  A theoretical formulation of lattice Boltzmann models on a general
curvilinear coordinate system is presented. It is based on a volumetric
representation so that mass and momentum are exactly conserved as in the
conventional lattice Boltzmann on a Cartesian lattice. In contrast to some
previously existing approaches for arbitrary meshes involving interpolation
approximations among multiple neighboring cells, the current formulation
preserves the fundamental one-to-one advection feature of a standard lattice
Boltzmann method on a uniform Cartesian lattice. The new approach is built on
the concept that a particle is moving along a curved path. A discrete
space-time inertial force is derived so that the momentum conservation is
exactly ensured for the underlying Euclidean space. We theoretically show that
the new scheme recovers the Navier-Stokes equation in general curvilinear
coordinates in the hydrodynamic limit, along with the correct mass continuity
equation.
