A conservative adaptive method for flame propagation

An adaptive one-dimensional finite-difference method aimed at the solution of flame-propagation problems is presented. This method uses a classical finite-difference approximation on a moving adaptive mesh. The discrete conservation of the variables is imposed for both the node displacements that occur at each timestep and for the interpolations that are performed at some time levels, when a static grid adaption is done. In particular, an interpolation procedure is presented that is conservative and also has the advantages of preserving the positivity and monotonicity of the interpolated variables.