An implicit compact scheme solver for modeling steady-state and time-dependent axisymmetric flows with application to laminar diffusion flame simulations.

摘要

A stable fully implicit compact scheme solver for modeling steady-state and time-dependent multicomponent reacting mixtures in the low Mach number regime has been developed for a two-dimensional axisymmetric configuration. The governing equations are written using the vorticity-velocity formulation. These stiff, highly nonlinear equations are discretized on inner nodes with sixth order accuracy on uniform grids and third order accuracy on nonuniform grids, and the discretized system is solved with a damped modified Newton's method. Regarding the almost-dense Jacobian matrix, exact algorithms for its generation, storage, and multiplication by a vector employ a new highly efficient component form, resulting in dramatic savings in both memory and computational time. Use of the exact Jacobian matrix-vector product in component form is shown to be especially important for flame calculations with a wide spread of scales in the dependent variables. The linearized system of equations is solved with a preconditioned Bi-CGSTAB solver. Based on threshold parameters for spatial derivatives, a partial Jacobian matrix is generated for use as a preconditioner. The decomposition of the partial Jacobian matrix is carried out with the recently reported MC64-ILUT preconditioning strategy. Applications of the implicit compact scheme solver to several nonreacting flows are given, such as: flow in a pipe; momentum jet flow; heated jet flow; and time-dependent periodic mixing of an oxygen-rich jet in quiescent air. The results display the excellent resolution characteristics of the new method leading to more than one order of magnitude reduction in memory and computational time over a first order accurate implicit solver. Calculations with the implicit compact scheme solver of the thermochemical variables in a steady-state laminar methane-air diffusion flame with detailed chemical kinetic and transport models are presented.