Analysis of box schemes for reactive flow problems

SL Mitchell, KW Morton, A Spence

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/20ee4aeb-b665-40ec-af8f-58f327325747 • DOI: https://doi.org/10.1137/030601910

Key properties of the box scheme are shown to be advantageous for reactive flow problems. Unconditional stability and compact conservation are shown by a detailed modified equation analysis to enable the scheme to reflect exactly the “reduced speed,” enhanced diffusion, and dispersion which are typical of such “hyperbolic conservation laws with relaxation.” A novel modified equation analysis is also used to show how the spurious checkerboard mode behaves and can be controlled. Numerical experiments for some nonlinear one-dimensional problems and a two-dimensional problem demonstrate that the behavior of the scheme deduced from a simple model problem has general validity.

Modified equation analysis Reactive flow problems Box scheme