Mohammad Vaghefi

This paper aims to present the Global Thin Plate Spline Dierential Quadrature (GTPS-DQM) method to achieve a numerical solution to viscous Burgers' equation. This meshless and high-order model is introduced with the motive of diminishing computational eort and dealing with irregular geometries. A Thin Plate Spline Radial Basis Function (TPS-RBF) is used as a test function to determine coecients of derivatives in dierential quadrature. The present algorithm is applied to discretize and solve the two-dimensional Burgers' equation in both rectangular and irregular non-rectangular computational domains with randomly distributed computation nodes. To evaluate the capability of the present model, several problems with dierent boundary and initial conditions and Reynolds numbers are solved and the obtained results are compared with the analytical solutions and other previous numerical models. The obtained results show the higher accuracy of the present model for solving Berger's equation with fewer computational nodes than the previous models even in irregular domains.