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The effects of an inhomogeneous magnetic medium,on the propagation of magneto-hydrodynamical (MHD) laminar flame,fronts are investigated. This investigation is motivated by the,occurrence of magnetized thermonuclear combustion in several,astrophysical systems. Magnetized thermonuclear burning occurs on the,surfaces of neutron stars during Type I X-ray bursts, within the,interiors of white dwarfs during Type~Ia supernovae, during classical,novae, and may be important for certain core collapse supernovae as,well. Thermonuclear flames that propagate in these systems travel,through inhomogeneous magnetic fields. I present the results of a,series of $1.5$-dimensional numerical simulations of magnetized flame,propagation conducted using the MHD extension to the High Speed,Combustion and Detonation (HSCD) code. A simplified flame model is,used with one-step Arrhenius kinetics, an ideal gas equation of,state, and constant thermal conductivity coefficients. Although,idealized, the model allows for the opportunity to study the physics,of the problem without the complexities of the nuclear,kinetics of thermonuclear burning. Steady-state solutions for this,simplified model were presented in \citet{RemmingKhokhlov:2016}. To confirm that,the solutions are indeed steady, as well as to verify the physics,algorithms programmed in HSCD, laminar flame solutions are mapped to,the HSCD computational grid and evolved in time without being exposed,to perturbations. They remain steady on the HSCD grid to a very high,degree for long integration times. After this verification step, I,simulate the propagation of laminar flames through inhomogeneous,magnetic media. A changing magnetic medium significantly alters,the structure of the flame through the generation of an electric,current that is directed out of the plane of the flame front. The,electric current rotates the direction of the magnetic field within,the flame and produces strong shear flows. Furthermore, for flames,that conduct heat anisotropically and that propagate at an angle $0 <,\psi \lesssim \pi/2$ to the magnetic field (where $\psi$ is relative,to the flame front normal), the flame speed increases due to the,non-uniform magnetic field. Naturally occurring flames in,astrophysical systems may experience similar changes to their,structure and speed that would influence the observational properties,of these systems.


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