Calculating geometric tortuosity of porous sound absorbers using the heat method

This work introduces the heat method as a powerful, efficient technique for evaluating tortuosity in porous acoustical materials. Tortuosity, a measure of how much pore-scale pathways deviate from straight lines, strongly affects sound absorption. We apply the heat method to two classes of unit-cell geometries (triply periodic minimal surfaces and cubic sphere packings), treating an entire inlet face as a heat source and simulating a single Euler time step of heat diffusion to generate a temperature gradient field. By solving Poisson’s equation on this field, we recover geodesic distances from the inlet to every point in the pore space and compute tortuosity directly. We then demonstrate the numerical convergence of these tortuosity estimates with respect to mesh resolution and time-step size and benchmark our results against traditional inverse-characterization and Laplace-equation approaches. This study shows that the heat method offers a clear, scalable path to quantifying tortuosity in complex acoustical materials.