Curvilinear High-Order Mimetic Differences that Satisfy Conservation Laws
<|reference_start|>Curvilinear High-Order Mimetic Differences that Satisfy Conservation Laws: 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.<|reference_end|>
@article{boada2024curvilinear,
    title={Curvilinear High-Order Mimetic Differences that Satisfy Conservation
  Laws},
    author={Angel Boada, Johnny Corbino, Miguel Dumett, Jose Castillo},
    journal={arXiv preprint arXiv:2407.01443},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.01443},
    primaryClass={math.AP cs.NA math.NA}
}