A FREE-LAGRANGE METHOD FOR UNSTEADY COMPRESSIBLE FLOW - SIMULATION OFA CONFINED CYLINDRICAL BLAST WAVE

A Free-Lagrange numerical procedure for the simulation of two-dimensio nal inviscid compressible flow is described in detail. The unsteady Eu ler equations are solved on an unstructured Lagrangian grid based on a density-weighted Voronoi mesh. The flow solver is of the Godunov type , utilising either the HLLE (2 wave) approximate Riemann solver or the more recent HLLC (3 wave) variant, each adapted to the Lagrangian fra me. Within each mesh cell conserved properties are treated as piece-wi se linear, and a slope limiter of the MUSCL type is used to give non-o scillatory behaviour with nominal second order accuracy in space. The solver is first order accurate in time. Modifications to the slope lim iter to minimise grid and coordinate dependent effects are described. The performances of the HLLE and HLLC solvers are compared for two tes t problems; a one-dimensional shock tube and a two-dimensional blast w ave confined within a rigid cylinder. The blast wave is initiated by i mpulsive heating of a gas column whose centreline is parallel to, and one half of the cylinder radius from, the axis of the cylinder. For th e shock tube problem, both solvers predict shock and expansion waves i n good agreement with theory. For the HLLE solver, contact resolution is poor, especially in the blast wave problem. The HLLC solver achieve s near-exact contact capture in both problems.