#### Name

Xiaomin Pan

#### Course

Integrated Ph.D Student (통합과정)

#### Research Area

Various projection methods have been widely studied and used for time-dependent incompressible Navier–Stokes equations, and stability and accuracy properties are the key issues for investigating the performance of projection methods. The present study focus on analyzing the stability property and temporal accuracy of the implicit projection methods, linearized convection projection method and velocity decoupled projection method, based on Kim et al.’s work (2002, An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations). In the linearized convection projection method, the Crank–Nicolson scheme is used for both the convection and diffusion terms with a block LU decomposition employed for pressure-velocity decoupling. For avoiding the iterative procedure, based on the linearized convection projection method, additional decoupling procedure is applied to the intermediate velocity components which leads to the velocity decoupled projection method. Three types of discrete operators, advective, skew-symmetric and divergence operators are is used for the nonlinear convection term.

We prove that the two methods are second-order accurate in time by evaluating the differences between the numerical solutions and Crank–Nicolson solutions (solutions without any decoupling procedure) for velocities and pressure in discrete L2-norm. We present the stability properties of the two methods via estimating the kinetic energy estimation for fully-discrete Navier-Stokes equations which confirms almost unconditionally stability of the methods and performing the von Neumann analysis of linearized Navier-Stokes equations for getting the distribution of maximum magnitude of the eigenvalues for the corresponding matrix. The influences of three discrete operators are considered in the theoretical discussion. Finally, we consider 2D lid-driven cavity flow and periodic forced flow to validate the theoretical assertions.

[Simulations based on the lid-driven cavity flow]

Re=100, CFL=130

Re=100, CFL=130

[Simulations based on the periodic forced flow]

velocity decoupled method

Linearized convection method

#### Email

sanhepanxiaomin@gmail.com

#### Entrance date

2012/09