A numerical method applied to forced and natural convection flows over arbitrary geometry

In this study, a numerical method based on Cartesian mesh method and gridless approach applied to forced and natural convection flows over arbitrary geometry is proposed. In the proposed method, a preconditioning method developed by the authors has been coupled with the building-cube method, owing to its simplicity and efficiency in mesh generation, implementation of solution algorithm, and post-processing. A gridless approach is further introduced as a wall boundary treatment for its adaptability to complex physics and arbitrary geometry problems. In this study, first, two classical cases of steady forced convection flow past a circular cylinder and natural convection flow over a circular cylinder are tested; the advantages of the gridless approach over the immersed boundary method are clearly shown. Then, further tests of unsteady forced convection flow past two side-by-side circular cylinders and natural convection flow over a Y-shaped fin are also conducted, which show that the present numerical method is also qualified for flow problems involving complex physics and arbitrary geometries. In addition, computational cost comparisons show that the time cost increase caused by the introduction of the gridless approach is within 20% for all test cases considered.