Numerical Approach for the two-dimensional heat equation problem with convective boundary conditions

Year 2017, , 343 - 349, 01.06.2017

Vildan Gülkaç

https://doi.org/10.16984/saufenbilder.283775

Abstract

In this work, we extended our earlier study on the solution of two-dimensional heat equation problem by considering
a class of time-split finite difference methods. Operator splitting is used as a procedure for computing, some derivatives
are computed explicitly and some of them computed implicitly during this procedure. The procedure is second order
accurate in time and in (x, y) coordinates. The results of computing by present procedure are in totally compatible with
the results obtained previously by other researches.  

Keywords

Flux limiters, LOD method, ADI method, moving boundary problems, Strang splitting

İki-Boyutlu Konvektif Sınır Koşullu Erime Problemi İçin Nümerik Yaklaşım

Abstract

Bu çalışmada, daha önce çözdüğümüz, iki-boyutlu konvektif sınır koşullu erime probleminde, türevlerin bir kısmında
açık yöntem kullanırken bir kısmında da kapalı yöntem kullanarak sonlu farklar oluşturulmuştur ve bu denklemlerin
çözümü için bir iteratif yöntem geliştirilmiştir. Metod (x, y) koordinatlarında ikinci dereceden doğruluğa sahiptir. Bu
metodla elde edilen sonuçlar, önceki araştırmacılar tarafından verilen sonuçlarla tamamen uyumludur.  

Keywords

Flux Limiters, LOD metodu, hareketli sınır problemleri, Strang splitting

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