Localized multiscale of 2D Burgers' equation with penalty using meshless approximation
Liew Siaw Ching, Yeak Su Hoe · AIP conference proceedings · 2014
A new numerical method which is based on the coupling between localized multiscale method and meshless method with penalty is developed for 2D Burgers' equation.In this paper, penalty method is employed to enforce the essential boundary conditions due to the lack of the Kronecker delta property in meshless shape function.For the area involving high rate of velocity changes, solution needs to be refined and improved in order to properly capture the solution behaviour in the corresponding area.Here, the problem is decomposed into a coarse and a fine scale based on the variational formulation.In this work, multiscale method is adopted locally at the critical area with coarse scale and fine scales to represent global and local behaviour, respectively.Finally a 2D Burgers' problem with penalty is solved by using the localized multiscale meshless approximation and the results have been compared with normal meshless technique.The numerical results show that the former method obtains higher accuracy result compared with the latter method.Therefore, this localized multiscale meshless method with penalty is an attractive approach for solving more general problems which involve large deformation.