A meshless generalized finite difference scheme for the stream function formulation of the Naiver-Stokes equations

Numerical Solutions of the Nonlinear Dispersive Shallow Water Wave Equations Based on the Space–Time Coupled Generalized Finite Difference Scheme

“…, n s represent the coordinates of the nodes in the supporting domain. By applying the n-order Taylor expansion and the weighting function, a residual function B n (u i ) can be written as [36,51],…”

“…Over the years, meshless methods have gained advantages such as simplified numerical procedures, easy implementation, flexibility, and the ability to construct hybrid numerical schemes tailored to specific research needs. At present, there are several meshless numerical methods, for example, the radial basis functions collocation method (RBFCM) [3], the virtual boundary meshless Galerkin method [20], the moving particle semi-implicit method [21], the radial point interpolation meshless method [22], the singular boundary method [23], the localized scheme based on boundary-type method [24][25][26], the generalized finite difference method (GFDM) [27][28][29][30][31][32][33][34][35][36][37], etc.…”

“…In addition, the resultant matrix system is a sparse matrix due to the localized property of the GFDM. The above characteristics make the GFDM capable of applying to complex problems, such as theoretical analysis [29], shallow water equation [30,31], porous media flow [32], wave propagation [33], elliptic interface problems [34], extended Fisher-Kolmogorov equation [35], stream function formulation [36], and elastic wave [37]. In this research, the space-time GFDM (ST-GFDM) was applied as the foundation of the proposed meshless numerical scheme, and it is an extended meshless method from the GFDM.…”