The　evolution　of　flow　structures　during　dynamic　stall　of　a　two-dimensional　pitching　National　Advisory　Committee　for　Aeronautics　0012　airfoil　is　studied　using　the　variational　Lagrangian　coherent　structures　(LCSs),　and　the　mass　transport　and　vorticity　transport　are　precisely　analyzed　using　LCSs　and　lobe　dynamics　for　further　understanding　the　nature　of　flow　phenomena　in　dynamic　stall.　First,　the　variational　LCS　algorithm　is　improved　to　be　efficiently　used　in　the　accurate　extraction　of　flow　structures.　Then,　both　the　hyperbolic　LCSs　and　elliptic　LCSs　are　computed　numerically　in　the　whole　process　of　dynamic　stall　to　analyze　the　evolution　of　flow　structures　in　detail.　Further,　a　high-accuracy　LCS-advection　method　is　used　in　the　advection　of　LCSs　to　quantitatively　analyze　the　mass　transport　and　vorticity　transport　in　the　evolution　of　LCSs　utilizing　lobe　dynamics　based　on　nonlinear　dynamics.　Finally,　the　evolution　and　motion　of　primary　leading　edge　vortex　(LEV)　and　trailing　edge　vortex　(TEV)　identified　by　elliptic　LCSs　are　analyzed　in　depth.　The　results　obtained　can　provide　a　deeper　insight　into　the　nature　of　flow　phenomena　in　dynamic　stall　from　the　viewpoint　of　nonlinear　dynamics.　Specifically,　the　nature　of　evolution　of　primary　LEV　and　the　TEV　and　the　reasons　for　the　changes　of　lift　coefficients　are　clarified　from　the　viewpoint　of　fluid　transport.　To　explain　it　briefly,　the　variational　LCSs　and　lobe　dynamics　are　powerful　tools　to　quantitatively　analyze　the　evolution　of　flow　structures　and　fluid　transport.　©　2022　Author(s).