We describe a novel way based on lattice-Boltzmann representation for realizing hydrodynamic boundary conditions at a solid surface. It is shown that using this approach the resulting physics properties are independent of the position and the orientation of the surface with respect to the lattice mesh. The fluxes of mass, energy as well as both normal and tangential momenta can be accurately controlled to correspond to various fluid dynamics situations.

Please cite this article in press as: W.T. Taitano et al., A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth-Fokker-Planck equation, J. Comput. Phys. (2015), http://dx. AbstractIn this study, we demonstrate a fully implicit algorithm for the multi-species, multidimensional RosenbluthFokker-Planck equation which is exactly mass-, momentum-, and energy-conserving, and which preserves positivity. Unlike most earlier studies, we base our development on the Rosenbluth (rather than Landau) form of the Fokker-Planck collision operator, which reduces complexity while allowing for an optimal fully implicit treatment. Our discrete conservation strategy employs nonlinear constraints that force the continuum symmetries of the collision operator to be satisfied upon discretization. We converge the resulting nonlinear system iteratively using Jacobian-free Newton-Krylov methods, effectively preconditioned with multigrid methods for efficiency. Single-and multi-species numerical examples demonstrate the advertised accuracy properties of the scheme, and the superior algorithmic performance of our approach. In particular, the discretization approach is numerically shown to be second-order accurate in time and velocity space and and to exhibit manifestly postive entropy production. That is, H-theorem behavior is indicated for all the examples we have tested. The solution approach is demonstrated to scale optimally with respect to grid refinement (with CPU time growing linearly with the number of mesh points), and timestep (showing very weak dependence of CPU time with time-step size). As a result, the proposed algorithm delivers several orders-of-magnitude speedup vs. explicit algorithms.

We present an outline description of some fundamental theoretical properties in the Digital Physics lattice-gas algorithm.

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Zonal flow helps reduce and control the level of ion temperature gradient turbulence in a tokamak. The collisional damping of zonal flow has been estimated by Hinton and Rosenbluth (HR) in the large radial wavelength limit. Their calculation shows that the damping of zonal flow is closely related to the frequency response of neoclassical polarization of the plasma. Based on a variational principle, HR calculated the neoclassical polarization in the low and high collisionality limits. A new approach, based on an eigenfunction expansion of the collision operator, is employed to evaluate the neoclassical polarization and the zonal flow residual for arbitrary collisionality. An analytical expression for the temporal behavior of the zonal flow is also given showing that the damping rate tends to be somewhat slower than previously thought. These results are expected to be useful extensions of the original HR collisional work that can provide an effective benchmark for numerical codes for all regimes of collisionality.

Knudsen layer losses of tail fuel ions can significantly reduce the fusion reactivity of multi-keV DT in capsules with small fuel ρr; sizable yield reduction can result for small inertial confinement fusion (ICF) capsules. This effect is most pronounced when the distance from a burning DT gas region to a nonreacting or cold wall is comparable to the mean free path of reacting fuel ions. A simplified asymptotic theory of Knudsen layer tail depletion is presented and a nonlocal reduced fusion reactivity model is obtained. Application of the model in simulations of ICF capsule implosion experiments gives calculated yields and ion temperatures that are in much closer agreement with observations than are the results of "nominal" or mixed simulations omitting the model.

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