A TWO-DIMENSIONAL FREE LAGRANGIAN HYDRODYNAMICS MODEL

This thesis describes development of a two-dimensional Lagrangian hydrodynamics computer model. The model numerically integrates the time-dependent, compressible fluid flow equations in two-dimensional Cartesian geometry by using an explicit finite difference scheme on a free Lagrangian grid of Lagrangian mass points. An artificial viscosity tensor is introduced into the flow equations to resolve shock discontinuities in two dimensions. Use of a free Lagrangian grid eliminates the classical mesh tangling problems associated with standard Lagrangian models. This is done by giving each Lagrangian mass point the freedom to associate with a variable set of nearest neighbors. Identifying the nearest neighbors of each mass point is accomplished through the construction of a Voronoi mesh made up of Voronoi cells (convex polygons). The common edges of each Voronoi cell identify pairs of nearest neighbors. Since the change in volume of a Voronoi cell is continuous, two nearest neighbors become associated and disassociated in a continuous manner as the edge of the Voronoi cell separating two neighbors grows and shrinks.; The concept of free Lagrangian hydrodynamics, as formulated in this thesis, is tested by modeling several example problems involving the development and propagation of shock waves in various geometric setups. The results of these test problems are compared with both analytic shock relations and experimental data. Through these comparison cases we find the free Lagrangian hydrodynamic scheme used in formulating the Free Lagrangian Model to be both consistent and stable.