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.

本文提出了一种计算高效且准确的方法，称为增量微分正交法 (IDQM)，用于分析非线性二维伯格方程。该方程用于模拟无量纲形式的沉积物颗粒下落现象。空间域和时间域都使用 DQM 进行离散化。通过将其结果与基于 FEM 的方法的结果以及分布式近似函数方法的结果进行比较，验证了 Burger 方程的增量微分正交方法。这个验证过程表明增量 DQ 方法在求解 Burger 方程时具有非常好的准确性，同时使用比这些方法更粗的网格。对下落颗粒的粘度和时间进行了一系列参数研究，并给出了由此产生的流场。重要的数值结果表明，在t  = 1 时，沉积物颗粒的水平和垂直速度均小于其他时间，因此在粘度为 0.25 时，这些参数几乎为零。同样在某些时间和地点，观察到负的垂直速度，这意味着粒子向上移动并在某些情况下悬浮。对结果的讨论和分析是本文提出的要点。