Assessment of numerical schemes for moving boundary problemswith reactions

Purpose The purpose of this study is to evaluate the performance of various numerical schemes for solving moving boundary problems that involve chemical reactions. Design/methodology/approach A one-dimensional test problem involving the infiltration of fluid into an initially dry porous media in the presence of a hydration reaction is posed. This problem is characterized by the advance of a sharp infiltration front. Analysis indicates that the late-time front movement asymptotes to a square root in time behavior. Three candidate moving boundary numerical schemes are introduced. Two schemes involve algorithms that explicitly track the advance of the front. The other implicitly tracks the front on a fixed space grid through specifying a liquid fraction term with values between 0 and 1. Findings Because of its conserved nature, the fixed-grid scheme is able to recover the expected late-time asymptotic behavior. The front-tracking schemes, however, are unable to resolve the reaction at late times and diverge away from the expected square root in time behavior. Practical implications This study provides a simple one-dimensional problem that can be used as a standard verification test problem for numerical moving boundary methods. Social implications The modeling provides a tool that can be used to assess the permanent storage of atmospheric CO2 in the subsurface. Originality/value This study can be used for the development and testing of schemes for modeling moving boundary problems with reactions. Also, this study demonstrates possible flaws in basic front-tracking moving boundary schemes.