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arXiv · 2605.12095

Leak localisation with a measure source convection-diffusion model

Thi Tam Dang·Tuomo Valkonen
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Abstract

We study the inverse problem of locating gas leaks from line-of-sight concentration measurements using a convection-diffusion model with the source term a Radon measure. By imposing sparsity-promoting regularisation on this measure, we recover point sources - identifying both their locations and intensities - rather than diffuse approximations. We jointly estimate the underlying physical convection (wind) and diffusion parameters. Our main theoretical contribution is the stability analysis of the convection-diffusion equation with respect to its parameters: the measure, and the convection and diffusion fields. Numerically, we employ a semi-grid-free optimisation approach for reconstructing the source measure. Our experiments demonstrate accurate localisation, highlighting the potential of the method for practical gas emission detection.

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Thi Tam Dang, Tuomo Valkonen. 2026-05-12. Leak localisation with a measure source convection-diffusion model. https://arxiv.org/abs/2605.12095

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