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A review is made of the mathematical problem of predicting the heat and mass transfer processes for the environmental/thermal control and life support systems of the International Space Station (ISS). These systems include, but are not limited to, pumps, flow control orifices, vent valves, heat exchangers, condensing heat exchangers, tubes, ducts, inter-module ventilation systems, contaminant gas removal systems, atmosphere revitalization and supply as well as temperature, total pressure, and humidity control. Existing techniques used for the Environmental Control and Life Support Systems (ECLSS) Resource Utilization Planning Modeling (RUPSM) are discussed. It is argued that the thermal systems networking approach required much smaller time steps and intensive matrix operations due to the explicit method used in the approach and that the continuum approach employed in the paper utilizing computational fluid dynamics techniques provides a high level of fidelity and quick turnarounds.