The　two-dimensional　shallow　water　equations　(SWEs)　are　a　hyperbolic　system　of　first-order　nonlinear　partial　differential　equations　which　have　a　characteristic　of　strong　gradient.　In　this　study,　a　newly-developed　numerical　model,　based　on　local　radial　point　interpolation　method　(LRPIM),　is　adopted　to　simulate　discontinuity　in　shallow　water　flows.　In　order　to　accurately　capture　the　information　of　wave　propagation,　the　LRPIM　is　combined　with　the　split-coefficient　matrix　(SCM)　method　to　transform　the　SWEs　into　a　characteristic　form　and　the　selection　of　the　direction　of　local　support　domain　is　introduced　into　the　LRPIM.　An　improved　meshless　artificial　viscosity　(MAV)　technique　is　developed　to　minimize　the　non-physical　oscillations　near　the　discontinuities.　Then,　the　LRPIM　and　the　second-order　Runge–Kutta　method　are　adopted　for　spatial　and　temporal　discretization　of　the　SWEs,　respectively.　The　feasibility　and　validity　of　the　proposed　numerical　model　are　verified　by　the　classical　dam-break　problem　and　the　mixed　flow　pattern　problem.　The　comparison　of　the　obtained　results　with　the　analytical　solution　and　other　numerical　results　showed　that　the　MAV　method　combined　with　LRPIM　can　accurately　capture　the　shocks　and　has　high　accuracy　in　dealing　with　discontinuous　flow　by　adding　appropriate　viscosity　to　the　equations　in　the　discontinuous　region.　©　2021　Elsevier　Ltd