Farhang Behrangi - Ph.D. Candidate in Hydraulic Structures, School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran
Mohammad Ali Banihashemi - Associate. Prof., School of Civil Engineering, College of Engineering, University of Tehran, Iran.
Masoud Montazeri Namin - Assistant. Prof., School of Civil Engineering, College of Engineering, University of Tehran, Iran.
Ali Khoshkholgh - Ocean Engineering and Technology Research Center, Iranian National Institute for Oceanography and Atmospheric Science (INIOAS), Tehran, Iran.

The main objective of this paper is to provide an efficient numerical method for solving the advection equation used in mixture multiphase model, two-dimensional time splitting method. For advection dominated problems, such as the multiphase flow the effect of the numerical diffusion in the advection schemes will adversely affect the accuracy of the numerical results. To this end, first schemes with different orders were evaluated. Using higher order schemes introduced a reduction in numerical diffusion. However, such schemes led to unreal, out of range and non-monotonic results. Subsequently, the solutions offered for solving these problems by other researchers in the previous studies were examined. With due regard of the mixture model characteristics, the most effective of these solutions were then selected and subsequently presented for solving the advection equation in the mixture model

advection equation, numerical scheme, mixture model