1:00 pm Friday, April 14, 2017
Math/ICES Center of Numerical Analysis Seminar : A Multiscale, Conservative, Implicit 1D-2V Multispecies Vlasov-Fokker-Planck Solver for ICF Capsule Implosion Simulations by Luis Chacon (Los Alamos National Laboratory) in POB 6.304
Plasma collisionality conditions during the implosion of an ICF capsule vary widely. Early in the implosion process, the plasma is cold and very collisional. Later in the implosion, however, the plasma becomes very hot, and the collisional mean free path becomes a large fraction of the system size. In this regime, kinetic phenomena may become important, and a fully kinetic treatment is needed to assess their impact on compression and yield in ICF capsules. Modeling such kinetic behaviors at any level of fidelity, however, demands a quantum leap in algorithmic complexity from standard radiation-hydrodynamics models currently in use. Kinetic physics in semi-collisional plasmas is governed by the multispecies Vlasov-Fokker-Planck equation, which is a high-dimensional (3D+3V+time), multiscale set of equations supporting very disparate time and length scales. The Fokker-Planck collision operator is nonlinear and nonlocal, and features strict conservation properties in the continuum that must be numerically enforced for long-term accuracy. Even in reduced dimensionality (1D-2V, spherically symmetric), a naive numerical treatment of this set of equations for ICF simulation is impractical, demanding circa 10^10 time steps and 10^12 degrees of freedom, which are way beyond exascale computing. In this talk, we present a fully conservative (mass, momentum, and energy), fully implicit multispecies Vlasov-Rosenbluth-Fokker-Planck solver in 1D-2V. The approach achieves exact numerical conservation by nonlinearly enforcing the collision operator symmetries, and by enslaving numerical truncation errors [1]. Positivity is enforced by taking advantage of the advection-diffusion structure of the Fokker-Planck collision operator [1,2]. The approach features an adaptive scheme in velocity space that optimally resolves the distribution function locally, thus substantially decreasing the velocity space resolution requirements regardless of temperature disparity and variations [2]. Solver-wise, the code relies on optimal multigrid-preconditioned Jacobian-free Newton-Krylov strategies [3], which we generalize here to deal with multiple ion species. Our proposed algorithm has been specifically designed to deal with spatio-temporal temperature disparities such as those present in ICF capsules, and as a result it is able to simulate ICF implosions at a fraction of the cost of the naive estimates (10^5 time steps and 10^6 degrees of freedom), well within current computational capabilities. The resulting code, iFP, has been thoroughly verified in planar and spherical geometries, and we have begun exercising it for the simulation of kinetic interfaces [4] and spherical ICF implosions [5]. In this talk, we will provide a number of numerical examples demonstrating the accuracy and efficiency of the scheme, and we will provide first insights into the importance of kinetic ion-species segregation effects in the reactivity of ICF capsules. [1] W. T. Taitano, L. Chacón, A. N. Simakov, K. Molvig, J. Comput. Phys., 297, 257-380 (2015) [2] W. T. Taitano, L. Chacón, A. N. Simakov, J. Comput. Phys., 318, 391–420 (2016) [3] L. Chacón, D. C. Barnes, D. A. Knoll, G. H. Miley, J. Comput. Phys., 157, 654-682 (2000). [4] L. Yin, B. J. Albright, W. Taitano, E. L. Vold, L. Chacón, and A. Simakov, Phys. Plasmas, 23, 112302 (2016) (2016) [5] W. Taitano, L. Chacón, A. N. Simakov, “An adaptive, mass, momentum, and energy conserving, 1D-2V mulit-ion Vlasov-Rosenbluth-Fokker-Planck solver with fluid electrons,” In preparation.
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