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Taşınım-Yayılım Denkleminin Sayısal Çözümlerinin Karşılaştırmalı İncelenmesi

Comparative Analysis of Numerical Solutions of Advection-Diffusion Equation

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Abstract (2. Language): 
The advection diffusion equation is one of the most popular and convenient equations in calculating the transport of energy and materials in flux areas. In this paper, one-dimensional advection-diffusion equation is solved using the finite difference, fourth order finite difference, finite volume, and differential quadrature methods in explicit condition. The quantitative comparative analysis involved two hypothetical cases and one experimental study. The results of the numerical solutions for the hypothetical cases are compared against the analytical solution. The experimental data are also simulated by the methods. The comparative analysis results revealed that the differential quadrature method performs as good as the analytical solution for the hypothetical cases. All the methods but the finite difference showed comparable performance in simulating the experimental data.
Abstract (Original Language): 
Taşınım-yayılım denklemi, akım alanlarında enerji ve malzemelerin taşınımının hesaplanmasında kullanılan en popüler ve kullanışlı denklemlerden biridir. Bu makalede, bir boyutlu taşınım-yayılım denkleminin, sonlu fark, dördüncü mertebeden sonlu farklar, sonlu hacim ve diferansiyel kuadratür yöntemleri kullanılarak açık çözümleri yapılmıştır. Kantitatif karşılaştırmalı inceleme, iki varsayımsal vaka ile bir deneysel çalışma içermektedir. Varsayımsal vakalar için sayısal çözümlerin sonuçları analitik çözüm ile karşılaştırılmıştır. Deneysel veriler de yöntemlerle simüle edilmiştir. Karşılaştırmalı inceleme sonuçları, diferansiyel kuadratür yönteminin varsayımsal durumlarda analitik çözüm kadar iyi performans gösterdiğini ortaya koymuştur. Çözümde kullanılan tüm yöntemler deneysel verilerin simülasyonu için karşılaştırmaya değer performans göstermiştir.
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