Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Zhongquan Zheng / A nano-material filter is an efficient device for improving indoor environmental quality (e.g. smoke reduction, air purification in buildings). Studying the effectiveness of nano-materials used in the device by computer simulation is challenging because very different size scales are involved. Therefore, numerical methods have to be developed to accommodate varying magnitudes of scales. In the current study, the simulation has been divided into three scales: macro-, micro- and nano-scale. The numerical schemes at each scale are targeted at a particular scale; however, the relationship of the general transport phenomena, physical mechanisms and properties among different scales are uniquely linked at the same time. The objective of the macro-scale simulation was to design and study a gas filter constructed with nano-material pellets. The filter was considered a packed-bed tube filled with manufactured nano-material pellets. Commercial computational fluid dynamics (CFD) packages were used along with the embedded programming macros. In the filtration process, we focused on the flow and species transport phenomena through the porous substrate. The mathematical/numerical models were built and tested based on the physical models used in the experimental setups for different materials that were tested. The results from the numerical models were validated and compared well to experimental data obtained from the pressure drop measurements and the adsorption (breakthrough) tests. In the micro-scale simulation, a modified immersed-boundary method (IBM) with the Zwikker-Kosten (ZK) porous model and the high-order schemes was validated and applied to simulate a representative porous unit that represented a periodic array of solid/porous cylinders. In the periodic unit, the solid cylinder case was used to validate the high-order schemes by comparing it to the results obtained from the commercial CFD software. The relationship between the pressure gradient and the porosity (Blake-Kozeny equation) was determined from this level and fed back to the macro-scale simulation, which provided a link between the two scales. In the porous cylinder case, both flow field and species transport were investigated with a porous model similar to the one used in the macro-scale. The species concentration change was calculated and found to be nonlinearly related to the adsorption coefficient. In the nano-scale simulation, a molecular dynamics (MD) simulation and a coupled molecular-continuum scheme were applied to solve the momentum and the mass transport problems at the molecular level at which the traditional continuum theory is no longer applicable. Both schemes were verified from the surface slip behavior study compared to the literature. The scale and shear effects in the Coutte flow were investigated, showing that in the micro-scale and macro-scale, the slip behavior could be neglected since it was only important in much smaller scales. The same hybrid scheme was then applied to a diffusion model with nano-pores constructed in the solid substrate. The adsorptions between various gases and the carbon substrate were simulated. The mass fluxes cross the fluid/solid interfaces were counted and both self-diffusivity and transport diffusivity were estimated and compared to their respective values found in the literature. The transport properties are closely related to the species transport (Fick’s law) in the macroscopic simulations. Linear concentration profiles in the channel were obtained based on those transport properties for various gases going through different sizes of nano-pores, which, as a connection to the continuum model, were to be used as boundary conditions in the continuum simulation.