The　reconstruction　operator　(RO),　which　calculates　the　distribution　functions　of　the　lattice　Boltzmann　method　(LBM)　by　the　macroscopic　variables,　is　important　for　the　information　exchange　in　the　coupling　simulation　between　LBM　and　macroscopic　numerical　methods.　In　the　present　work,　different　ROs　are　derived　based　on　the　first-　and　second-order　expansions.　The　derivations　show　that　the　second-order　ROs　can　conserve　the　momentum　but　the　first-order　ROs　fail.　The　first-order　models　can　be　modified　to　guarantee　the　momentum　conservation.　The　numerical　tests　are　employed　to　evaluate　the　precisions　of　different　models.　The　results　demonstrate　that　the　multiple-relaxation-time　LBM　is　more　stable　than　the　single-relaxation-time　LBM,　and　the　first-order　models　are　more　stable　than　the　second-order　models.　The　second-order　models　give　better　reconstructions　of　the　non-equilibrium　parts　of　the　distribution　functions　than　the　first-order　models.　However,　the　modified　first-order　models　have　similar　accuracy　to　the　second-order　models　when　they　are　employed　as　boundary　conditions　or　used　in　coupling　simulations.　Therefore,　the　second-order　models　are　suggested　for　the　initial　conditions.　The　modified　first　order　models　are　suggested　for　the　boundary　conditions　and　the　coupling　simulations.　Moreover,　CPU　time　for　coupling　simulation　decreases　with　the　increase　of　the　ratio　between　the　time　steps　of　finite　volume　method　and　LBM,　and　an　optimized　time　ratio　exists　to　minimize　the　errors.　Finally,　the　flow　past　a　porous　medium　is　simulated　by　both　the　coupling　methods　and　the　multi-block　LBM.　The　results　show　that　the　coupling　methods　are　more　efficient　when　using　a　large　time　step　for　the　finite　volume　method.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.