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The HLLC Riemann solver, which resolves both the shock waves and contactdiscontinuities, is popular to the computational fluid dynamics communitystudying compressible flow problems with mesh methods. Although it was reportedto be used in meshless methods, the crucial information and procedure torealise this scheme within the framework of meshless methods were not clarifiedfully. Moreover, the capability of the meshless HLLC solver to deal withcompressible liquid flows is not completely clear yet as very few relatedstudies have been reported. Therefore, a comprehensive investigation of adimensional non-split HLLC Riemann solver for the least-square meshless methodis carried out in this study. The stiffened gas equation of state is adopted tocapacitate the proposed method to deal with single-phase gases and/or liquidseffectively, whilst direct applying the perfect gas equation of state forcompressible liquid flows might encounter great difficulties in correlating thestate variables. The spatial derivatives of the Euler equations are computed bya least-square approximation and the flux terms are calculated by the HLLCscheme in a dimensional non-split pattern. Simulations of gas and liquid shocktubes, moving shock passing a cylinder, internal supersonic flows in channelsand external transonic flows over aerofoils are accomplished. The currentapproach is verified by extensive comparisons of the produced numericaloutcomes with various available data such as the exact solutions, finite volumemesh method results, experimental measurements or other reference results.

A meshless method for compressible flows with the HLLC Riemann solver