Lagrangian computer code

The computational code used in solving the hydrodynamic equation is developed based on the CFDLIB, a finite-volume hydro-code using a common data structure and a common numerical method (Kashiwa et al., 1994). An explicit time-marching, cell-centered Implicit Continuous-fluid Eulerian (ICE) numerical technique is employed to solve the governing equations (Amsden and Harlow, 1968). The computation cycle is split to two distinct phases a Lagrangian phase and a remapping phase, in which the Arbitrary Lagrangian Eulerian (ALE) technique is applied to support the arbitrary mesh motion with fluid flow. 

Chapter 7 deviates from the rest of the book in that it describes computational methods for solving the transported PDF transport equation. Although Lagrangian PDF codes are... 

Whatever the approach (Eulerian or Lagrangian) for the prediction of particle dispersion, the turbulence field in which the particles disperse must be known. To test the dispersion model itself, this knowledge can be acquired through accurate experiments. However, for practical purposes, another option is to predict the turbulence properties in a first module of the computational codes. This provides the user with a complete computational package, but it is clear that any inaccuracy of the turbulence model and predictions will then be echoed to the dispersion predictions. 

W.F. Noh, CEL A Time-Dependent, Two-Space-Dimensional, Coupled Eulerian-Lagrangian Code, in Methods in Computational Physics, Volume 3 (edited by B. Alder, S. Fernbach and M. Rotenberg), Academic Press, New York, 1964. 

Relative to Lagrangian composition PDF codes that use an LES description of the flow, the turbulence models used in velocity, composition PDF codes have a limited range of applicability. However, the computational cost of the latter for reacting flows with detailed chemistry will be considerably lower. 

Recently various computational hydro codes have been adapted to the determination of underwater shock parameters. A Lagrangian code (with artificial viscosity) augmented by a sharp shock routine was used by Sternberg Hurwitz (Ref 12) to generate the curves shown in Figs 22,23 24... 

The finite difference numerical simulation was carried out by solving the Euler equations by the Lagrangian approach. The DANE code was used for computation. The air bubble radius was 1.0 mm and the shock overpressure was 1 kbar. Computational grids were, in the axlsymmetric Cartesian coordinates, 150 x 300 and one grid size was 0.025 mm. Figure 5 shows the sequential isobars. It is clearly seen that the peak pressure appear on the side where the shock first impinged the bubble, and the bubble deformation starts which indicates the microjet initiation. However, the rebound shock is so weak that, if compared with the incident shock, the wave front could not be resolved in this numerical scheme. 

Experiments have not yet confirmed this model. However, computer simulations have been done that illustrate the behavior. These use a version of the SALE code developed at Los Alamos for two-dimensional, time-dependent compressible flow in either Eulerian or Lagrangian coordinates. It incorporates artificial viscosity to accommodate shock fronts. The equation of state used is the Van der Waals equation as generalized by Callen to include the internal energy. ... 

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