Genişletilmiş Yumuşak Eğim Eşitlikleri İçin Sonlu Farklar Yaklaşımı

Yıl 2013, Cilt: 28 Sayı: 2, 401 - 408, 27.03.2014

Asu İnan Lale Balas

Öz

Bu çalışmada dalgaların ilerlerken geçirdikleri değişimler irdelenmiştir. Hazırlanan sayısal modelde hızlı değişen topografyalarda geçerli olan genişletilmiş yumuşak eğim eşitlikleri çözülmüştür. Bu eşitlikler sapmayı, kırınımı, sığlaşmayı, yansımayı, liman rezonansını, yüksek dereceden taban etkilerini, dalga kırılması ve taban sürtünmesine bağlı sönümleyici terimleri içermektedir. Doğrusal olmayan dalga hızı ve grup hızı, daha hassas sonuçlar elde edebilmek için çözüme dâhil edilmiştir. Mac Cormack ve Noktasal Gauss Seidel yöntemleri bu yeni yaklaşımda bir arada kullanılmıştır. Sayısal model, yarı sığlaşma alanına [1] ve kıyıya paralel dalgakıran [2] fiziksel deneylerine uygulanmış, literatürdeki sayısal model ve fiziksel deney sonuçları ile karşılaştırılmıştır. Elde edilen sonuçlar, sayısal modelin düzensiz topograflarda dalga ilerlemesini başarıyla benzeştirdiğini ortaya koymuştur.

Anahtar Kelimeler

Sapma, Kırınım, Sayısal Model, Genişletilmiş Yumuşak Eğim Eşitliği, Sonlu Farklar Metodu

A FINITE DIFFERENCE APPROACH FOR EXTENDED MILD SLOPE EQUATION

Öz

In this study, the numerical model for the determination of transformations of waves while propagating has been presented. This numerical model was developed to solve the extended mild slope equation that is applicable to the rapidly varying topographies. It includes the effects of wave refraction, diffraction, shoaling, reflection, harbor resonance, higher order bottom configurations; dissipative terms due to wave breaking and bottom friction. Nonlinear wave celerity and group velocity were introduced in the solution to obtain results that are more accurate. Mac Cormack Method and Point Gauss Seidel Method were applied together in the proposed new solution approach. The numerical model was tested on the semicircular shoaling area [1] and shoreparallel breakwater [2]. The comparison of the numerical model in the current study and the physical experiments that are present in the literature shows the reliability of the model for wave transformations and dissipations over uneven bottoms.

Anahtar Kelimeler

Refraction, Diffraction, Numerical Model, Extended Mild Slope Equation, Finite Difference Method

Kaynakça

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