Gaussian–Cubic Backward Substitution Method for Fourth-Order Stream Function in Transient Two-Dimensional Incompressible Viscous Flows

This paper presents a meshless collocation technique for the fourth-order transient stream function formulation of the Navier–Stokes equations. The technique employs a hybrid kernel function and is augmented by the ghost point method and Picard iteration. The reduction in unknowns inherent in this stream function approach simplifies the solution process. Introducing vorticity and stream functions enables mathematical reformulation of the coupled, time-dependent Navier–Stokes system as a fourth-order partial differential equation in one variable. The Gaussian–cubic backward substitution method and time difference method are used to solve the corresponding equation, in which the nonlinear part is generally transformed into linear equations through Picard iteration methods. This paper simulates three flows to prove the feasibility of the scheme.