Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Civil Engineering

First Advisor

Hector Gutierrez

Second Advisor

Gerald J Micklow

Third Advisor

Rainer Meinke

Fourth Advisor

Francisco Yumiceva


Performing quench propagation simulations of full size superconducting coils is a challenging problem due to complex coil structures and internal arrangements of superconducting wires. In addition, superconducting wires and cables themselves constitute complex 3D arrangements comprised of superconductor, matrix, stabilizer, insulation and other materials. Modelling quenches in complete coils is therefore a complex multi-scale and multi-physics problem that is difficult to solve with conventional techniques like finite element or finite difference methods. Monte-Carlo methods have been successfully used to simulate various multi-scale and multi-physics problems, but to our knowledge have not been applied to quench propagation simulations. In the first chapter, the application of the Monte-Carlo method for quench propagation problems has been studied and first results are presented. A mesh free Monte-Carlo method has been used that lends easily to parallelization. A novel mesh-free Monte-Carlo method for two-dimensional transient heat conduction in composite media with temperature dependent thermal properties is presented in the second chapter. The proposed approach is based on expressing the solution of the transient conductive heat transfer equation, in domains with temperature-dependent material properties, as a combination of two solutions: Bessel functions and integrals of peripheral temperature. The proposed approach is used to solve transient conduction in composite layered materials with temperature dependent thermal diffusivity. Results are compared against others obtained using a conventional finite element approach. Experimental results for heat transfer in a non-homogeneous domain (composite layered material) are presented to demonstrate the performance of the proposed approach. A new solution for the three-dimensional transient heat conduction from a homogeneous medium to a non-homogeneous multi-layered composite material with temperature dependent thermal properties using a mesh-free Monte-Carlo method is proposed in chapter three. The novel contributions include a new algorithm to account for the impact of thermal diffusivities from source to sink in the calculation of the particles’ step length (particles are represented as bundles of energy emitted from each source), and a derivation of the three-dimensional peripheral integration to account for the influence of material properties around the sink on its temperature. Simulations developed using the proposed method are compared against both experimental measurements and results from a finite element simulation. Finally, in chapter four, a state-of-the-art method is established to undertake the immense and complex Multiphysics problems involving heat conduction, electrical current sharing and joule heating. The innovative improvement includes an algorithm that eliminates the requirement of particles scattering from conventional Monte-Carlo methods. This algorithm encapsulate a volume around each point that the solution for the point is affected by in corresponding time span. This volume consists of other points of geometry that can slightly move to reconcile along the path of energy transfer. The proposed method benefits from high parallelizability of Monte-Carlo method while its performance is escalated substantially by dispose of interpolation steps. The accuracy and simulation time of the method is examined and compared against Finite Element Method. The results are within strict margin of error and the speed up performance is promising.


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