Weighted Moving Square-Based Solver for Unsteady Incompressible Laminar Flow Simulations

For computational fluid dynamics simulations, grid systems are generally used in the Eulerian frame for both structured and unstructured grids and solvers designed for the chosen grid systems. In contrast to the grid-based method, in which the connection information with neighboring grids must be maintained, gridless methods do not require an underlying connectivity in the form of control volumes or elements. Hence, gridless methods are feasible and robust for the problems with moving boundary and/or complicated boundary shapes. In this study, a Eulerian gridless solver is proposed, and its application for simulating two-dimensional unsteady viscous flows in low Reynolds number regions is investigated. The solver utilizes the weighted moving square method to obtain the spatial derivatives of the governing equations and solve the pressure Poisson equation iteratively. Simple remedies to satisfy the boundary conditions in the finite difference method are applied. The fractional step method with the second-order Adams-Bashforth method is used for time integration. Some benchmark problems were solved using the developed solver, and the results were compared with those of other experimental and computational methods. Good agreement with the results of other methods confirmed the validity of the proposed solver.