Parallel kinetic scheme for transport equations in complex toroidal geometry. (English) Zbl 1508.82048
A new numerical method (based on a kinetic formulation resembling the Lattice-Boltzmann approach) for solving nonhomogeneous conservative transport equations in toroidal geometries (as is in tokamaks) is proposed. This permits to handle unstructured meshes of the poloidal plane, and allow a parallelization. The algorithm has been tested in a few model problems including the diocotron case (the slipping stream plasma instability).
Reviewer: Piotr Biler (Wrocław)
MSC:
| 82D10 | Statistical mechanics of plasmas |
| 76M28 | Particle methods and lattice-gas methods |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
| 82D75 | Nuclear reactor theory; neutron transport |
| 82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
| 65Y05 | Parallel numerical computation |
| 65D30 | Numerical integration |
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35Q49 | Transport equations |
| 35Q82 | PDEs in connection with statistical mechanics |
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