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Numerical modeling of Forchheimer flow to a pumping well in a confined aquifer using the strong-form mesh-free method |
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| Authors: | Zhang Wen Zhuangtian Liu Menggui Jin Hongbin Zhan |
| Institution: | 1. School of Environmental Studies, China University of Geosciences, Wuhan, Hubei, 430074, People’s Republic of China 2. Pearl River Hydraulic Research Institute, Guangzhou, Guangdong, 510611, People’s Republic of China 3. Department of Geology and Geophysics, Texas A&M University, College Station, TX, 77843-3115, USA |
| Abstract: | A numerical analysis of non-Darcian flow to a pumping well in a confined aquifer using the strong-form mesh-free (MFREE) method is described. This technique is targeted at problems that use advanced numerical approaches for modeling non-Darcian flow and it supports the assumption that the non-Darcian flow follows the Forchheimer equation. Interpolation functions including the multi-quadrics (MQ) basis function (containing shape factors q and α) and the Gaussian (EXP) basis function (with shape factor ω) were found to be important defining parameters which had significant influence on the numerical results. A series of numerical experiments revealed that when q?=?2 and α?=?0.1, the mesh-free method yielded good results and the range of 10?6?–?10?3 might be a good choice for the shape factor ω in the EXP basis function. A comparison between the strong-form MFREE method and the finite difference method was done; the results showed that the strong-form MFREE method was very effective for solving non-Darcian flow near a pumping well in a confined aquifer, and was favorable over the finite-difference method, which could undergo oscillation and converging problems at early times. |
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