# Two models for the computation of laminar flames in dust clouds

## TL;DR

This paper compares two models for simulating premixed dust cloud combustion, introducing a phase-field approach for the second model and developing a finite volume scheme to ensure physical bounds.

## Contribution

It presents a novel phase-field-like model for dust flame simulation and a finite volume scheme that maintains physical bounds, assessing their consistency.

## Key findings

- Both models are consistent with physical bounds.
- The phase-field model effectively tracks flame location.
- Finite volume scheme ensures numerical stability.

## Abstract

We address two models for the simulation of dust clouds premixed combustion: the first one consists in usual balance equations, to derive the second one, we suppose that the solution takes the form of a travelling combustion wave and track the location of the flame brush by a phase-field-like technique. We build a finite volume fractional step scheme for both models, which respects the natural physical bounds of the unknowns. Then we assess the consistency of both formulations.