Abstract Details
Abstracts
Author: Bradley A Shadwick
Requested Type: Consider for Invited
Submitted: 2023-03-23 19:15:27
Co-authors: Roland Hesse
Contact Info:
Univ of Nebraska - Lincoln
208 Jorgensen Hall
Lincoln, NEBRASKA 68588-0111
United States
Abstract Text:
An Eulerian finite-difference method for solving the Vlasov equation, coupled to either electrostatic or electromagnetic fields, is developed with a static, non-uniform momentum grid. The solver is unconditionally stable [1,2] and has excellent conservation properties. The momentum grid in constructed via a transformation from a uniform logical grid to the physical momentum grid. The computational cost of employing this transformation differs negligibly from the uniform case with the same number of grid points. A general grid parametrization is tested using classic instabilities and driven cases and is found to provide significant efficiencies over the uniform grid case. This technique allows for the distribution of computational resources based on the relative importance of kinetic activity in phase-space while preserving conserved properties. This method can be readily extended to multiple dimensions and is compatible with dynamically adapting the momentum grid. Obtaining correct conservation properties requires careful attention to how finite-difference approximations are performed; this can be best understood by appealing to the noncanonical Hamiltonian structure of this system.
References
[1] Carrie, M, and Shadwick, B A, "A Time-Implicit Numerical Method and Benchmarks for the Relativistic Vlasov–Ampere Equations," Phys. Plasmas 23, 012102 (2016).
[2] Carrie, M, and Shadwick, B A , "An Unconditionally Stable, Time-Implicit Algorithm for Solving the One-Dimensional Vlasov–Poisson System," J. Plasma Phys. 88, 905880201 (2022).
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