Residual Carleman lift for nonlinear lattice Boltzmann simulations
Abstract
Low-order Carleman embeddings replace nonlinear dynamics by a larger linear system, but truncation errors can accumulate even when the underlying nonlinear model is accurately approximated by a quadratic equation. We construct a residual Carleman lift (RC2) of lattice Boltzmann dynamics in which an independently evolved spectral background supplies the coefficients and forcing of a second-order residual lift. In a double-shear-layer test, conventional fixed-rest Carleman reaches 87.3% final error, whereas prepared RC2 achieves 0.136% through vortex roll-up, without restarting the lift or using fine-reference feedback. The results demonstrate control of the finite-time accuracy of a fixed-order linear embedding through nonlinear preparation.
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BibTeX
@misc{karlin2026residual,
title = {{Residual Carleman lift for nonlinear lattice Boltzmann simulations}},
author = {Ilya Karlin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24041},
eprint = {2610.24041},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24041},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Residual Carleman lift for nonlinear lattice Boltzmann simulations
AU - Ilya Karlin
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24041
UR - https://arxiv.org/abs/2610.24041
AB - Low-order Carleman embeddings replace nonlinear dynamics by a larger linear system, but truncation errors can accumulate even when the underlying nonlinear model is accurately approximated by a quadratic equation. We construct a residual Carleman lift (RC2) of lattice Boltzmann dynamics in which an independently evolved spectral background supplies the coefficients and forcing of a second-order residual lift. In a double-shear-layer test, conventional fixed-rest Carleman reaches 87.3% final error, whereas prepared RC2 achieves 0.136% through vortex roll-up, without restarting the lift or using fine-reference feedback. The results demonstrate control of the finite-time accuracy of a fixed-order linear embedding through nonlinear preparation.
ER -