Stable Fourth Order Stream-Function Methods for Incompressible Flows with Boundaries

Stable Fourth-order Stream-function Methods for Incompressible Flows with Boundaries

Fourth-order stream-function methods are proposed for the time dependent, incompressible Navier-Stokes and Boussinesq equations. Wide difference stencils are used instead of compact ones and the boundary terms are handled by extrapolating the stream-function values inside the computational domain to grid points outside, up to fourth-order in the noslip condition. Formal error analysis is done f...

High-order Discontinuous Galerkin Methods for Incompressible Flows

Abstract. The spatial discretization of the unsteady incompressible Navier-Stokes equations is stated as a system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Runge-Kutta methods applied to the solution of the resulting index-2 DAE system are analyzed, allowing a critical comparison...

A Compact Fourth-Order Finite Difference Scheme for Unsteady Viscous Incompressible Flows

In this paper, we extend a previous work on a compact scheme for the steady Navier Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137 1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier Stokes equations are discretized in space within a 3_3 stencil such that a fourth order accuracy i...

Velocity-Correction Projection Methods For Incompressible Flows

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence