ME595M: Computational Methods for Nanoscale Thermal Transport

Course Syllabus

Profs. Jayathi Murthy and Tim Fisher*

Course description: This one-credit course will provide an introductory understanding of numerical methods for solving phonon transport problems in spatially confined materials. Methods to be studied include: the atomistic Green’s function (AGF) method, the finite volume (FV) method, and the Monte Carlo (MC) method.

Pre-requisites: ME 597F or permission of instructor

Textbook: None (course notes only)

Computer programming: Experience with Matlab’s matrix tools is helpful. Alternatively, other scientific computing languages can be used.

Course Dates/Times/Location: normally MTWTh, May 14 to June 7, 8:40 to 9:40 AM, Room ME118

Course grading: The overall course grade will be based entirely on homework.

Tentative Lecture schedule:

Week 1	Assignments (all homework is due the following lecture unless otherwise noted)
May 14 Lattice dynamics (TSF) - 1D atomic chain - Lattice glossary	Reading (Sections 1-5)
May 15 Statistical mechanics (TSF) - Statistical ensembles - Definition of temperature	Reading, Homework 1, Demo Code
May 16 No lecture
May 17 No lecture
Week 2
May 21 AGF introduction (TSF) - General problem description - Harmonic matrix - Green’s functions	Homework 2 (due May 23)
May 22 AGF energy transport (TSF) - Energy flux and transmission - Introduction to the nanoHUB atomic chain tool
May 23 AGF DOS and multi-dimensionality (TSF) - 1D chain results - Density of states - Introduction to multi-dimensional systems	Homework 3
May 24 No lecture
May 25 Introduction to BTE (JYM) - General derivation - General form of scattering term - U, N processes, impurity and boundary scattering - Relaxation time form and single mode relaxation time - Thick limit of the BTE	BTE Homework (due June 4) BTE code How-to-run instructions Other files
Week 3
May 28 No lecture
May 29 Gray BTE (JYM) - Derivation of gray energy form - Thick limit of gray BTE - Boundary and initial conditions – diffuse, specular, mixed, Fourier+BTE interfaces
May 30 Introduction to finite volume method (JYM) - Space and angle integration - Upwinding schemes - Time stepping - Linear solvers - Accuracy and convergence issues
May 31 Introduction to finite volume code (JYM) - Discuss FV code data structures and usage - Assign problem and discuss
June 1 Extensions and modifications to FV (JYM) - Issues with sequential solutions and coupling - Accuracy issues – false scattering, false diffusion - Point-coupled techniques - Ray-tracing techniques
Week 4
June 4 Higher Order BTE Models (JYM) - Semi-gray models – limiting behavior and discussion - Non-gray models - Full BTE simulation
June 5 Monte Carlo method (TSF) - Introduction - Equation of motion - Scattering	Homework (see lecture notes): Due June 7
June 6 Monte Carlo (TSF) - Statistical sampling - Relation to the BTE
June 7 Course wrap-up (TSF and JYM)

*TSF gratefully acknowledges partial support of this work by the Chemical and Transport Systems division of NSF through its CAREER program