Estimation of geometric tortuosity for bulk acoustic absorbers using the heat method

Geometric tortuosity-the ratio of arc length to the straight-line distance between its endpoints-is among the key parameters needed to predict a porous material's acoustic properties. Here, we adapt the heat method, commonly used for surface calculations, to measure tortuosity within the fluid volume of complex three-dimensional porous lattice unit cells. Our implementation in Python relies on the open-source scikit-fem library to handle finite element operations on a hexahedral mesh of the fluid domain. Adiabatic boundary conditions are applied at both the fluid-solid interfaces and the unit cell faces, allowing heat to flow from an inlet face through the fluid domain for a brief period. Poisson's equation is then solved using the resulting temperature gradient field. Tortuosity is evaluated at a discharge face opposite the inlet, and path-lines through the gradient field are visualized. A histogram and spatial map of tortuosity values on the discharge face is generated, revealing a strong dependence on local geometric features, including through-holes. Overall, results show that the heat method offers a viable computational alternative to estimating the tortuosity of porous acoustical materials.