Solving degenerate quenching-combustion equations by an adaptive splitting method on evolving grids

Various types of partial differential equations have been playing increasingly important roles in the study of theoretical and numerical combustion. In this paper, we are particularly concerned with the numerical solution of certain premixed model problems in rectangular spatial domains. The two-dimensional reaction–diffusion equations involved are associated with an ignition type nonlinearity involving a mathematical degeneracy at a corner point. A Peaceman–Rachford–Strang splitting based adaptive method is proposed on exponentially evolving grids. Rigorous numerical analysis are given to ensure the satisfactory effectiveness, efficiency, and numerical stability of the algorithm developed. Simulation experiments are provided to illustrate our accomplishments.

► A highly effective adaptive splitting method for solving 2D degenerate quenching-combustion equations is implemented. ► Exponentially evolving grids in space and adaptive steps in time are developed. ► Solution positivity, monotonicity and stability are investigated. ► Computer simulation experiments are given and discussed.