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Abstract
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This paper aims to present the Global Thin Plate Spline Di erential
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 e ort 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 di erential 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 di erent 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.
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