  We study the dynamics of thermonuclear flames propagating in fuel stirred by
stochastic forcing. The fuel consists of carbon and oxygen in a state which is
encountered in white dwarfs close to the Chandrasekhar limit. The level set
method is applied to represent the flame fronts numerically. The computational
domain for the numerical simulations is cubic, and periodic boundary conditions
are imposed. The goal is the development of a suitable flame speed model for
the small-scale dynamics of turbulent deflagration in thermonuclear supernovae.
Because the burning process in a supernova explosion is transient and spatially
inhomogeneous, the localised determination of subgrid scale closure parameters
is essential. We formulate a semi-localised model based on the dynamical
equation for the subgrid scale turbulence energy $k_{\mathrm{sgs}}$. The
turbulent flame speed $s_{\mathrm{t}}$ is of the order
$\sqrt{2k_{\mathrm{sgs}}}$. In particular, the subgrid scale model features a
dynamic procedure for the calculation of the turbulent energy transfer from
resolved toward subgrid scales, which has been successfully applied to
combustion problems in engineering. The options of either including or
suppressing inverse energy transfer in the turbulence production term are
compared. In combination with the piece-wise parabolic method for the
hydrodynamics, our results favour the latter option. Moreover, different
choices for the constant of proportionality in the asymptotic flame speed
relation,
  $s_{\mathrm{t}}\propto\sqrt{2k_{\mathrm{sgs}}}$, are investigated.
