Curvilinear High-Order Mimetic Differences that Satisfy Conservation Laws
arXiv preprint arXiv:2407.01443, 2024•arxiv.org
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 …
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 …
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.
arxiv.org