Steady and unsteady solutions of the incompressible Navier-Stokes equations

Abstract

An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The equations are solved with a line-relaxation scheme that allows the use of very large pseudotime steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. The steady-state solution of flow through a square duct with a 90-deg bend is computed, and the results are compared with experimental data. Good agreement is observed. Computations of unsteady flow over a circular cylinder are presented and compared to other experimental and computational results. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented.

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

“…They often rely on the use of suitable relaxation parameters [28] in order to reach convergence for the stiff coupled problem. In [68], a comparison between ACM and pressure-correction techniques is given and in [2], a comparison of two pressure-correction algorithms showed the overall better performances of PISO-like algorithms over SIMPLE ones.…”

Computational challenges of viscous incompressible flows

“…To obtain timedependent solutions using this method, an iterative procedure can be applied in each physical time step such that the continuity equation is satisfied. Merkle and Athavale [30] and Rogers et al [31] reported successful computations using this pseudo-time iteration approach.…”

“…A variety of iterative schemes can be implemented in conjunction with the upwind schemes. For example, Rogers et al [31] solved the resulting set of numerical equations using an unfactored line relaxation scheme similar to that employed by MacCormack [a].…”

Artificial Compressibility 3-D Navier-Stokes Solver for Unsteady Incompressible Flows with Hybrid Grids

“…We use the artificial compressibility method which was first developed by Chorin (1967) and since then has been developed by various researchers for the solution of steady and unsteady flow fields (e.g. Rogers et al, 1990;Rogers et al, 1991;Pappou and Tsangaris, 1997). Our time accurate solver utilizes hybrid meshes of triangles and quadrilaterals in 2D and tetrahedra, pyramids, prisms and hexahedra in 3D.…”