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The nature of ICF target explosions and plasma transport channels create steep gradients in many physical quantities. Lagrangian grid schemes automatically resolve only density gradients, yet because the density is low where other quantities (i.e., temperature) peak, the mesh in this region will be elongated. This effect will tend to smear whatever gradient occurs there, thus causing a lack of resolution needed to follow such non-linear problems. The explicit adaptation scheme based on the equidistribution principle is easily applied to solve hyperbolic conservation laws in one dimension. The first-order upwind finite difference scheme has survived Sod's shock tube problem with the help of the grid adaptation. A local grid refinement factor of was found compared to a fixed mesh distribution. Finer mesh spacing would require smaller timesteps and thus a higher cost. When compared to a lagrangian radiation diffusion calculation of plasma channels, our method brings finer grid refinement (a factor of 2) and more accurate description of the radiative transfer in the channel. Applications to z-pinch plasma channels made an impact on the channel designs by showing the feasibility of high atomic number (argon, nitrogen) gases for the cavity. The applications to ICF target explosions are also expected to utilize the new model in the near future. The issue of using a higher-order accurate method should be considered next. Improvements in plasma modelling include separate electron and ion temperatures and multimaterials. The ion and electron temperature coupling time constant, which depends on the specific heat ratio, may very well be longer than some characteristic timescales in the system. In conclusion, the use of an explicit adaptive grid system has proven to be quite useful and multigradient problems are the best candidates to utilize it.

Osman Yasar
Thu Mar 21 14:48:13 EST 1996