Finite point solver for the simulation of 2-D laminar incompressible unsteady flows

Abstract

A finite point solver has been developed to simulate 2-D laminar incompressible unsteady flow fields in the low Reynolds number regime (Reynolds of the order of 100–1000). Grid points, without connectivity in the classic sense, are scattered all over the computational domain, and a certain flow functional behaviour is assumed to hold in a small region around each point. Two types of functional behaviour have been tested: a truncated and a full second-order Taylor expansion. The expansion coefficients are obtained by using a least squares approximation in the cloud of points located around the point under consideration. An artificial compressibility formulation has been used for the continuity equation. The validity of this approach to deal with unsteady flow situations has also been discussed. Time integration has been performed by using a Lax–Wendroff formulation. Because of numerical stability concerns, three artificial viscosity terms have been introduced. Concerning solver validation, a detailed sensitivity analysis is performed with regard to the three artificial viscosity terms, the pseudo-compressibility coefficient, the number of grid points in the flow field, and the Reynolds number. The results obtained: Strouhal number, average drag, and lift root mean square values, were compared with experimental results and, also, with the numerical results obtained by other researchers. Application of the solver to the steady regime is also presented.