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Abstract
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Background: It is not possible to obtain an analytical solution for some nonlinear partial differential equations, except in certain conditions, that such equations can be solved numerically. The equation in this thesis is the Burger’s equation in time-dependent two-dimensional mode, which models the phenomenon of the fall velocity of particle in a near-stagnant fluid, such as sedimentary water behind a dam.
Aim: Since the velocity of fall of sediment particles is a basic requirement for sediment transport studies, it can be important to calculate it in three directions. The main objective of this thesis is to evaluation the ability of numerical methods to solve the three dimensional Burger’s equation and predicting of the fall velocity of sediment particles in three dimensions, as well as the effect of time and viscous parameters on the fall velocity of particles.
Methodology: Due to the high potential of the differential quadrature method (DQM), this method can be a good alternative to finite difference (FDM) and finite element (FEM) methods. This method approximates the differential equations governing the problem as a linear and weighted sum of the function values at specific points, which is a high order method, and unlike low-order methods such as FDM and FEM, there are fewer mesh points to achieve accurate results. This method can achieve accurate resolution with computational effort less than other methods. Therefore, the thesis used the capabilities of this method.
Achivements: In the two-dimensional mode, in general, the magnitude of longitudinal and deep velocity of the particle’s fall decreases with increasing viscosity and time. Also, in some of the viscosities and times (small viscosities and initial times), there was an upward flow of about 70% of the water surface up to the bottom of the bed, indicating that particles are suspended in some of the viscosities and times. In the three-dimensional mode, with plotting of the distribution of longitudinal,
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