Birol Kaya

Differential Quadrature Method for Linear Long Wave Propagation in Open Channels

The St. Venant equations which are written for the calculation of free surface, gradually varied unsteady flows can only be solved analytically in very special limited problems. Apart from this they can be solved by numerical solution methods. Depending on the problem’s characteristics, St. Venant equations can be arranged in different forms such as kinematic wave, dynamic wave, gravity wave, quasi-steady dynamic wave, and non-inertia wave may emerge. In the solution of non-linear St. Venant equations, different numerical solution techniques may be used by linearization of the equations by mathematical approaches. In this study the St. Venant equations made linear have been solved by using the Differential Quadrature Method (DQM), and the results have been compared by the Finite Difference Method (FDM) and Finite Volume Method’s (FVM) results.

Differential Quadrature Method in Open Channel Flows: Aksu River, Turkey

AbstractA diffusion wave equation, which is derived from the Saint-Venant equations for one-dimensional, gradually varied, unsteady open-channel flow, describes the wave propagation in open channels. Therefore, it is important to solve the diffusion wave equation accurately and efficiently. In this paper, a numerical solution for a diffusion wave equation is developed by using the Differential Quadrature Method (DQM). The performance of DQM is tested against two other numerical solution methods, the finite difference method (FDM) and finite volume method (FVM). In order to demonstrate the applicability of DQM, first a hypothetical example is solved with both DQM and the two other numerical methods. Then, the DQM is applied to a real flooding event that occurred in Aksu River, Sutculer Basin, located in Mediterranean Region, Turkey. The measured flow rates are routed through the Aksu River by the diffusion wave equation and the outflow is obtained by DQM. Finally, this flood event is also solved by explici...

DENGEDE OLMAYAN ŞARTLAR ALTINDA KATI MADDE TAŞINIMININ İKİ BOYUTLU OLARAK SAYISAL İNCELENMESİ

A two-dimensional model, under non equilibrium condition, consists of three components has been developed to determine suspended load over an erodible layer. The first component, prepares unstructured triangular meshes. The second component, employs the shallow water equation system to calculate flow treatment, is hydrodynamic component. The last component, determines suspended sediment and bed deformation, is morphodynamic component. The governing equations solved by explicit Finite volume method and discretized by Total Variation Diminishing scheme. In addition, in order to obtain a more accurate solution, two turbulence models has been adjoined to the governing equation. The numerical results of developed model are compared with the results of Flower 3D software. The model was examined for two hypothetical cases. The acceptable compatibility between numerical results of developed model and Flow3D software had been recognized. However, results of mixing length turbulence model are compatible than eddy viscosity model.

DİFERANSİYEL KUADRATUR YÖNTEMİ KULLANILARAK DİFÜZYON DALGA YAKLAŞIMI İLE TAŞKINLARIN ÖTELENMESİ

Taskin, yeryuzune dusen yagislarin, akarsu yatak kapasitesinin disina cikarak tasmasi olayidir. Yuksek veengebeli topografik yapisi ve yari kurak iklim kusaginda yer alan Turkiye’de yagislarin hem mevsimsel hem dealansal dagilimi oldukca duzensizdir. Bu duzensiz yagislar yuzey sekilleri, topografik yapi, arazi kullanimi,carpik kentlesme, orman arazilerinin tahribati ve insan faaliyetleri neticesinde taskinlara donusmektedir.Akarsular uzerinde insa edilecek tum yapilar icin akimin hizi, akimin seviyesi ve kesit boyunca tasidigi hacimmiktari gibi taskina ait karakteristiklerin bilinmesi ve bu karakteristiklere gore onlemlerin alinmasi gerekir.Taskin karakteristiklerinin belirlenmesi amaciyla yapilan ve taskinlarin otelenmesi olarak tanimlanan hesaplarSt.Venant denklemleri ile yapilmaktadir. St.Venant denklemleri degisik dalga yaklasimlari altindacozulebilmekte ve taskin otelenmesinde hidrolik yontemler olarak tanimlanmaktadir. Bunun yaninda sadecekutlenin korunumu esasina dayanan hidrolojik yontemler de kullanilabilmektedir. St.Venant denklemlerimatematiksel olarak bazi kabullerle dogrusallastirilabilmekte, farkli dalga yaklasimlari kullanilsa da difuzyondalga denklemi seklinde ifade edilebilmektedir. Elde edilen denklem sonlu farklar, sonlu hacimler gibi sayisalcozum yontemleri ile cozulebilmektedir. Bu calismada difuzyon dalga denkleminin cozumunde DiferansiyelKuadratur Yontemi (DKY) kullanilmis ve Sivapalan (1997) ve Ozdogan (2010)’dan alinan gercek taskinornekleri uzerinde uygulanmistir. Elde edilen sonuclar, sonlu fark yontemleri ile elde edilen sonuclarlakarsilastirilmistir [1, 2]. Her iki ornek cozumden de goruldugu uzere, cozum icin DKY’de az sayida hesapnoktasi kullanilmasi yeterli olmaktadir.