A study of moving mesh methods applied to a thin flame propagating in a detonator delay element

We study the application of moving mesh methods to a one-dimensional (time dependent) detonator delay element problem. We consider moving mesh methods based on the equidistribution principle derived by Huang et al. [1]. Adaptive mesh methods have been widely used recently to solve time dependent partial differential equations having large solution gradients. Significant improvements in accuracy and efficiency are achieved by adapting the nodes (mesh points) so that they are concentrated about areas of large solution variations. Each system of equations for the moving mesh methods is solved in conjunction with the detonator problem. In this paper, the system of ordinary differential equations that results (after discretising in space) is solved using the double precision version of the stiff ordinary differential equation solver DASSL. The numerical results clearly demonstrate that the moving mesh methods are capable of tracking the deflagration wave as it travels down the detonator delay element more accurately and more efficiently than a fixed mesh method.