Orthogonal transformations of differential-difference schemes. Introduction to discrete analysis

Vladimir A. Korobitsyn; Yuri I. Shokin

doi:10.1515/rnam-2014-0017

Article

Orthogonal transformations of differential-difference schemes. Introduction to discrete analysis

Vladimir A. Korobitsyn and Yuri I. Shokin

Published/Copyright: July 23, 2014

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From the journal Russian Journal of Numerical Analysis and Mathematical Modelling Volume 29 Issue 4

Abstract

Transformations of consistent discrete approximations of first derivatives in the passage from Cartesian coordinates to an orthogonal curvilinear system and transformations of discrete operations of vector analysis on skewed grids on a plane are studied in the paper. It is established that the transformation algorithm for discrete operators preserves symmetries of discrete solutions relative to coordinate curves inherent from differential system of equations. It also maintains the consistency of discrete operators, which allows us to construct completely conservative differential-difference schemes for discrete domains with curvilinear boundaries.

Keywords: Compatible discrete approximations; basis operators; discrete analogue of integral relation; volume change law.

Published Online: 2014-7-23

Published in Print: 2014-8-1

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Articles in the same Issue

https://doi.org/10.1515/rnam-2014-0017

Keywords for this article

Compatible discrete approximations; basis operators; discrete analogue of integral relation; volume change law.