Süreksiz fonksiyonlar sınıfında hiperbolik korunum kuralları için sonlu fark şemaları ve gaz dinamiği problemine uygulanması
Küçük Resim Yok
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
İstanbul Beykent Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
2D korunum kurallarını ifade eden nonlineer hiperbolik tür denklem için başlangıç profilinde birden fazla sıçrayış doğruları mevcut olan Riemann tipli problemin entropi çözümünün bulunması için süreksiz fonksiyonlar sınıfında sonlu farklar metodu önerilmiştir. Bu amaçla ana problemde bulunmayan avantajlara sahip ve ana probleme belli anlamda denk olan yardımcı problem dahil edilmiştir. Önerilen yardımcı problemin avantajlarını kullanarak yüksek hassasiyete sahip sonlu farklar metodu işlenmiştir. Yardımcı problemin çözümünü kullanarak ana problemin fiziksel yapısını düzgün ifade eden çözümü elde edilmiştir. Önerilen metot yardımıyla dalgaların karşılıklı etkisi de incelenmiştir.
The finite difference method in a class of discontinuous functions for obtaining the entropy solution of the Riemann problem of nonlinear hyperbolic equation having more than one lines of discontinuity in initial profile which describing of the 2D conservation rules is proposed. For this purpose, an auxiliary problem, which has advantages not found in the main problem and is equivalent to the main problem in a certain sense, is proposed. Using the advantages of the proposed auxiliary problem, the finite difference method with high precision is developed. By using the solution of the auxiliary problem, the solution that expresses the physical structure of the main problem properly has been obtained. With the help of the proposed method, the mutual effect of the waves has also been studied.
The finite difference method in a class of discontinuous functions for obtaining the entropy solution of the Riemann problem of nonlinear hyperbolic equation having more than one lines of discontinuity in initial profile which describing of the 2D conservation rules is proposed. For this purpose, an auxiliary problem, which has advantages not found in the main problem and is equivalent to the main problem in a certain sense, is proposed. Using the advantages of the proposed auxiliary problem, the finite difference method with high precision is developed. By using the solution of the auxiliary problem, the solution that expresses the physical structure of the main problem properly has been obtained. With the help of the proposed method, the mutual effect of the waves has also been studied.
Açıklama
Anahtar Kelimeler
Matematik, Mathematics
