Special treatment of pressure correction based on continuity conservation in a pressure-based algorithm

The special features of pressure-correction equations and their effects on the performance of the SIMPLE algorithm have been systematically investigated based on the concept of continuity conservation. Except for use of the same iterative method as for the momentum equations, iterative solution of the pressure-correction equation has special features in three respects: initial values, boundary conditions (BCs), and iterative procedure. First, the initial values in each outer loop are independent and should be reset as zeroes. Second, the BCs are fully reverse to that of velocity: Dirichlet velocity BCs correspond to Neumann BCs of pressure correction, and Neumann velocity BCs lead to pressure-correction Dirichlet BCs. Third, more inner iterations for the pressure-correction equation are required to better satisfy continuity conservation. Dealing properly with these features can greatly improve the efficiency of the SIMPLE algorithm. Computational results and comparisons have shown that global mass conservation BCs are favorable to convergence, but may be slowed down by the local conservation BCs. During the course of convergence, the BCs of the pressure-correction equation are vital: only correct BCs can boost convergence, incorrect BCs cannot. Increasing the inner iterations of the pressure-correction equation will significantly decrease the outer-loop iterations, and therefore effectively improve the performance of the SIMPLE algorithm.