SUMMARY
Effcient, accurate numerical simulation of coupled heat transfer and fluid dynamics systems continues to be a challenge. Direct numerical simulation (DNS) packages like FLUENT exist and are suffcient for design and predicting ow in a static system, but in larger systems where input parameters can change rapidly, the cost of DNS increases prohibitively. Major obstacles include handling the scales of the system accurately - some applications span multiple orders of magnitude in both the spatial and temporal dimensions, makingan accurate simulation very costly. There is a need for a simulation method that returns accurate results of multi-scale systems in real time. To address these challenges, the Multi-Resolution Discontinuous Galerkin (MRDG) method has been shown to have advantages over other reduced order methods. Using multi-wavelets as the local approximation space provides an inherently effcient method of data compression, while the unique features of the Discontinuous Galerkin method make it well suited to composition with wavelet theory. This research further exhibits the viability of the MRDG as a new approach to effcient, accurate thermal system simulations. The development and execution of the algorithm will be detailed, and several examples of the utility of the MRDG will be included. Comparison between the MRDG and the "vanilla" DG method will also be featured as justifcation of the advantages of the MRDG method.