Employing the Moving Least‐Squares Aided Finite Element Method to Study Heat Transfer Phenomenon in Closed‐Cell Polymeric Foam

ABSTRACT A new technique based on the finite element method (FEM) is introduced that couples the fluid flow and heat transfer processes within a gas‐filled porous medium, such as closed‐cell polymeric foam. For such an analysis the classic FEM relies on a mesh fitting the solid–fluid boundaries; however, the new approach requires a fixed background mesh independent of the foam morphology. We term the method the moving least‐squares aided finite element method (MLS‐FEM), as it employs moving least‐squares interpolants to enhance the pressure, velocity, and temperature shape functions in the active elements or the elements intersected by the solid–fluid interface. The accuracy of the MLS‐FEM for a single‐void foam patch is assessed against a classical boundary‐fitted FEM, showing that the field variables, such as velocity components and temperature, are in close agreement across different mesh resolutions. The comparison is then extended to multivoid patches, with similarly close agreement between the two approaches. Notably, the MLS‐FEM reuses the same background mesh regardless of geometry, whereas the classical FEM requires remeshing whenever the foam morphology changes.