Abstract:

In several problems related to the propagation of shock waves it was found that at the beginning the shock wave propagates in a resting cold material, and after reaching the axis (or center) of symmetry the shock wave is reflected and flows in the previously heated plasma. The shock wave can be thought as a mathematical surface propagating at the speed of the shock. If both pressure and internal energy of the rest material are negligible in comparison with the pressure and internal energy, respectively, of the plasma behind the shock, then the speed of the shock relative to the plasma behind it depends only on the plasma parameters. Using a mixed Eulerian-Lagrangian method, a code that runs as fast as a standard code with artificial viscosity has been developed. If the thickness of the reflected shock wave is not small in comparison with other physically relevant dimensions of the system, then neither the approximation discussed above nor the artificial viscosity can be used. It has been shown that it is possible to estimate the viscosity of a plasma in the transition zone produced by collision of two plasmas having the same ion temperature. This method was used for calculating cylindrical and spherical implosions, and no numerical instabilities or oscillations were observed.