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Application of a local meshless modified characteristic method to incompressible fluid flows with heat transport problem
Engineering Analysis With Boundary Elements  (IF2.964),  Pub Date : 2021-11-18, DOI: 10.1016/j.enganabound.2021.09.033
Zineb Tabbakh, Rachid Ellaia, Driss Ouazar

Radial basis function (RBF) has been accurately used for the spatial discretization to solve PDE problems. In this paper, a practical stabilization of the local formulation of the radial basis function (RBF) method is presented to solve the incompressible fluid flows with heat transport problems. To avoid the nonlinearity of the convective term, we include the modified method of characteristics to construct stable and efficient methods. The governing equations are the incompressible Navier–Stokes equations/Boussinesq approximation coupled with the heat transport equation. The spatial discretization carried out using the local radial basis function (LRBF) method on a uniform and non-uniform nodes distribution in a complex domain. The proposed method can be described as a fractional step splitting where the convective and generalized Stokes parts are treated separately. To solve the generalized Stokes problem, we used a projection/fractional step method that requires velocity–pressure decoupling. The proposed approach’s performance is tested on three benchmark problems and natural convection flow in a regular and irregular domains. We compare the results with different numerical solutions published in the literature. The obtained numerical results demonstrate the accuracy and stability of the proposed meshless method.