Discrete Hamilton's equations for viscous compressible fluid dynamics

A kernel free particle‐finite element method for hypervelocity impact simulation

“…Figures 1-4 plot the simulation results for velocity, density, pressure, and temperature at the stop time of 0.3, for a model composed of 200 particles. The numerical results show good agreement with the exact solution, although better results have been obtained using finite difference and finite element methods [29,30]. Table II shows convergence of the simulation results, as the particle count is increased, in Table I.…”

“…and the parameters shown in Table 1 better results have been obtained using finite difference and finite element methods [31,35]. Table 2 shows convergence of the simulation results, as the particle count is increased, in terms of the velocity error norm…”

Discrete Lagrange equations for reacting thermofluid dynamics in arbitrary Lagrangian–Eulerian frames

“…In previous work the authors and co-workers [1,2,3] have developed new discrete energy methods for continuum fluid dynamics modeling. Employing entropies or internal energies as generalized coordinates, and a finite element interpolation of the flow field, the cited works formulated discrete Hamiltonian or Lagrange equation formulations for viscous compressible fluid dynamics in Lagrangian, Eulerian, and arbitrary Lagrangian-Eulerian (ALE) frames.…”

Structures Under Crash and Impact

“…Hamiltonian descriptions for simulations of viscous compressible fluid dynamics as well as hypervelocity impact processes can be found in Fahrenthold and Koo[124] and[124], respectively.2 Thermo-Mechanical Basics…”