  Given the need to develop zero-carbon combustors for power and aircraft
engine applications, $S_d$ of a turbulent premixed flame, especially for
H$_2$-air, is of immediate interest. The present study investigates 3D DNS
cases of premixed H$_2$-air turbulent flames at varied pressures for different
$Re_t$ and $Ka$ with detailed chemistry to theoretically model $S_d$ at
negative curvatures. Prior studies at atmospheric pressure showed
$\widetilde{S_d}$ to be enhanced significantly over $S_L$ at large negative
$\kappa$ due to flame-flame interactions. 1D simulations of an imploding
cylindrical H$_2$-air laminar premixed flame used to represent the local flame
surfaces undergoing flame-flame interaction in a turbulent flame at the
corresponding pressure conditions are performed to understand the interaction
dynamics. These simulations emphasized the transient nature of the flame
structure during flame-flame interactions and enabled analytical modeling of
$\widetilde{S_d}$ at these regions of extreme negative $\kappa$ of the 3D DNS.
The JPDF of $\widetilde{S_d}$ and $\kappa$ and the corresponding conditional
averages from 3D DNS showed a negative correlation between $\widetilde{S_d}$
and $\kappa$. The model successfully predicts the variation of
$\langle\widetilde{S_d}|_{\kappa}\rangle$ with $\kappa$ for the regions on the
flame surface with $\kappa\delta_L \! \ll \! -1$ at all pressures, with good
accuracy. This shows the aforementioned configuration to be fruitful in
representing local flame-flame interaction in 3D turbulent flames. Moreover, at
$\kappa=0$, on average $\widetilde{S_d}$ can deviate from $S_L$, manifested by
the internal flame structure, controlled by turbulence transport in the large
$Ka$ regime. Thus, the correlation of $\langle\widetilde{S_d}\rangle/S_L$ with
$\langle|\widehat{\nabla c}|_{c_0}\rangle$ at $\kappa =0$ is explored.
