flow Modeling and Control Branch at NASA Langley Research Center. Previous to that, he was a visiting assistant professor in the Center for Research in Scientific Computation at North Carolina State University. He is a six-time recipient of NASA Summer Faculty Research Fellowship and spent the summers of 2003, 2006, 2009, 2010, 2012 and 2015 at the NASA Marshall Space Flight Center (MSFC). As principal investigator of various research grants, he has conducted research for agencies such as the National Science Foundation, DOD, NASA Langley Research Center and NASA Marshall Space Flight Center. He has to his credit numerous refereed publications in journals such as Numerishe Mathematik,SIAM Journal of Scientific Computing, SIAM Journal of Control and Optimization, Numerical Methods for Partial Differential Equation, Numerical Functional Analysis and Optimization, Journal of Computational Physics, Computer Methods in Applied Mechanics and Engineering, AIAA Journal of Propulsion and Power, Numerical Methods for Fluids and other professional journals and proceedings. He has also given invited lectures in France, Austria, Spain, India, Canada and the United States, and at professional societies such as SIAM, IEEE, AIAA, and ASME. His scientific expertise has been recognized by over 1400 citations of his publications and, by invitations to consult by industry and government labs and to serve in the Editorial Boards of a number of international journals including International Scholarly Research Notices, Mathematical Problems in Engineering and Engineering Mathematics Letters. He has taught many graduate and undergraduate level courses in areas most related to computational mechanics such as finite element methods, partial differential equations, numerical analysis, linear algebra and matrix computations.

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