Extending MLPG primitive variable-based method for implementation in fluid flow and natural, forced and mixed convection heat transfer

The purpose of the current study is to empower the MLPG primitive variable-based method using the characteristic-based split (CBS) scheme to solve the laminar fluid flow and natural, forced, and mixed convection heat transfer at, respectively, higher Rayleigh, Reynolds and Peclet, and Reynolds and Grashof numbers than those that the MLPG approach has ever solved. In this work, the CBS scheme with unity test function is employed for discretization and the moving least square (MLS) method is used for interpolation. As some test cases, natural convection within a square cavity, forced convection by fluid flow over a bundle of tubes, and mixed convection within a lid-driven square cavity are solved by the proposed method. For verifications, the obtained results are compared with those of the conventional numerical methods in the literature. Being entirely meshless, strong in nature, and able to give accurate and stable results for the broadest range of laminar fluid flow involving any of the three modes of convection heat transfer, the proposed method shows to be a flexible and reliable technique which can replace many available meshfree methods in the literature.