A Lagrangian finite element method for 3D compressible flow applications

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.