An Eulerian Vlasov-Fokker–Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules

Taitano, William; Keenan, Brett; Chacon, Luis; Simakov, Andrei N.; Anderson, Steven Edward; Hammer, Hans Ruediger; Albright, Brian James

doi:10.1016/j.cpc.2021.107861

Title: An Eulerian Vlasov-Fokker–Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules

Journal Article · Thu Feb 04 00:00:00 EST 2021 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2021.107861· OSTI ID:1868221

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Here, we present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov–Fokker–Planck (VFP) simulation of inertial confinement fusion (ICF) capsule implosions. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma’s evolving temperature and drift velocity. The mesh motion is dealt with by transforming the underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: (1) an elastic moving wall boundary; (2) a time-dependent Maxwellian Dirichlet boundary; and (3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems — the first-ever reported using a Vlasov–Fokker–Planck model.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1868221

Alternate ID(s):: OSTI ID: 1815200

Report Number(s):: LA-UR-20-26872; TRN: US2306245

Journal Information:: Computer Physics Communications, Vol. 263; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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