Module MATH3101: CONTINUUM MECHANICS III

Department: Mathematical Sciences

MATH3101: CONTINUUM MECHANICS III

Prerequisites

• (Problem Solving and Dynamics I (MATH1041) AND Analysis in Many Variables II (MATH2031) AND one extra 20 credit Level 2 mathematics module) OR (Analysis in Many Variables II (MATH2031) AND Analysis I (MATH1051) (if taken in Year 2) AND Problem Solving and Dynamics I (if taken in Year 2)) OR (Foundations of Physics I (PHYS1122) AND Analysis in Many Variables II (MATH2031) AND one extra 20 credit Level 2 mathematics module.)

Corequisites

• One 20 credit Level 3 mathematics module.

Excluded Combination of Modules

• Continuum Mechanics IV (MATH4081).

Aims

• To introduce a mathematical description of fluid flow and other continuous media to familiarise students with the successful applications of mathematics in this area of modelling.
• to prepare students for future study of advanced topics.

Content

• Kinematic description of fluid flows: streamlines and trajectories, mass conservation and continuity equation
• Review of tensors, stress and rate of strain.
• Dynamical models of fluid flows: Euler and Navier-Stokes equation.
• Some methods to solve Euler and Navier-Stokes equations.
• Waves: sound and water waves, linear and nonlinear
• Topics from: thermodynamics, scaling and dimensional analysis, hydrodynamic stability, NSE and turbulence, non-Newtonian fluid flows

Learning Outcomes

• By the end of the module students will: be able to solve novel and/or complex problems in Continuum Mechanics.
• have a systematic and coherent understanding of theoretical mathematics in the field of Continuum Mechanics.
• have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: Kinematics of fluid flows.
• Equations of motion and their derivation for fluids.

• In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling.
• They will be able to formulate and use mathematical models in various situations.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University