On second-order mimetic and conservative finite-difference discretization schemes
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| Format: | Artículo científico |
| Sprache: | en |
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Sociedad Mexicana de Física A.C.
2008
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| _version_ | 1876434021081153536 |
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| author | S. Rojas |
| author_facet | S. Rojas |
| contents | On second-order mimetic and conservative finite-difference discretization schemes S. Rojas J.M. Guevara-Jordan Física, Astronomía y Matemáticas boundary layer finite difference Taylor expansions diffusion equation Mimetic discretizations Although the scheme could be derived on the grounds of a relatively new numerical discretization methodology known as Mimetic Finite- Difference Approach, the derivation of a second-order mimetic finite difference discretization scheme will be presented in a more intuitive way, using Taylor expansions. Since students become familiar with Taylor expansions in earlier calculus and mathematical methods for physicist courses, one finds this approach of presenting this new discretization scheme to be more easily handled in courses on numerical computations of both undergraduate and graduated programs. The robustness of the resulting discretized equations will be illustrated by finding the numerical solution of an essentially hard-to-solve, one-dimensional, boundary-layer-like problem, based on the steady diffusion equation. Moreover, given that the presented mimetic discretization scheme attains second-order accuracy in the entire computational domain (including the boundaries), as a comparative exercise the discretized equations can be readily applied in solving examples commonly found in texbooks on applied numerical methods and solved numerically via other discretization schemes (including some of the standard finite- diffence discretization schemes). 2008 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57028302011 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.54 |
| format | Artículo científico |
| id | redalyc_57028302011 |
| institution | Redalyc |
| language | en |
| publishDate | 2008 |
| publisher | Sociedad Mexicana de Física A.C. |
| spellingShingle | On second-order mimetic and conservative finite-difference discretization schemes S. Rojas Física, Astronomía y Matemáticas boundary layer finite difference Taylor expansions diffusion equation Mimetic discretizations On second-order mimetic and conservative finite-difference discretization schemes S. Rojas J.M. Guevara-Jordan Física, Astronomía y Matemáticas boundary layer finite difference Taylor expansions diffusion equation Mimetic discretizations Although the scheme could be derived on the grounds of a relatively new numerical discretization methodology known as Mimetic Finite- Difference Approach, the derivation of a second-order mimetic finite difference discretization scheme will be presented in a more intuitive way, using Taylor expansions. Since students become familiar with Taylor expansions in earlier calculus and mathematical methods for physicist courses, one finds this approach of presenting this new discretization scheme to be more easily handled in courses on numerical computations of both undergraduate and graduated programs. The robustness of the resulting discretized equations will be illustrated by finding the numerical solution of an essentially hard-to-solve, one-dimensional, boundary-layer-like problem, based on the steady diffusion equation. Moreover, given that the presented mimetic discretization scheme attains second-order accuracy in the entire computational domain (including the boundaries), as a comparative exercise the discretized equations can be readily applied in solving examples commonly found in texbooks on applied numerical methods and solved numerically via other discretization schemes (including some of the standard finite- diffence discretization schemes). 2008 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57028302011 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.54 |
| title | On second-order mimetic and conservative finite-difference discretization schemes |
| topic | Física, Astronomía y Matemáticas boundary layer finite difference Taylor expansions diffusion equation Mimetic discretizations |
| url | https://www.redalyc.org/articulo.oa?id=57028302011 |