Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
High-order ENO schemes applied to two- and three-dimensional compressible flow
Applied Numerical Mathematics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Numerical study on Landau damping
Physica D
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Strong Stability Preserving Two-step Runge-Kutta Methods
SIAM Journal on Numerical Analysis
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We present a numerical study aimed at assessing the validity of certain approximations, chiefly the fluid and quasi-neutral ones, generally used in the theoretical and computational study of fusion plasmas. The impact of numerical artifacts has been minimised by using the very precise weighted essentially non-oscillatory (WENO) method, which can be applied to both kinetic and fluid simulations. This is the first application of WENO schemes to Eulerian simulations of Vlasov plasmas. The fluid modelling of plasmas appears adequate even when collisions are negligible, provided certain relationships hold between the characteristic speed of the phenomenon under consideration and the thermal velocities of the species which make up the plasma. The breakdown of this behaviour is probably caused by non-linear Landau damping; it appears linked with filamentation, which suggests that the magnitude of the departure from Maxwellian equilibrium may not be the one and only measurement of non-fluid behaviour. As for quasi-neutrality, our study suggests that the generally accepted criteria should be used with great care, according to the degree of neutrality expected.