» Research Note « Novel Numerical Approach for Modeling Dynamic Wave by Finite Volume and ULTIMATE Strategy

Document Type : Technical Note



A wide range of natural phenomena is modeled by Saint-Venant equations or the dynamic wave model, such as: dam breaks and flood routing. Flood routing is a mathematical method to forecast the changes of the volume, velocity and the shape of the flood wave as a function of time and space. Knowing flood intensity and its wave propagation manners plays a substantial role in minimizing human and financial disasters. A fairly significant change of dependent variable within a short distance is a primary criterion of those phenomena. Therefore, there are often non-physical and non-uniform oscillations in the result of their numerical model, which could entirely invalidate the solution which is obtained. Hence, in addition to an efficient discretization method, some measures must be utilized to reduce cited error and prevent unrealistic results. In this investigation the dynamic wave model was discretized by Finite Volume Method, which is a novel and absolutely reliable method. Then a straightforward algorithm was introduced to solve discrete equations set which prevents spurious numerical oscillations by putting ULTIMATE strategy in use. Furthermore, take advantages of different schemes is possible in innovative algorithm and it could be implemented in various coding programs. Finally, to examine discrete equations set and proposal algorithm, a code was written in MATLAB and its outputs were compared with Chow et al. (1988). Comparison demonstrated that discrete equations set were absolutely correct and the presented algorithm is efficient and well-established.


صالحی نیشابوری ع.ا. و تقدیسیان س.م.، (1376)، جریان در کانال‌های باز (ترجمه)، چاپ اول، انتشارات جزیل.
Chow V.T., Maidment D. R. and Mays L. W., (1988), Applied Hydrology. McGraw Hill Book Company. New York. Inc.
Chow V.T., (1973), Open Channel Hydraulics. Third Edition. McGraw Hill Book Company. New York. Inc.
Das A., (2004), "Parameter estimation for Muskingum models", Journal of Irrigation and Drainage Engineering. ASCE. 130(2): 140-147.
Knight Donald W., (2013), "River hydraulics- A view from midstream", Journal of Hydraulic Research, 51:1, 2-18.
Leonard B.P., (1991), "The Ultimate conservative difference scheme applied to unsteady one-dimensional advection", Computer Methods in Applied Mechanics an Engineering 88: 17-74.
Qureshi, A. L., Mahessar, A. A. and Baloch, A., (2014), "Verification and application of finite element model developed for flood routing in Rivers", International Journal of Environmental, Chemical, Ecological, Geological and Geophysical Engineering, 8(2): 86-89.
Siing, M. and Widodo, T. B., (2011), "Numerical solution of flood routing model using finite volume methods", The International Conference on Numerical Analysis and Optimization (ICeMATH 2011), Yogyakarta, Indonesia: NA8_1-NA8_9