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Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. (English) Zbl 1030.82011

Summary: A new scheme for solving the Vlasov equation using an unstructured mesh for the phase space is proposed. The algorithm is based on the semi-Lagrangian method which exploits the fact that the distribution function is constant along the characteristic curves. We use different local interpolation operators to reconstruct the distribution function \(f\), some of which need the knowledge of the gradient of \(f\). We can use limiter coefficients to maintain the positivity and the \(L^{\infty}\) bound of \(f\) and optimize these coefficients to ensure the conservation of the \(L^1\) norm, that is to say the mass by solving a linear programming problem. Several numerical results are presented in two and three (axisymmetric case) dimensional phase space. The local interpolation technique is well suited for parallel computation.

MSC:

82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
82D10 Statistical mechanics of plasmas
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
76M20 Finite difference methods applied to problems in fluid mechanics

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References:

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