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We develop a conservative phase-space grid-adaptivity strategy for theVlasov-Fokker-Planck equation in a planar geometry. The velocity-space grid isnormalized to the thermal speed and shifted by the bulk-fluid velocity. Theconfiguration-space grid is moved according to amesh-motion-partial-differential equation (MMPDE), which equidistributes amonitor function that is inversely proportional to the gradient-length scalesof the macroscopic plasma quantities. The grid adaptation ensures discreteconservation of the collisional invariants (mass, momentum, and energy). Theconservative grid-adaptivity strategy provides an efficient scheme whichresolves important physical structures in the phase-space while controlling thecomputational complexity at all times. We demonstrate the favorable features ofthe proposed algorithm through a set of test cases of increasing complexity.

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