Foams are ubiquitous low density materials used for a variety of applications including shock, thermal, and vibration isolation of electronic component, disposable containers, and energy production. Despite their many uses, foams are still not well understood at a fundamental level. Here we are trying to develop models of the foaming process, which include blowing by either physical blowing agents or chemical blowing agents. The dynamics of foam self-expansion are quite different from pressure driven flows in that the flow is driven by density changes as the foam transforms itself from a single phase incompressible material to a bubbly multiphase compressible one. We are developing homogenized, continuum-level models that seek to understand the dynamics of self-expansion based on a finite element discretization. For large-scale, parallel computation in complex 3D geometries we are developing reduced order foaming models that use an empirically developed time- and temperature-dependent density model to encapsulate the complexity of the true foaming processes while including the most relevant physics. This model is then coupled to a volume fraction dependent viscosity to determine the foam self-expansion as a function of time. We compare model results to experimental data in the same geometry, demonstrating the validity of our approach. A model such as this is useful for designing molds and determining areas for potential void formation. We are also developing more complex foaming models that include the complexity of chemical reactions, nucleation phenomena, and creaming, but are limited to 2D geometries.