2024/07/01 by Boada, Angel, Corbino, Johnny, Dumett, Miguel +1
#65M06 #Analysis of PDEs (math.AP) #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2407.01443
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.