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

S. S. Ravindran


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.


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

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DOI: http://dx.doi.org/10.11121/ijocta.01.2018.00325


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