Zaman Değişkeninde Kesirli Türev İçeren Navier-Stokes Denklemlerinin Sayısal Çözümü

Yıl 2018, Cilt: 39 Sayı: 4, 900 - 911, 24.12.2018

İnci Çilingir Süngü Hüseyin Demir

https://doi.org/10.17776/csj.384509

Cited By: 3

Öz

Bu çalışmada zaman değişkenine göre kesirli türev
içeren Navier-Stokes denklemleri çözülmüştür. Denklemlerin çözümünde
genelleştirilmiş diferansiyel dönüşüm ve sonlu fark metotları beraber farklı
alt aralıklara bölünerek çok adımlı olarak kullanılmıştır. Bu melezleme ile
sonlu fark metodunun kararlılık özelliği ve diferansiyel dönüşüm metodunun
uygulama kolaylığı özelliklerinin birleştirilmesi amaçlanmıştır. Ele alınan
örneklerde karmaşık hesaplamaların getirdiği işlem yükünün azaldığı ve çok
boyutlu problemlerde ise başlangıç koşulu nedeniyle oluşan süreksizliğin
aşılabildiği görülmüştür. Zamana bağlı seri çözümünün yakınsaklığı ise çok
zaman adımlı metot kullanılarak sağlanmıştır. Yapılan çalışma melezleme
metodunun bu tür denklemlerin çözümünde etkili, güvenilir ve uygulanması kolay
olduğunu göstermiştir.

Anahtar Kelimeler

Diferansiyel Dönüşüm/Sonlu Fark Metodu, Kesirli Navier-Stokes Denklemleri, Sayısal Çözüm

A Computational Method for the Time-Fractional Navier-Stokes Equation

Öz

In this
study, Navier-Stokes equations with fractional derivate are solved according to
time variable. To solve these equations, hybrid generalized differential
transformation and finite difference methods are used in various subdomains.
The aim of this hybridization is to combine the stability of the difference
method and simplicity of the differential transformation method in use. It has
been observed that the computational intensity of complex calculations is
reduced and also discontinuity due to initial conditions can be overcome when
the size increased in the study. The convergence of the time-dependent series
solution is ensured by multi-time-stepping method. This study has shown that
the hybridization method is effective, reliable and easy to apply for solving
such type of equations.

2010 Mathematics Subject Classification: 35Q30, 35R11, 65M06, 65N55.

Anahtar Kelimeler

Hybrid Differential Transform/Finite Difference Method, Numerical solution, Time-Fractional Navier-Stokes Equations

Kaynakça

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