A High Order Adaptive Semi-Lagrangian WENO Method for the Vlasov Equation

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This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The investigator and her colleagues consider a novel high order adaptive semi-Lagrangian approach for kinetic plasma simulations. The major challenge of kinetic simulations is the huge computational cost, from the high dimensionality (3-D in physical space and 3-D in phasespace) and from the spatial and temporal multi-scale features of the problem. To address these challenges, the proposed methodology consists of three advanced numerical techniques: 1) a conservative semi-Lagrangian method with high order weighted essentially non-oscillatory (WENO) reconstructions; 2) a high order Strang split spectral deferred correction method to bridge time scales of different species and integrate in time with high order accuracy; 3) mesh adaptivity by incorporating the Strang split Semi-Lagrangian WENO method into the framework of adaptive mesh refinement. As a result of high order accuracy and adaptivity in both space and time, the investigator and her collaborators hope to apply the algorithm in realistic plasma applications with affordable computational cost by using relatively coarse and dynamically adaptive mesh. The eventual goal is to enable large-scale parallel simulations in order to predict/confirm/explain the physical phenomenon observed in a broad range of applications.The investigator and her collaborators aim at developing robust and highly efficient numerical algorithms. The well-developed algorithm will have a direct impact in plasma applications, such as developing fusion energy, the modeling of magnetosphere, among many others. Besides, there is large room for further extensions and applications. The algorithm can be extended to solve the more general Boltzmann equation. It can served as a microscopic solver in a mix kinetic-hydrodynamic model via the heterogeneous multi-scale method. While designed for the plasma simulations, the proposed algorithm can be further extended to astrophysics applications, semi-conductor device simulations among many others. The broader impact comes from the multi-disciplinary nature of the proposed research. The proposed research will initiate and serve as a solid foundation for collaborative research work with applied mathematicians, plasma physicists and astrophysicists. The collaborative work will not only expedite the development of the research in both sides of collaborations, but also help training graduate students with a diverse background and multidisciplinary skills.