  We propose an innovative difference-free scheme that combines the one-fluid
lattice Boltzmann method (lBM) with the conservative phase-field (CPF) lBM to
effectively solve large-scale two-phase fluid flow problems. The
difference-free scheme enables the derivation of the derivative of the order
parameter and the normal vector through the moments of the particle
distribution function (PDF). We further incorporate the surface tension force
in a continuous surface stress form into the momentum equations by modifying
the equilibrium PDF to eliminate the divergence operator. Consequently, the
entire computation process, executed without any inter-grid finite difference
formulation, demonstrates improved efficiency, making it an ideal choice for
high-performance computing applications. We conduct simulations of a single
static droplet to evaluate the intensity of spurious currents and assess the
accuracy of the scheme. We then introduce the density or viscosity ratio and
apply an external body force to model the Rayleigh-Taylor instability and the
behavior of a single rising bubble, respectively. Finally, we employ our method
to study the phenomenon of a single bubble breaking up in a Taylor-Green
vortex. The comparison between the difference-free scheme and the finite
difference method demonstrates the scheme's capability to yield accurate
results. Furthermore, based on the performance evaluation, the current scheme
exhibits an impressive $47\% $ increase in efficiency compared to the previous
method.
