The University of Southampton
Courses

# ISVR6142 Numerical Methods for Acoustics

## Module Overview

This module introduces students to numerical methods available to solve practical problems in acoustics. It provides a self-contained review and derivation of the equations of acoustics in the time and frequency domains, and introduces benchmark analytical solutions which illustrate the general characteristics of problems that can be solved readily only by the use of numerical schemes. The course focusses on methods which are commercially available but describes the underpinning analysis in sufficient technical detail to serve as starting point for those seeking to apply or extend them to research problems.

### Aims and Objectives

#### Module Aims

The specific aim of this module is to introduce the fundamental principles of the most commonly used numerical methods for acoustics and to train students in their practical application.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Understand the equations that govern the propagation of sound in a stationary medium.
• Formulate boundary conditions for practical acoustic problems
• Understand and evaluate some simple benchmark solutions for acoustics
• Understand the underpinning theory and practical application to acoustics of: • frequencydomain Finite Elements • frequency-domain Boundary Elements • The Finite Difference timedomain method • numerical methods based on ray acoustics
• Assess the cost, accuracy and practical limitations of the above.
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Define the equations which govern different classes of acoustical problems.
• Obtain analytic solutions for simple benchmark problems.
• Be able to assess the suitability of different numerical methods for a wide range of practical acoustical problems
• Be able to further develop and apply the numerical methods presented in the course to new types of analysis in acoustics and other areas.
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Able to write simple computer programs and reports.
• Able to apply critical analysis and evaluation skills.
• Able to read, understand and interpret scientific papers.
• Able to synthesise information from a range of sources.
• Able to communicate clearly in written reports.
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Reduce real world acoustical problems to more simple problems amenable to numerical solution
• Select an appropriate numerical method for a broad range of problems in acoustics.
• Determine the mesh or grid resolution required for different numerical methods
• Validate a numerical code against a relevant benchmark problem.
• Read and understand user documentation for commercial acoustic codes

### Syllabus

• Review of fluid mechanics, derivation of the multi-dimensional equations for linear acoustics. • Simple solutions of the unsteady equations. • Time-harmonic acoustics. Complex notation and the Helmholtz eqn. • Acoustic boundary conditions on finite and infinite boundaries • Time-harmonic benchmark solutions. • Acoustic Finite Elements for the Helmholtz problem: 1-D elements • Numerical dispersion and dissipation, the pollution effect. • Acoustic Finite Elements for the Helmholtz problem: 2-D and 3-D elements. • Boundary element methods for Helmholtz problems. • Particular issues for unbounded problems. • Finite Difference time-domain methods. • Numerical methods based on Ray acoustics.

### Learning and Teaching

#### Teaching and learning methods

Teaching methods include three lectures per week which will be used to present the theory and worked examples. (Lecture notes will be available in electronic format.) Problems sheets will be provided which contain exercises similar to the worked examples presented during the lectures. Solutions to the exercises will be provided on Blackboard. An additional weekly ‘tutorial’ class will b timetabled to allow discussion of exercises and worked examples. This will also be used to introduce and provide feedback on marked assignments Revision lectures will be given at the end of the course to prepare students for the exam. Marked coursework assignments will require the students to write simple matlab or Python programmes (TBD) or to solve problems using commercial acoustics FE, BE and ray acoustics software.

TypeHours
Seminar2
Tutorial3
Lecture31
Preparation for scheduled sessions32
Follow-up work32
Total study time150

Software requirement. Access to classkit Licence for COMSOL (acoustics module). BE and other software class licenses (TBD)

### Assessment

#### Summative

MethodPercentage contribution
Coursework 25%
Coursework 25%
Examination  (120 minutes) 50%

#### Referral

MethodPercentage contribution
Coursework 25%
Coursework 25%
Examination 50%

#### Repeat Information

Repeat type: Internal & External