Noise reduction via dual-grid charge averaging

Numerical heating in particle-in-cell simulations arises primarily from statistical noise during the deposition process, which has long been a critical bottleneck limiting long-term simulation accuracy. This work proposes a dual-grid scheme that enhances sampling accuracy by leveraging complementary spatial information from two staggered grids, thereby reducing statistical noise. Analytical derivations show that, through its distinctive deposition mechanism, the scheme effectively elevates bilinear interpolation to a higher-order formulation. Numerical experiments validate this conclusion: compared to quadratic interpolation, the proposed method achieves comparable noise suppression and mitigation of noise-driven heating, while exhibiting superior capability in controlling grid heating and preserving energy conservation in long-term simulations. Most importantly, phase-space diagnostics confirm that the scheme delivers the highest simulation accuracy among the tested methods. These results demonstrate that the proposed approach provides an effective pathway for advancing noise control in particle-in-cell simulations.