Research, Education, and More

CE5890: Multiphysics in Porous Materials

This is a "special topic" graduate-level course based on the instructor's research experience. This course touches upon the state-of-the-art multiphysics techniques in porous materials. It is possibly one of the few, or even the only one, that is being offerred on the topic in the world at this time. The course starts with a questionare to gather information regarding the backgrounds of the participants, based on which the following schedule and course materials are adjusted.

Course Description

This course introduces the fundamental theories and essential numerical skills for multiphysics in porous materials. Multiphysics is a rapidly developing area in engineering which provides connections between disciplines on the level of physical mechanisms and mathematical descriptions. This state-of-the-art technique has widespread applications in porous materials, from the safety and sustainability of infrastructure to environment and energy applications, due to the multiphase and multicomponent nature of the porous material. The course will offer necessary mathematical background (partial differential equations, tensor analysis, functional analysis, etc.), theoretical descriptions of typical problems (thermohydraulics, hydrodynamics, poroelasticity, etc.) and related numerical methods (finite difference, finite element, and finite volume). This is a new course offered at only a few universities all over the world for an interdisciplinary technique of rapidly increasing interest. The course will be homework and project based with one mid-term exam and a few mini-projects. The course contents will be adjusted based on the backgrounds of the attendees.

Instructor: Dr. Zhen Liu


Course Schedule

Duration:         Jan 12, 2015 - Apr 24, 2015 (Since spring 2015 and every spring thereafter)
Course Content:
Part 1 Mathematics: 1. Partial differential equations (1);  2. tensor analysis (2) functional analysis
Part 2 Monolithic Physics: 1. Heat Transfer (3); 2. Groudwater Movement (4); 3. Mechanical Problems (5)
Part 3 Multiphysics: 1. Thermomechanics (6); 2. Hydrodynamics (7); 3. Poromechanics (8)
Part 4 Numerical Methods: 1. FDM (9) 2. FVM (10) 3. FEM (11)
1. Jan 11 – 17, 2015 (Jan 12 No Class, Jan 16 Intro)
2. Jan 18 – 24, 2015 (Jan 19 MLK) (1, HW1: Using Matlab PDE tools solve each)
3. Jan 25 – 31, 2015 (2, Quiz 1)
4. Feb 1 – 7, 2015 (3, HW2: Getting familiar with FlexPDE)
5. Feb 8 – 14, 2015 (4, HW3: Solving a given linear problem using FlexPDE)
6. Feb 15 – 21, 2015 (5, HW4: Solving a real non-linear problem using FlexPDE)
7. Feb 22 – 28, 2015 (5)
8. Mar 1 – 7, 2015 (6, Project 1 Begins: Identify and a multiphysical problem and describe it mathematically)
9. Mar 8 – 14, 2015 (Spring Break)
10. Mar 15 – 21, 2015 (7)
11. Mar 22 – 28, 2015 (8, Project 1 Ends)
12. Mar 29 – Apr 4, 2015 (9, Project 2 Begins: Solve the problem in Project 1)
13. Apr 5 – 11, 2015 (10)
14. Apr 12 – 18, 2015 (11)
15. Apr 19 – 25, 2015 (12, Project 3: Deliver results from Projects 1&2)


Course Work Showcase

The students have four labs and two projects, which generated some nice results. Typical theories and algorithems contained in the course schedule were implemented with computer programs. The two projects involved reproducing some results from a journal paper and a free-style multiphysics simulation targeting at a final report at a conference paper standard, respectively. Updates will be offered later to show some interesting results with the students' permission.

Diffusohydrodynamics: 2-D Plume Tracking in a Designed Water Body

Hydroelasticity: Research about the Hydro-Mechanical Coupling Effect on the Process of Rock Failure

Electroosmosis: Feasibility Study of Using External Electric Field to Reduce Lighting Hazards

Thermohydraulics: Strongly Coupled Heat and Moisture Transfer in Soils

Poroelasticity: Implementation of Biot’s Model in OpenFoam

Cryothermohydraulics: Heat Transfer and Water Migration in Saturated Freezing Soils


Course Materials

A textbook is under development based on the instructor's notes and all the computer code and implementation procedures. The materials will be shared once ready.