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| Numerical solution for unsteady incompressible N-S equations by least-squares-based operator-splitting finite element method |
| Received:April 11, 2013 Revised:October 25, 2013 |
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| DOI：10.7511/jslx201405016 |
| KeyWord:least-squares-based operator-splitting finite element N-S equations driven square flow flow over a circular cylinder |
| Author | Institution |
| 水庆象 |
西南科技大学 环境与资源学院, 绵阳 |
| 王大国 |
西南科技大学 环境与资源学院, 绵阳 |
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| Abstract: |
| A method for simulation of unsteady incompressible N-S(Navier-Stokes) equations is presented.In the each time step,the N-S equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm.For the diffusive equation,the temporal discretization is performed by the backward difference method and the spatial discretization is performed by the standard Galerkin method.For the convective equation,it is the first-order nonlinear partial differential equation;the temporal discretizaton is also performed by the backward difference method and Newton's method for the linearization of the nonlinear part.The spatial discretization is performed by the least square scheme and the resulting matrix is symmetric and positive definite.The driven square flow and flow over a circular cylinder are conducted to validate.Numerical results agree well with benchmark solution for the simulations of the driven square flow.Especially,for the flow over a circular cylinder,the numerical results such as the forces of cylinder,Strouhal number and the pressure on the cylinder surface agree well with experimental and numerical results,which prove that it can exactly and reliably to simulate the characteristics of flow over a circular cylinder in laminar flow. |