1. A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation.
- Author
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Einkemmer, Lukas and Joseph, Ilon
- Subjects
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VLASOV equation , *ALGORITHMS , *PHASE space , *CONSERVATIVES , *EQUATIONS , *HIGH-dimensional model representation - Abstract
• First dynamical low-rank algorithm that is mass, momentum, and energy conservative. • Can be combined with an explicit integrator that maintains conservation. • Conserves the underlying continuity equations in addition to the invariants. • Low-rank breaks the curse of dimensionality for high-dimensional kinetic equations. The primary challenge in solving kinetic equations, such as the Vlasov equation, is the high-dimensional phase space. In this context, dynamical low-rank approximations have emerged as a promising way to reduce the high computational cost imposed by such problems. However, a major disadvantage of this approach is that the physical structure of the underlying problem is not preserved. In this paper, we propose a dynamical low-rank algorithm that conserves mass, momentum, and energy as well as the corresponding continuity equations. We also show how this approach can be combined with a conservative time and space discretization. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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