Mathematical Models in Ocean Renewable Energy

Course ID:  M51015EQ

Credits: 3

Objective: 

1. Understand the basic control equations and boundary conditions related to mathematical models of Wave Energy Converters (WEC).  

2. Familiarize with the fundamentals of characteristic function expansion methods, least squares approximation methods, and boundary element methods for handling physical models of WEC.  

3. Develop MATLAB code to determine the efficiency and functionality of WEC.  

4. Analyze the impact of wave and WEC parameters on WEC efficiency.  

5. Conduct seminars on WEC mathematical models in groups or individually.

Course Prerequisites: 

Calculus, Engineering Mathematics

Outline:

In the recent decade, the use of wave energy converter (WEC) devices has gained popularity for the extraction of renewable wave energy because they are inexpensive and environmentally friendly. Generally, near- and off-shore WEC devices are designed based on the principles of oscillating water columns, wave overtopping, wave absorption, and submerged oscillations. However, the reliability and cost-effectiveness of these systems are highly sensitive to environmental conditions. Thus, for a clear understanding of wave energy distribution and attenuation, modelling and simulation of wave interaction with various WEC devices is a problem of fundamental interest. In the present course, the mathematical models of various WECs will be discussed. Different possible mathematical techniques such as eigenfunction expansion method, least-square approximation method, Boundary element method, etc. will be discussed to tackle the physical boundary value problem. We will develop and discuss MATLAB code to explore the efficiency and robust functionality of the WEC. The physical models will be created by students individually or in groups, with assistance from the instructor.

Teaching Method: 

I believe that teaching is an integral part of academic profession, and I have great passion for it. One of my fundamental career goals is to develop skills for teaching Mathematics at various academic levels ranging from basic undergraduate courses to advanced Ph.D. level research courses and seminars. As a teacher, I always prefer a student-friendly environment, so that students feel comfortable in approaching me and in asking questions any time without hesitation. That helps them to ask questions freely during lectures and think critically and deeply about the material. In order to introduce any new topic in mathematics, I try to come up with some motivation on the topic, at least whenever possible, and to explain why the topic is necessary and what their applications are in our day-to-day life. Teaching Plan: 

1. Giving lecture notes 

2. Course completion 

3. Assignments/Presentation 

4. Exams

Reference: 

1. Water Wave Mechanics for Engineers and Scientists, Robert George Dean, Robert A. Dalrymple, World Scientific, 1991. Transform methods, Dean G Duffy. 

2. Integral transform and their applications, Lokenath Debnath, Dambaru Bhatta, CRC Press, 2007 

3. Mathematical techniques for wave interaction with flexible structures, Trilochan Sahoo. CRC Press, 2012. 

4. D.V. Evans and R. Porter, Hydrodynamic characteristics of an oscillating water column device, Applied Ocean Research, Vol-ume 17, Issue 3, Pages 155-164 (1995).