Differential Quadrature Method (DQM) to integrate the one-dimensional Advection-diffusion Equation (ADE) is presented. This method was applied to two examples and the results were compared with the performance of the Explicit Finite Difference Method (EFDM) and Implicit Finite Differences Method (IFDM). Based on the comparison with the exact solution, and both the explicit and implicit finite difference solutions, it was concluded that the DQM provides similar results but less grid points; besides the results are converged quickly. A numerical comparison for a case in which the exact solution is known, DQM gives closer results to the exact values than EFDM and IFDM.

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Differential Quadrature Method (DQM) has been applied to the solution of aquifer flow problems. Three examples from of each of the three one-dimensional aquifer flow equation problems, a confined aquifer flow with time dependent boundary conditions, a composite confined aquifer and an unconfined aquifer with seepage, were examined. The results of DQM solution were then compared with the results obtained from analytical solution, the Explicit Finite Differences Method and Implicit Finite Differences Method. Based on the comparison results, it was concluded that the DQM provides similar results but with relatively faster calculation speed, less nodes and memory usage.

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In recent years, many researchers have suggested various numerical techniques to solve the engineering problems like fluid flow intricacies. The objective of this paper is to introduce a numerical approach to simulate treatment of incompressible fluid flow in two-dimensional unsteady flow with the shallow water equations system. The governing equations were solved by Finite Volume Method in explicit conditions. Moreover, to discretize the governing equations, total variation diminishing scheme was employed in the unstructured triangular grid systems, directly. For evaluating the numerical results of developed model, the Flow3D software was used. In this direction, two hypothetical cases have been developed to investigate the accuracy of the results of the suggested model by Flow3D software. The comparison between numerical results of developed model and simulations of Flow3D software, shows good agreement. Furthermore, the suggested model can obtain acceptable results with less number of meshes than Flow3D software.