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.

翻译：本文研究了曲线交错网格中拟态算子的构建与应用。具体而言，我们扩展了Corbino-Castillo算子，使其能够用于求解非平凡几何结构中的问题。我们证明了所得曲线算子满足扩展高斯散度定理的离散形式。此外，我们针对声波方程在曲线坐标系中展示了能量与质量守恒特性。这些结论通过二维与三维椭圆/双曲型方程进行了验证，并可推广至其他偏微分方程。