MC-Smooth: A Mass-Conserving, Smooth Vorticity-Velocity Formulation for Multidimensional Flows

摘要

In this study, a novel vorticity-velocity formulation - the Mass-Conserving, Smooth (MC-Smooth) formulation - is developed. Compared to some existing vorticity-velocity formulations, MC-Smooth is appealing because it can generate smooth and mass-conservative solutions without employing staggered grids. Furthermore, MC-Smooth can preserve ellipticity and favorable convergence properties of the governing equations and does not require follow-up simulations (e.g., replacing one of the equations with continuity and then recon-verging). The performance of MC-Smooth is compared with that of two vorticity-velocity formulations from the literature for three test cases: a laminar jet of air with an inhomogeneous density field and two laminar methane/air flames with detailed chemistry. Since each test problem is either axisymmetric or two-dimensional (2D) planar, a 2D computational domain with a nonuniform grid was employed. The governing equations and boundary conditions were discretized on the mesh by a finite difference approach, and the resulting set of nonlinear equations was solved by a damped, modified Newton's method. By comparing the performance of each vorticity-velocity formulation without any follow-up simulations, MC-Smooth is shown to generate more physically accurate results by ensuring both mass conservation and smoothness of the velocity field.