Applying and comparing finite difference, differential quadrature, and radial basis function-based differential quadrature numerical methods in confined aquifers

Subject Areas : Water resource management

Atena Naghipour ¹ , Ali Khoshfetrat ²

1 - Graduated from Civil Engineering Department, Shahid Ashrafi University of Isfahani, Isfahan, Iran
2 - Department of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran

Received: 2024-10-20 Accepted : 2024-12-07 Published : 2024-12-24

Keywords: DQ Method, RBF-DQ Method, Unsteady Flow, Steady Flow, Groundwater Equations, Confined aquifers,

Abstract :

The Differential Quadrature (DQ) method is a high-order numerical approach known for its remarkable accuracy and low computational cost, making it an attractive option for numerical modeling. However, a notable limitation of this method is its lack of geometric flexibility in modeling domains. The Radial Basis Function-based Differential Quadrature (RBF-DQ) method addresses this limitation by combining the DQ method's direct derivative estimation with the flexibility of mesh-free numerical techniques, making it suitable for both regular and irregular domains. This study compares the performance of the DQ, RBF-DQ, and Finite Difference (FD) methods — an established numerical technique in solving groundwater flow equations in confined aquifers for both steady-state and unsteady-state conditions. Exact solutions for these problems are derived using the Thiem and Theis methods. The results demonstrate the high accuracy of both the DQ and RBF-DQ methods in modeling groundwater flow in confined aquifers. Additionally, the DQ method outperforms the RBF-DQ method in terms of both accuracy and computational efficiency.

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