Global thin plate spline differential quadrature as a meshless numerical solution for two-dimensional viscous Burgers' equation

This paper is aimed to present the Global Thin Plate Spline Differential Quadrature method for the numerical solution of viscous Burgers’ equation. This mesh-less and high-order model is introduced with the motive of diminishing computational effort and dealing with irregular geometries. Thin Plate Spline Radial basis function is used as a test function to determine coefficients of derivatives in differential quadrature. The present algorithm is applied to discretize and solve 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 different 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 compared to the previous models even in irregular domains.