Visualizing Lagrangian Heat Transport Paths and Density Structures in Unsteady Heat Transfer

Besm Osman; Andrei Jalba; Michel Speetjens; Anna Vilanova

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arXiv · 2607.00909

Visualizing Lagrangian Heat Transport Paths and Density Structures in Unsteady Heat Transfer

Besm Osman·Andrei Jalba·Michel Speetjens·Anna Vilanova

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Abstract

Convective heat transfer is traditionally visualized from a Eulerian perspective using scalar temperature fields, offering limited insight into the underlying transport mechanisms. A Lagrangian view, analogous to mass transport along fluid paths, can reveal coherent structures and transport routes invisible from a Eulerian view of temperature. However, heat transport is aperiodic and non-conservative, hampering the application of fluid mixing and transport visualization techniques, developed primarily for time-periodic, conservative transport. We present a particle-based visualization technique that addresses these challenges by advecting massless particles along a time-reparameterized spacetime formulation of thermal transport, accumulating path contributions to reveal coherent transport routes and finite-time attracting and repelling structures that conventional methods cannot show.

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Besm Osman, Andrei Jalba, Michel Speetjens, Anna Vilanova. 2026-07-01. Visualizing Lagrangian Heat Transport Paths and Density Structures in Unsteady Heat Transfer. https://arxiv.org/abs/2607.00909

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