Incompressible flows with combustion simulated by a preconditioning method using multigrid acceleration and MUSCL reconstruction

摘要

A numerical algorithm for the steady state solution of three-dimensional incompressible flows is presented. A preconditioned time marching scheme is applied to the conservative form of the governing equations. The preconditioning matrix multiplies the time derivatives of the system and circumvents the eigenvalue-caused stiffness at low speed. The formulation is suitable for constant density flows and for flows where the density depends on non-passive scalars, such as in low-speed combustion applications. The k-ε model accounts for turbulent transport effects. A cell-centred finite volume formulation with a Runge-Kutta time stepping scheme for the primitive variables is used. Second-order spatial accuracy is achieved by developing for the preconditioned system an approximate Riemann solver with MUSCL reconstruction. A multi-grid technique coupled with local time stepping and implicit residual smoothing is used to accelerate the convergence to the steady state solution. The convergence behaviour and the validation of the predicted solutions are examined for laminar and turbulent constant density flows and for a turbulent non-premixed flame simulated by a presumed probability density function PDF) model.