Abstract
In this paper, a new upwind technique for local radial basis function differential quadrature (LRBF-DQ) method is proposed to solve the convection-dominated flow problems. By using a modified Euclidean distance function according to the local flow direction and the value of parameter that controls the convection effect, the local support in the formulation of LRBF-DQ can be chosen in a way shifting towards the upstream direction to form a comet-like shape. The upwind effect is therefore naturally incorporated when computing the weighting coefficients for LRBF-DQ method. The capability of the proposed method is examined by solving two-dimensional convection–diffusion equation with various Peclet numbers and magnetohydrodynamics (MHD) problems with very high Hartmann numbers. The results show that remarkable improvement of accuracy can be achieved by the current upwind-based LRBF-DQ method than the conventional ones.
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