Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); University of Tennessee, Knoxville, TN (United States)
The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $$f$$ = $$\mathscr{E}$$[$$ρ_f$$] + g, where $$\mathscr{E}$$ is a local equilibrium distribution, depending on the macroscopic moments $$ρ_f$$ = $$∫_{\mathbb{R}}$$ $efdv$ = $$\langle$$$$ef$$$$\rangle$$$$_{\mathbb{R}}$$, where e = (1, $$v$$, $$\frac{1}{2}$$ $v^2$)T, and $$g$$, the microscopic distribution, is defined such that $$\langle$$$$eg$$$$\rangle$$$$_{\mathbb{R}}$$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $$ρ_f$$ and $$g$$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $$\langle$$$$eg$$$$\rangle$$$$_{\mathbb{R}}$$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $$f$$.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC05-00OR22725
- OSTI ID:
- 2538513
- Alternate ID(s):
- OSTI ID: 1962905
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 462; ISSN 0021-9991
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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