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We discuss a Lagrangian approach for the simulation of 3D compressible flows on non-structured tetrahedral meshes. The formulation is nodal-based, in the sense that kinematic and thermodynamic variables are all interpolated with continuous P1 polynomials. The equations are solved with an explicit time-marching scheme without stabilizing terms and with the inclusion only of a shock-capturing viscosity. Several examples featuring shock propagations and mixing of fluids are addressed, with particular emphasis on the stability of the approach and on possible strategies for mesh update. [ABSTRACT FROM AUTHOR]

We present a Lagrangian nodal integration method for the simulation of Newtonian and non-Newtonian free-surface fluid flows. The proposed nodal Lagrangian method uses a finite element mesh to discretize the computational domain and to define the (linear) shape functions for the unknown nodal variables, as in the standard Particle Finite Element Method (PFEM). In this approach, however, the integrals are performed over nodal patches and not over elements, and strains/stresses are defined at nodes and not at Gauss points. This allows to limit the drawbacks associated with the remeshing and leads to a more accurate stress computation than in the classical elemental PFEM. Several numerical tests, in 2D and in 3D, are presented to validate the proposed nodal PFEM. In all cases, the method has shown a very good agreement with analytical solutions and with experimental and numerical results from the literature. A thorough comparison between nodal and elemental PFEMs is also presented, focusing on crucial issues, such as solution accuracy, convergence, mass conservation and sensitivity to mesh distortion. • Derivation of a new node-based Particle Finite Element Method for free-surface fluid flow. • Comparison of results accuracy and convergence between nodal-PFEM and standard elemental-PFEM. • Application to both Newtonian and non-Newtonian fluid models. • Presentation and analysis of several validation tests, in 2D and 3D. [ABSTRACT FROM AUTHOR]