Abstract:We develop an unstaggered, potential-based particle-in-cell method for the nonrelativistic Vlasov-Maxwell system in the Lorenz gauge. The field update is written as a Crank-Nicolson discretization of first-order wave systems for the scalar potential, the vector potential, and their time derivatives. The charge density is not deposited directly; instead, it is advanced from the discrete continuity equation using the current deposited from the particles. This opens up algorithmic flexibility with a range of innovation, including unstaggered mesh layouts that preserve the Lorenz gauge and Gauss's law at the discrete level. In the potential formulation, this source ordering also permits preservation of the Lorenz gauge and Gauss's law at the discrete level. To extend the paradigm to an energy-conserving formulation, we introduce a consistent orbit-averaged scatter, gather, and particle push. For energy consistency, the update of the canonical momentum is modified by replacing the pointwise midpoint derivative of the vector potential with an orbit-averaged discrete gradient of the mesh-interpolated vector potential consistent with the orbit-average maps. This construction satisfies an exact finite-difference chain rule along each particle orbit. As a result, the particle work equals the mesh work appearing in the Crank-Nicolson field-energy balance, yielding exact total-energy conservation up to nonlinear solver tolerance and roundoff. We demonstrate exact energy conservation of the method in 3D on the cold two-stream instability.
From: Sining Gong [view email]
[v1]
Sat, 13 Jun 2026 00:33:53 UTC (349 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。