Uyumlu Kesirli Navier-Stokes Denkleminin Güçlü Yöntemle Yeni Sayısal Çözümleri

Abstract

Bu çalışmada, uyumlu kesirli Navier-Stokes denkleminin yeni sayısal çözümleri, uyumlu q-Shehu homotopi analiz dönüşümü yöntemi ile elde edilmiştir. Kesirli Navier-Stokes denklemi, hafıza etkileri ve anormal difüzyon gibi karmaşık akış davranışlarını hesaba katmak için kesirli türevleri içeren klasik Navier-Stokes denklemlerinin bir genişlemesidir. Özellikle Newton olmayan akışkanlar, gözenekli ortamlar ve karmaşık zaman veya mekansal bağımlılıklara sahip diğer sistemlerdeki akışkan dinamiğini tanımlamada faydalıdır. Ayrıca, elde edilen çözümlerin iki ve üç boyutlu grafikleri çizilmiştir. Ayrıca, şemanın doğruluğunu değerlendirmek için bir hata analizi yürütüyoruz. Yaklaşan yöntemin doğruluğunu doğrulamak için hesaplamalı simülasyonlar gerçekleştirilir. Bu makale, sayısal ve grafiksel analizden elde edilen sonuçları sunmaktadır.

Keywords

• Navier-Stokes denklemi
• Uyumlu q-Shehu homotopi analiz dönüşüm metodu
• Shehu dönüşümü

The Novel Numerical Solutions of Conformable Fractional Navier-Stokes Equation with the Robust Method

Abstract

In this study, new numerical solutions of the conformable fractional Navier-Stokes equation are obtained by the conformable q-Shehu homotopy analysis transform method. The fractional Navier-Stokes equation is an extension of the classical Navier-Stokes equations that incorporates fractional derivatives to account for complex flow behaviors such as memory effects and anomalous diffusion. It is particularly useful in describing fluid dynamics in non-Newtonian fluids, porous media, and other systems with intricate time or spatial dependencies. In addition, two and three-dimensional graphs of the obtained solutions were drawn. We also conduct an error analysis to evaluate the accuracy of the scheme. Computational simulations are performed to validate the accuracy of the upcoming method. This paper presents the conclusions derived from the numerical and graphical analysis.

Keywords

• Navier-Stokes equation
• Conformable q-Shehu homotopy analysis transform method
• Shehu transform

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