Space–time generalized finite difference nonlinear model for solving unsteady Burgers’ equations

Abstract

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.