document: Hybrid simulation of space plasmas : models with massless fluid representation of electrons . IV . Kelvin-Helmholtz instability For pt.III . see Prikl . Mat . Informatika , MAKS Press , no. 4 , p. 5-56 -LRB- 2000 -RRB- . This is a survey of the literature on hybrid simulation of the Kelvin-Helmholtz instability . We start with a brief review of the theory : the simplest model of the instability - a transition layer in the form of a tangential discontinuity ; compressibility of the medium ; finite size of the velocity shear region ; pressure anisotropy . We then describe the electromagnetic hybrid model -LRB- ions as particles and electrons as a massless fluid -RRB- and the main numerical schemes . We review the studies on two-dimensional and three-dimensional hybrid simulation of the process of particle mixing across the magnetopause shear layer driven by the onset of a Kelvin-Helmholtz instability . The article concludes with a survey of literature on hybrid simulation of the Kelvin-Helmholtz instability in finite-size objects : jets moving across the magnetic field in the middle of the field reversal layer ; interaction between a magnetized plasma flow and a cylindrical plasma source with zero own magnetic field
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