Space-time generalized finite difference nonlinear model for solving unsteady Burgers' equations

In this study, the space-time (ST) generalized finite difference method (GFDM) was combined with Newton's method to stably and accurately solve two-dimensional unsteady Burgers' equations. In the coupled ST approach, the time axis is selected as a spatial axis; thus, the temporal derivative in governing equations is treated as a spatial derivative. In general, the GFDM is an optimal meshless collocation method for solving partial differential equations. Moreover, one can avoid the construction of a mesh for simulation by using the GFDM. The derivatives at each node are described as a linear combination of nearby functional values by using weighting coefficients in the computational domain. Due to the property of the moving least-square approximation in the GFDM, the resultant matrix system can be formed as a sparse matrix so that the GFDM is suitable for solving large-scale problems. In this study, two benchmark examples were used to demonstrate the consistency and accuracy of the proposed ST meshless numerical scheme. (C) 2020 Elsevier Ltd. All rights reserved.