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arXiv · 2610.24041

Residual Carleman lift for nonlinear lattice Boltzmann simulations

Ilya Karlin
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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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Ilya Karlin. 2026-10-16. Residual Carleman lift for nonlinear lattice Boltzmann simulations. https://arxiv.org/abs/2610.24041

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