A class of high-resolution algorithms for incompressible flows

作者：Lee Long^*

来源：Computers & Fluids, 2010, 39(6): 1022-1032.

DOI：10.1016/j.compfluid.2010.01.012

• High-resolution
• Finite volume methods
• Incompressible Navier-Stokes equations
• Finite-amplitude density variation
• Liddriven cavity flow
• Rayleigh-Taylor instability
• Rayleigh-Benard convection

We present a class of a high-resolution Godunov-type algorithms for solving flow problems governed by the incompressible Navier-Stokes equations. The algorithms use high-resolution finite volume methods developed in LeVeque (SIAM J Numer Anal 1996;33:627-665) for the advective terms and finite difference methods for the diffusion and the Poisson pressure equation. The high-resolution algorithm advects the cell-centered velocities using the divergence-free cell-edge velocities. The resulting cell-centered velocity is then updated by the solution of the Poisson equation. The algorithms are proven to be robust for constant-density flows at high Reynolds numbers via an example of lid-driven cavity flow. With a slight modification for the projection operator in the constant-density solvers, the algorithms also solve incompressible flows with finite-amplitude density variation. The strength of such algorithms is illustrated through problems like Rayleigh-Taylor instability and the Boussinesq equations for Rayleigh-Benard convection. Numerical studies of the convergence and order of accuracy for the velocity field are provided. While simulations for two-dimensional regular-geometry problems are presented in this study, in principle, extension of the algorithms to three dimensions with complex geometry is feasible.

• 出版日期2010-6