On the accuracy of block implicit and operator-splitting algorithms in confined flame propagation problems

Abstract

The propagation of a one-dimensional, confined, laminar flame is studied by means of two operator-splitting methods, four linear block implicit schemes and the standard implicit and Crank-Nicolson techniques. It is shown that the implicit method underestimates the flame speed and pressure because of first-order temporal truncation errors. Second-order accurate, in both space and time, methods yield nearly the same flame location and pressure as the operator-splitting techniques and the Crank-Nicolson scheme. Block linear methods which are first-order accurate in time and second-order accurate in space show temperature oscillations in the burned gas region near the flame front. These methods are found to be unstable when a delta formulation is used and the flame approaches the combustor wall. The instabilities are attributed to the large magnitude of the source terms and the rate of change of these terms with respect to time. A reduction in the time step brings the results of first-order accurate block methods into agreement with those of second-order accurate block methods. The flame speed and pressure increase as the size of the initial burned gas packet decreases. Operator-splitting methods are found more stable and more efficient than block methods in confined flame propagation problems.

Keywords:

• Linear block methods
• operator-splitting techniques
• integro-differential reaction-diffusion equations
• combustion

C.R. Categories:

• 5.17