Abstract
In this work, a hybrid localized meshless method is developed for solving transient groundwater flow in two dimensions by combining the Crank–Nicolson scheme and the generalized finite difference method (GFDM). As the first step, the temporal discretization of the transient groundwater flow equation is based on the Crank–Nicolson scheme. A boundary value problem in space with the Dirichlet or mixed boundary condition is then formed at each time node, which is simulated by introducing the GFDM. The proposed algorithm is truly meshless and easy to program. Four linear or nonlinear numerical examples, including ones with complicated geometry domains, are provided to verify the performance of the developed approach, and the results illustrate the good accuracy and convergency of the method.
Highlights
As an important component of the hydrological cycle system, groundwater is a key source of domestic and industrial water supply
Due to the complexity of the problem, an analytical solution is rarely available for most models of groundwater flow
As a new approach in recent years, the meshless method is widely applied in various fields [11,12,13,14,15,16,17,18,19], in computational fluid dynamics (CFD)
Summary
As an important component of the hydrological cycle system, groundwater is a key source of domestic and industrial water supply. The GFDM, as a popular localized meshless collocation method, employs the Taylor series expansions and moving least squares (MLS) approximations [45,46] to form the system of algebraic equations with a spare matrix [47,48]. Thanks to this spare system, this method is highly efficient and suitable for the numerical simulations of large-scale problems. A hybrid localized meshless method is proposed in this paper for the solution of transient groundwater flow in a two-dimensional space by combining the Crank–Nicolson scheme and the GFDM.
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