  We investigate the construction and usage of mimetic operators in curvilinear
staggered grids. Specifically, we extend the Corbino-Castillo operators so they
can be utilized to solve problems in non-trivial geometries. We prove that the
resulting curvilinear operators satisfy the discrete analog of the extended
Gauss-Divergence theorem. In addition, we demonstrate energy and mass
conservation in curvilinear coordinates for the acoustic wave equation. These
findings are illustrated in two-dimensional and three-dimensional
elliptic/hyperbolic equations and can be extended to other partial differential
equations as well.
