تقرير
Curvilinear High-Order Mimetic Differences that Satisfy Conservation Laws
| العنوان: | Curvilinear High-Order Mimetic Differences that Satisfy Conservation Laws |
|---|---|
| المؤلفون: | Boada, Angel, Corbino, Johnny, Dumett, Miguel, Castillo, Jose |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis, 65M06, G.1.8 |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.01443 |
| رقم الأكسشن: | edsarx.2407.01443 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |