用虚拟黏性法构造Navier-Stokes方程黏性项的隐式格式

doi:10.7527/S1000-6893.2014.0344

Abstract

Abstract:

In this paper, a new algorithm called pseudo-viscosity method is introduced. It is a new concept used to construct implicit finite difference scheme about the viscosity item of Navier-Stokes equations. The construction of implicit scheme is greatly simplified via introducing pseudo-time and pseudo-viscosity item. Thus, the common way of getting solutions of large complex implicit finite difference equations is avoided. And a tridiagonal matrix is generated for the coefficient matrix of implicit finite difference equations. It can be solved easily and has a little operation counts. Numerical simulation are made for this implicit scheme in model equation and Navier-Stokes equations. The effects of parameters in this implicit scheme are discussed with numerical simulation. What's more, the accuracy and efficiency are compared with explicit scheme to prove the validity and advantage of the implicit scheme. Finally, conditions for using this implicit scheme are analyzed in detail.

Key words: Navier-Stokes equations, operator-splitting, implicit scheme, pseudo-viscosity, pseudo-time

CLC Number:

V211.3
O35

DONG Haitao, LIU Dingsong. Implicit scheme for viscosity item of Navier-Stokes equations with pseudo-viscosity method[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(7): 2186-2196.

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Implicit scheme for viscosity item of Navier-Stokes equations with pseudo-viscosity method

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