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Curvilinear High-Order Mimetic Differences that Satisfy Conservation Laws
- Publication Year :
- 2024
-
Abstract
- 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.
- Subjects :
- Mathematics - Analysis of PDEs
Mathematics - Numerical Analysis
65M06
G.1.8
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.01443
- Document Type :
- Working Paper