The component-consistent pressure correction projection method for the incompressible Navier-Stokes equations

• Published in: Computers & mathematics with applications (1987) 1996, Vol.31 (11), p.1-21
• Main Authors: Huang, Lan Chieh, Wu, Ya Dan
• Format: Article
• Language: English
• Subjects: Component-consistency; Deviation; Differential-algebraic equations; Exact sciences and technology; Incompressible Navier-Stokes equations; Mathematics; Nonlinear algebraic and transcendental equations; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Numerical methods in mathematical programming; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Numerical methods in probability and statistics; Numerical simulation; Ordinary differential equations; Pressure correction projection; Sciences and techniques of general use
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/0898-1221(96)00057-0

In this paper, we propose the component-consistent pressure correction projection method for the numerical solution of the incompressible Navier-Stokes equations. This projection preserves a discrete form of the component-consistent condition between components of the solution at every time step. We also propose, in particular, the CNMT2 + CCPC method and the RKMT + CCPC method, both involving one pressure Poisson solution per time step. We show that they are both of O( Δt 2) for the velocity and O( Δt) for the pressure on fixed meshes and finite time intervals. Numerical tests on flow simulation support our claim that the component-consistent pressure correction projection method solves the deviation problem encountered sometimes by the original pressure correction projection method.