No abstract

Adaptive mesh and algorithm refinement (AMAR) embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement (AMR) hierarchy. The coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of AMR. Direct simulation Monte Carlo (DSMC) is used as the particle algorithm embedded within a Godunov-type compressible Navier-Stokes solver. Several examples are presented and compared with purely continuum calculations.

The use of approximate projection methods for modeling low Mach number flows avoids many of the numerical complications associated with exact projection methods, but introduces additional design choices in developing a robust algorithm. In this paper we first explore these design choices in the setting of inviscid incompressible flow using several computational examples. We then develop a framework for analyzing the behavior of the different design variations and use that analysis to explain the features observed in the computations. As part of this work we introduce a new variation of the approximate projection algorithm that combines the advantages of several of the previous versions.

We present an adaptive projection method for modeling unsteady, low-Mach reacting flow in an unconfined region. The equations are based on a model for low-Mach number combustion that consists of evolution equations coupled with a constraint on the divergence of the flow. The algorithm is based on a projection methodology in which we first advance the evolution equations and then solve an elliptic equation to enforce the divergence constraint. The adaptive mesh refinement (AM R) scheme uses a time-varying hierarchy of rectangular grids. The integration scheme is a recursive procedure in which coarse grids are advanced, fine grids are advanced to the same time as the coarse grids, and the coarse and fine grid data are then synchronized.The method is currently implemented for laminar, axisymmetric flames with a reduced kinetics mechanism and a Lewis number of unity. Three methane-air flames, two steady and one flickering, are presented as numerical examples.