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Vlasov-Ampère equation (two stream instability): time evolution of the electric energy in semi-log scale (top left) and of the deviation of the total energy (top right), snapshot of f (t = 0) (bottom left) and snapshot of f (t = 300) (bottom right). Lawson-DG RK(3,3) and P 2 (∆t = 0.1, N x = 31(P 2 ), N v = 121).
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In this work, an exponential Discontinuous Galerkin (DG) method is proposed to solve numerically Vlasov type equations. The DG method is used for space discretization which is combined exponential Lawson Runge-Kutta method for time discretization to get high order accuracy in time and space. In addition to get high order accuracy in time, the use o...
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... which the same physical and numerical parameters as previously are kept except the final time which is T = 300. In Figures 2, we plot the time evolution of the electric energy in semi-log scale (and the corresponding instability rate in red) and the deviation of the total energy. For this test, a linear instability is first observed (up to t ≈ 30) during which a vortex in phase space is created (see 2), and it is followed by a nonlinear phase. ...
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