A pressure correction local defect correction algorithm for laminar flame simulation

Abstract

We have developed a numerical simulation code for laminar premixed flames, based on the isobaric model. The main numerical techniques employed are: the finite volume method in combination with an exponential flux approximation scheme for space discretisation, a pressure-correction (PC) method to decouple the computation of the velocity and pressure and a multi-level local defect correction (LDC) method to solve the resulting boundary value problems (BVPs). The pressure correction scheme we use [2] is based on the expansion equation "nabla cdot v = s", where the source term s describes expansion of the gas mixture due to combustion, whereas classical pressure correction methods are based on the continuity equation. As a result of the PC algorithm, we obtain a set of BVPs, characterised by a high activity region, i.e. the flame front, where virtually all reactions and heat production take place. We solve these BVPs using the LDC method. LDC is an iterative multilevel method to solve BVPs characterised by a high activity region [1]. Roughly speaking, the method works as follows. In the first stage of the method, we compute a solution on a relatively coarse global grid. Second, from this coarse grid solution we determine the high activity region, cover it with a much finer grid, an recompute the solution there. Boundary conditions for this local problem are provided by the coarse grid solution. Next, we compute from the fine grid solution a defect that is subsequently used to improve the coarse grid solution. The method can be extended recursively to include several levels of refinement. Finally, this procedure is repeated several times in an iterative fashion. Convergence of LDC is usually very fast, typically only one or two iterations are needed. The combined PC LDC algorithm has the following advantages. First, the computation of the pressure and velocity is decoupled. Second, the number of control volumes can be reduced significantly, and third, we only have to solve BVPs on simple (uniform, rectangular) grids. Uniform grids have several advantages: accurate discretisation methods exist and efficent iterative solution methods for the resulting algebraic systems are available. We have applied the method to a two-dimensional methane/air flame, and compared the results with the local uniform grid refinement (LUGR) method