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arXiv · 1903.05467

A conservative phase-space moving-grid strategy for a 1D-2V Vlasov-Fokker-Planck Equation

William Tsubasa Taitano·Luis Chacon·Andrei Simakov·Steven Anderson
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Abstract

We develop a conservative phase-space grid-adaptivity strategy for the Vlasov-Fokker-Planck equation in a planar geometry. The velocity-space grid is normalized to the thermal speed and shifted by the bulk-fluid velocity. The configuration-space grid is moved according to a mesh-motion-partial-differential equation (MMPDE), which equidistributes a monitor function that is inversely proportional to the gradient-length scales of the macroscopic plasma quantities. The grid adaptation ensures discrete conservation of the collisional invariants (mass, momentum, and energy). The conservative grid-adaptivity strategy provides an efficient scheme which resolves important physical structures in the phase-space while controlling the computational complexity at all times. We demonstrate the favorable features of the proposed algorithm through a set of test cases of increasing complexity.

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William Tsubasa Taitano, Luis Chacon, Andrei Simakov, Steven Anderson. 2019-03-11. A conservative phase-space moving-grid strategy for a 1D-2V Vlasov-Fokker-Planck Equation. https://arxiv.org/abs/1903.05467

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