MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM
This paper presents the general modified equation for a family of finite-difference schemes solving one-dimensional advection equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (up...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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CTU Central Library
2021-02-01
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| Series: | Acta Polytechnica |
| Subjects: | |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/6304 |
| _version_ | 1818911252546584576 |
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| author | Tomáš Bodnár Philippe Fraunié Karel Kozel |
| author_facet | Tomáš Bodnár Philippe Fraunié Karel Kozel |
| author_sort | Tomáš Bodnár |
| collection | DOAJ |
| description | This paper presents the general modified equation for a family of finite-difference schemes solving one-dimensional advection equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (upwind, Lax-Friedrichs, Lax-Wendroff) are discussed as examples, showing the possible implications arising from the modified equation to the properties of the considered numerical methods. |
| first_indexed | 2024-12-19T22:55:45Z |
| format | Article |
| id | doaj.art-8af70d27084843cab07eda45b5a5bf65 |
| institution | Directory Open Access Journal |
| issn | 1210-2709 1805-2363 |
| language | English |
| last_indexed | 2024-12-19T22:55:45Z |
| publishDate | 2021-02-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica |
| spelling | doaj.art-8af70d27084843cab07eda45b5a5bf652022-12-21T20:02:39ZengCTU Central LibraryActa Polytechnica1210-27091805-23632021-02-0161SI495810.14311/AP.2021.61.00493430MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEMTomáš Bodnár0Philippe Fraunié1Karel Kozel2Czech Technical University in Prague, Faculty of Mechanical Engineering, Department of Material Engineering, Karlovo náměstí 293/13, Prague, 12000, Czech Republic; Czech Academy of Sciences, Institute of Mathematics, Žitná 25, 115 67 Prague, Czech RepublicUniversité de Toulon, Mediterranean Institute of Oceanography - MIO, BP 20132 F-83957 La Garde cedex, FranceCzech Technical University in Prague, Faculty of Mechanical Engineering, Karlovo Náměstí 13, 121 35 Prague, Czech RepublicThis paper presents the general modified equation for a family of finite-difference schemes solving one-dimensional advection equation. The whole family of explicit and implicit schemes working at two time-levels and having three point spatial support is considered. Some of the classical schemes (upwind, Lax-Friedrichs, Lax-Wendroff) are discussed as examples, showing the possible implications arising from the modified equation to the properties of the considered numerical methods.https://ojs.cvut.cz/ojs/index.php/ap/article/view/6304modified equationfinite differenceadvection equation |
| spellingShingle | Tomáš Bodnár Philippe Fraunié Karel Kozel MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM Acta Polytechnica modified equation finite difference advection equation |
| title | MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM |
| title_full | MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM |
| title_fullStr | MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM |
| title_full_unstemmed | MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM |
| title_short | MODIFIED EQUATION FOR A CLASS OF EXPLICIT AND IMPLICIT SCHEMES SOLVING ONE-DIMENSIONAL ADVECTION PROBLEM |
| title_sort | modified equation for a class of explicit and implicit schemes solving one dimensional advection problem |
| topic | modified equation finite difference advection equation |
| url | https://ojs.cvut.cz/ojs/index.php/ap/article/view/6304 |
| work_keys_str_mv | AT tomasbodnar modifiedequationforaclassofexplicitandimplicitschemessolvingonedimensionaladvectionproblem AT philippefraunie modifiedequationforaclassofexplicitandimplicitschemessolvingonedimensionaladvectionproblem AT karelkozel modifiedequationforaclassofexplicitandimplicitschemessolvingonedimensionaladvectionproblem |