A LOCAL DIFFERENTIAL QUADRATURE METHOD WITH VARIABLE SHAPE MULTIQUADRICS: TESTS ON POISSON EQUATION AND FLUID DYNAMICS USING CONSISTENT CLOUD REFINEMENTS

Abstract

A meshless Local Differential Quadrature Method for solving partial differential equations is presented in this paper. It is based in a point cloud discretization and local supports. A basis set of Multiquadric functions is employed for determining the weight coefficients in derivative approximations. Tests with the Poisson equation are presented for verifying the converge behavior of the method in Clouds with Unstructured Generation (CUG’s). A consistent refinement procedure for varying the multiquadric shape parameter between local supports is proposed. The method is finally applied for solving the classical benchmark problem of natural convection in a square cavity. Satisfactory results were obtained in comparison with the reference literature.