A higher order compact finite difference algorithm for solving the incompressible Navier–Stokes equations

International Journal for Numerical Methods in Engineering - Tập 88 Số 6 - Trang 511-532 - 2011
Zhenfu Tian1, Xian Liang2, Peixiang Yu1
1Department of Mechanics and Engineering Science and School of Mathematical Sciences, Fudan University, Shanghai 200433, People's Republic of China
2LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

Tóm tắt

AbstractOn the basis of the projection method, a higher order compact finite difference algorithm, which possesses a good spatial behavior, is developed for solving the 2D unsteady incompressible Navier–Stokes equations in primitive variable. The present method is established on a staggered grid system and is at least third‐order accurate in space. A third‐order accurate upwind compact difference approximation is used to discretize the non‐linear convective terms, a fourth‐order symmetrical compact difference approximation is used to discretize the viscous terms, and a fourth‐order compact difference approximation on a cell‐centered mesh is used to discretize the first derivatives in the continuity equation. The pressure Poisson equation is approximated using a fourth‐order compact difference scheme constructed currently on the nine‐point 2D stencil. New fourth‐order compact difference schemes for explicit computing of the pressure gradient are also developed on the nine‐point 2D stencil. For the assessment of the effectiveness and accuracy of the method, particularly its spatial behavior, a problem with analytical solution and another one with a steep gradient are numerically solved. Finally, steady and unsteady solutions for the lid‐driven cavity flow are also used to assess the efficiency of this algorithm. Copyright © 2011 John Wiley & Sons, Ltd.

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Thông tin xuất bản

International Journal for Numerical Methods in Engineering

Tập 88 Số 6

511-532

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