Ali Ruhşen ÇETE, Adil YÜKSELEN

Değişen hücre yönlü kapalı formülasyon yöntemi

Bu çalışmada, "Değişen Ardışık Hücre Yönlü Kapalı Formülasyon - DAHYKF" adlı kısmi diferansiyel denklem çözen yeni bir sayısal yöntem geliştirilmiştir. Yöntemde "Değişen Yönlü Kapalı Formülasyon -DYKF (Alternating Direction Implicit - ADI) yöntemindeki değişen yönler kavramınından ilham alınmıştır. Fakat yeni yöntemdeki değişen yön DYKF 'de olduğu gibi eğrisel koordinat değil, "Ardışık Hücre Yönleri" dir. Ardışık Hücre Yönleri dörtgen elemanların karşılıklı kenarlarını takip ederek oluşan ardışık yönlerdir. DAHYKF yöntemi ile daire etrafındaki sıkıştırılamaz potansiyel akım elde edilen sonuçlar analitik çözümlerle, klasik DYKF yöntemi sonuçlarıyla ve Runge-Kutta zaman integrasyonu kullanan bir Sonlu Hacimler yöntemi sonuçlarıyla karşılaştırılmıştır. Sonuçlar yöntemin yapısal ve yapısal olmayan çözüm ağlarında aynı yüksek performansı gösterdiği ve bunun yanında kullanımının kolay olduğunu göstermiştir.

Alternating cell directions implicit method

In this study, a new numerical method named as "Alternating Cell Directions implicit - ACDI" for solving partial differential equations is developed. In this study, testing of this method is targetted, since the method is being newly developed. Therefore, the method is applied on two-dimensional problems, and the incompressible potential flow is considered as an example test problem. Application of the method for three-dimensional cases is possible. This method is inspired by alternating directions concept of "Alternating Directions Implicit - ADI) method. In the new method, alternating direction is not curvilinear coordinate like as in the ADI method, but this is "Sequential Cell Directions". Cell direction is formed by following from one edge to its opposite edge on quadrilateral. Sequential directions means a chain of directions formed by sequantial cells. In this study, a cell centered finite volume variation of potential ACDI methods is presented. The solutions obtained by the ACDI method for the incompressible potential flow around a circular cylinder is compared with the analytical solutions, with the results of the classical ADI method and a finite volume method using Runge-Kutta time integration. The results show that this method has the same high performance on structured and unstructured grids, and its usage is easy.

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