비압축성 Navier-Stokes 방정식에 대한 내재적 속도 분리 방법

An implicit velocity decoupling procedure for the incompressible Navier-Stokes equations

An efficient numerical method to solve the unsteady incompressible Navier-Stokes equations is developed. A fully implicit time advancement is employed to avoid the CFL(Courant-Friedrichs-Lewy) restriction, where the Crank-Nicholson discretization is used for both the diffusion and convection terms. Based on a block LU decomposition, velocity-pressure decoupling is achieved in conjunction with the approximate factorization. Main emphasis is placed on the additional decoupling of the intermediate velocity components with only n th time step velocity The temporal second-order accuracy is Preserved with the approximate factorization without any modification of boundary conditions. Since the decoupled momentum equations are solved without iteration, the computational time is reduced significantly. The present decoupling method is validated by solving the turbulent minimal channel flow unit.