Solar energy paper index
A Local Macroscopic Conservative Low-Rank Discontinuous Galerkin Method for the Vlasov-Poisson Equation with Dougherty-Fokker-Planck Collisions
One-line summary
A solar energy research paper on A Local Macroscopic Conservative Low-Rank Discontinuous Galerkin Method for the Vlasov-Poisson Equation with Dougherty-Fokker-Planck Collisions.
Engineering notes
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Chinese explanation / 中文解读
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Original abstract
In this paper, we construct a low-rank, structure preserving discontinuous Galerkin (DG) method to simulate the Vlasov-Poisson (VP) system coupled with the Dougherty Fokker-Planck (DFP) collision operator. When Coulomb collisions occur in dense or weakly-collisional plasmas, electrons get pushed to a low-rank steady state. In many cases, the plasma arrives to this steady state quickly, meaning that for most of the run-time, the plasma consists mainly of numerical low-rank structures. Our new low-rank scheme is constructed to exploit these numerical low-rank structures to greatly reduce the needed storage complexity of simulations for the VP-DFP system. It is constructed as an extension of the previously established Local Macroscopic Conservative (LoMaC) method by incorporating Coulomb collisions into the system. The LoMaC property ensures local conservation of macroscopic mass, momentum, and energy at the discrete level. Details of the new method are discussed in this paper. Numerical experiments are performed to show the efficacy of the method.
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