Abstract
This paper presents a computationally efficient and an accurate methodology called the incremental differential quadrature method (IDQM) for analysis of the nonlinear two-dimensional Burger’s equation. This equation is used to model the phenomenon of the fall of sediment particles in its dimensionless form. Both the spatial and the temporal domains are discretized using the DQM. Incremental differential quadrature approach for Burger’s equation is validated by comparing its results with the results of a FEM-based method and also the results of a distributed approximating functional approach. This process of validation demonstrates the very good accuracy of incremental DQ method in the solving Burger’s equation while using a mesh coarser than that of those methods. A series of parametric studies for viscosity and time of falling particles were performed, and the resulting flow field was presented. The important numerical results indicated that at t = 1, the horizontal and vertical velocities of sediment particles are less than all other times, so that in the viscosity of 0.25, these parameters become almost zero. Also in some times and places, the negative vertical velocity was observed, which means that the particles move upwards and are suspended in some cases. The discussion and analysis of the results are the points raised in this paper.
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Vaghefi, M., Rahideh, H., Boveiri, S. et al. Numerical Study of Two-Dimensional Burger’s Equation: The Phenomenon of the Fall of Sediment Particles Using Incremental Differential Quadrature Method. Iran J Sci Technol Trans Civ Eng 45, 2799–2815 (2021). https://doi.org/10.1007/s40996-021-00657-0
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DOI: https://doi.org/10.1007/s40996-021-00657-0