A novel fully decoupling algorithm for the incompressible Navier-Stokes equation

Unsteady Navier-Stokes (NS) equations possess the energy stability in the continuous case. In the process of the energy stability analysis, the inner product of the nonlinear term and the velocity term is equal to 0. Such a property is known as' zero-energy-contribution'. Making use of this property, if a related artificial variable function is introduced, during numerical calculation the nonlinear advection term could be treated explicitly, and meanwhile its energy stability can be main-tained. Note that the traditional decoupled method is to introduce the intermediate variable velocity field, and the pressure field is first treated explicitly. Then by means of solving Poisson-type equations, the velocity field and pressure field of the original equation are obtained. By combining use of these two methods, i.e., treating both the nonlinear terms and advection term explicitly, a symmetric positive definite system is generated. Therefore, in determining numerical solution, the conjugate gradient method can be adopted to enhance the computing efficiency. Some numerical examples are cited to verify the accuracy, and some comparisons are made in contrast with the traditional decoupled methods.