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On modeling subsurface flow using a novel hybrid Trefftz-MFS method

机译：使用新型Trefftz-MFS混合方法对地下流动进行建模

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摘要

In this paper, a novel hybrid Trefftz-MFS method for modeling subsurface flow problems is presented. The proposed method constructs its nonsingular basis function as a series using T functions from the Trefftz method instead of using the singular solution in the method of fundamental solutions (MFS). Numerical solutions are approximated by superpositioning basis functions that are expressed in terms of many source points. Because of the use of the nonsingular basis function, the position of the source point in the proposed method is not sensitive to the results; thus, it resolves a major issue in the MFS for finding a satisfactory location for the source point. Additionally, the order of the nonsingular basis function can be reduced, because the addition theorem is used for approximating the solution for many source points. Consequently, the ill-posedness resulting from the adoption of higher order terms for the solution with only one source point in the collocation Trefftz method (CTM) is mitigated. The proposed method is validated for several test problems. Application examples are also performed. The results reveal that this novel method provides a promising solution that combines the benefits of the CTM and the MFS, such as the boundary collocation only and high accuracy. Moreover, the limitations to the practical application of the CTM and the MFS can be overcome using the proposed method.
机译：在本文中，提出了一种新型的Trefftz-MFS混合方法来模拟地下流动问题。所提出的方法使用Trefftz方法的T函数将其非奇异基函数构造为一系列，而不是在基本解（MFS）方法中使用奇异解。通过叠加基函数来近似数值解，基函数以许多源点表示。由于使用了非奇异基函数，因此所提出方法中源点的位置对结果不敏感；因此，它解决了MFS中的一个主要问题，即为源点找到满意的位置。另外，可以减少非奇异基函数的阶数，因为加法则用于逼近许多源点的解。因此，可减轻因搭配Trefftz方法（CTM）中只有一个源点而对解决方案采用高阶项而导致的不适感。所提出的方法针对几个测试问题进行了验证。还执行了应用示例。结果表明，这种新颖的方法提供了一种有前途的解决方案，该解决方案结合了CTM和MFS的优点，例如仅边界配置和高精度。此外，使用所提出的方法可以克服CTM和MFS实际应用的局限性。

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