A volumetric sculpting based approach for modeling multi-scale domains
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This dissertation addresses the problem of creating computer simulations for multi-scale domains. These domains span a wide range of both spatial and temporal scales. Creating realistic simulations based on computer models for such domains requires very large memory overhead and computing resources. A framework for modeling such multi-scale domains is described here. The proposed approach creates an initial geometric scaffold (grid) for the domain. This scaffolding can be further (locally) refined to closely match the geometric features of the domain. Functions can be defined on this grid to model different physical parameters of interest. These piecewise linear functions are interpolated within a cell to provide uniform global C 0 functions over the complete domain. Of particular interest are the geometry and physics viii functions that are formulated over this scaffold, which enable geometric and computational modeling of the domain. Given a set of processes of interest on the domain, the next step focuses on creation of a computational model of the domain by defining another set of functions over the same scaffold. Finally, the physics model is numerically solved over the domain geometry in an attempt to simulate the physical process. To demonstrate that the approach works, a case study of the classical problem of heat conduction through porus media is presented. For this, high resolution geometric models for a powder bed in the Selective Laser Sintering (SLS) process are developed. This comprehensive multi-scale model is then validated with a simulation of the percolation process to study the effect of heat conduction through the media. The key phenomenon of interest is the manner in which the heat flows through the domain containing a given configuration of the composite. The main focus of this research is to provide a robust and comprehensive framework for creating realistic computational and geometric multi-scale models. These models are then interleaved to yield a comprehensive numerical simulation of the process.