Effectiveness of meshless methods for advection dominant groundwater contaminant transport problems

•Meshless methods can effectively simulate advection dominant flows.•Three meshless methods belonging to different categories are considered and compared.•RPCM, MLPG and hybrid MWS are tested for transport in high Peclet number flows.•MLPG is most stable and accurate and is best suited for complex problems.•MWS can delay the failure of RPCM transport model with respect to high advection.