Authors: Samuel Granovsky (Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102, USA), Alexander G. Kosovichev (Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102, USA, NASA Ames Research Center, Moffett Field, Mountain View, CA 94035, USA), Irina N. Kitiashvili (NASA Ames Research Center, Moffett Field, Mountain View, CA 94035, USA)

While solar flares are primarily associated with enhanced ultraviolet and X-ray emission, a subset of flares exhibit significant continuum brightening in visible light and are classified as white-light flares (WLFs). Despite extensive observational and modeling efforts, the physical mechanisms responsible for the compact, short-lived photospheric brightenings in WLF kernels observed during the impulsive phase of solar flares remain uncertain. Thick-target electron-beam models typically deposit energy in the upper chromosphere, and their ability to reproduce the magnitude and spatial localization of photospheric continuum enhancements observed in white-light flare kernels remains an open question. To investigate the role of realistic atmospheric structuring and multidimensional transport in flare energy deposition, we perform three-dimensional radiative MHD simulations of electron-beam heating using the StellarBox code for beam fluxes of 10^12 erg\,s^{-1} cm$^{-2} and low-energy cutoffs of 10 – 25 keV. We then compute Fe I 6173 Å Stokes profiles using the RH 1.5D radiative transfer code for direct comparison with Helioseismic and Magnetic Imager (HMI) observations. The simulations produce strong upper-chromospheric heating, multiple shock fronts, and continuum enhancements up to a factor of 2.5 relative to pre-flare levels, comparable to continuum enhancements observed during strong X-class white-light flares. Comparison with one-dimensional RADYN simulations highlights the influence of fine-scale structuring on flare dynamics and continuum emission that arises in three-dimensional geometry.