Office of Technology Transfer – University of Michigan

A Computationally Efficient Graph Theoretical Based Numerical Method for Analyzing Conduction Problems on Arbitrary Geometries

Technology #7019

Heat conduction is an active research area for researchers dealing with problems related to a great amount of fields ranging from thermodynamics to reacting flow processes, combustion, unconfined groundwater flow, composite structures, wave propagation, and to microscale/nanoscale heat transport. Existing numerical solution methods applicable to these problems are dependent on geometry of the continuous domain and it can be difficult to implement them for heat transfer analysis in domains with complicated geometries. For instance, geometries of Finite Element Analysis elements that are used for discretization of Cartesian, polar and spherical domains are completely different. Therefore, element mismatching may exist when geometry of the problem is complicated. This may generate unreliable results if high accuracy is required. As a result, new geometry-independent and efficient methods to analyze problems in important fields such as heat transfer, solid mechanics and fluid mechanics are desirable in numerical analysis software market that is around $1B in size.

A Computationally Efficient Graph Theoretical Based Method for Analyzing Conduction Problems on Arbitrary Geometries

Researchers at University of Michigan have presented a methodology for analyzing computational problems with any complicated geometry and boundary conditions in mechanical engineering by direct use of graph theory. The proposed method is advantageous compared to available numerical approaches, like finite element, because it possess the least computation cost and does not face element mismatching for problems with complicated geometries. It can be applied to both steady-state and transient analysis in continuous domains with arbitrary geometries. The Graph Theory Based (GTB) method proposed provides the basis for a numerical method to analyze problems in mechanical engineering including heat transfer, solid mechanics, and fluid mechanics by direct application of graph theory.

Applications

  • Conduction problems in heat transfer, solid mechanics, fluid mechanics, distributed control

Advantages

  • Geometry independent
  • Least computation cost and does not face element mismatching for problems with complicated geometries
  • There is no constraint on the conditions imposed on the boundary nodes