Code verification and validation has become a hot issue. 'Verification' means to check if the implemented code does solve the equations it is intended to. 'Validation' compares numerical results with experimental data; it is thus also a measure of how well the governing equations represent the physics of the problem. Suitable validation data is often not available or has insufficient quality. In such cases, it might be acceptable to use high-fidelity numerical results for validation. For example, DNS (Direct Numerical Simulation) results are often used for comparison with LES (Large Eddy Simulation) or RANS (Reynolds-averaged Navier-Stokes) results.
In this talk, similar benchmark results will be provided for molecular-level simulations. For dilute and rarefied flows, the Boltzmann equation (from which the Euler and Navier-Stokes equations follow from a zero- & first-order expansion in Knudsen number, respectively) is the applicable governing equation. Efficient solution algorithms for it exist such as DSMC (Direct Simulation Monte Carlo). For dense rarefied fluids, however, no efficient, usable, physics-based theoretical or numerical treatment exists to date. This is mostly due to correlated and multi-particle collisions, which are neglected in the Boltzmann equation. Various approaches will be discussed in the seminar.
MD (Molecular Dynamics), where the motion of individual molecules is simulated using Newton's equations of motion is the last resort. The results of large-scale MD simulations of the shock structure in dense argon and nitrogen will be presented. The level of detail goes beyond bulk quantities such as density, temperature and macroscopic flow velocity. Histograms, higher statistical moments,radial distribution functions, collision operators, etc. are available across the shock wave. This allows a detailed comparison with alternative, more efficient techniques and makes it possible to track down the source of modeling errors. The relationship between the microscopic state of the system (molecular positions and velocity vectors) and macroscopic variables is introduced.
Also presented are the unsteady cases of shock wave formation by an impulsively accelerated piston, shock wave reflection from a solid wall, and shock wave reflection from a plane of (statistical) symmetry.
