Abstract: A new approach。a strong form of discontinuous Galerkin method(DGM),was developed to solve level set equation on unstructured drids.A weak form is only suitable for incompressible flow,while the strong form can used to solve level set equation in any case,including incompressible and compressible flows.Thc approach allows arbitrarib higlI order accuracy through Legendre-Gauss.Lobatto nodal distribution.Several numerical tests on one-,two-and three-dimensional unstructured grids demonstrate versatility and validity of the method.Besides,implementation ofthe strong form ofDGM brings benefits,such as high order,mars conservation, dimension independence,resolving interface location at the sub-cell level,handling complex domains,avoiding reinitialization and so on.

Key words: discontinuous Galerkin, strong form, level set, unstructured grids, free surface, compressible flow, Legendre-Gauss-Lobatto