Course syllabus for Computational continuum physics

Course syllabus adopted 2021-02-08 by Head of Programme (or corresponding).

Overview

  • Swedish nameBeräkningsmetoder för kontinuumfysik
  • CodeTIF330
  • Credits7.5 Credits
  • OwnerMPPHS
  • Education cycleSecond-cycle
  • Main field of studyEngineering Physics
  • DepartmentPHYSICS
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 85129
  • Block schedule
  • Open for exchange studentsNo

Credit distribution

0119 Project 7.5 c
Grading: TH		 7.5 c

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Basic undergraduate physics and mathematics, computing and numerical analysis. Computing at the level reached in the courses Learning from Data (Python) and FKA121 Computational Physics (C), and numerical methods at the level FKA121 Computational Physics. It is an advantage to have basic knowledge of fluid mechanics and/or electromagnetic field theory at the advanced undergraduate level.

Aim

The aim of the course is to outline modern computational methods to describe the properties and dynamics of continuum systems, such as fluids and gases, electromagnetic fields, and plasmas. The aim is furthermore to exemplify how such methods can be used to calculate the properties of such systems, of importance for a wide range of applications. Furthermore, the course provides a tool box for computational physics applicable to a broad set of problems, of in-terest both in basic and applied research and development. The course provides practice in using Python, C and elements of C++ for solving problems of computa-tional physics.

Learning outcomes (after completion of the course the student should be able to)

· Able to construct discretize equations governing a physical process with respect to the variables involved
· Explain basic time-integration methods
· Explain how to implement initial and boundary conditions
· Explain how to solve stationary problems, such as the Poisson equation
· Explain how to solve such equations in a reliable manner
· Explain how to treat multi-physics problems
· Able to discuss common computational methods and tools in computational continuum systems
· Use methods such as finite-difference time-domain, finite-element, plane-wave expansion, methods of moments
· Use methods such as finite-volume, spectral, pseudo-spectral
· Use methods such as CFL condition, explicit and implicit integration, operator splitting, geometric integration, stability preserving integration schemes
· Identifying and mitigating numerical artefacts and effects.
· Identify and explain conservation properties, such as particle number/mass conservation, energy conservation, phase-space incompressibility, positivity preserving schemes, and know how to test schemes for conservation properties
· Identify and evaluate classical test problems, checking convergence properties, method of manufactured solutions
· Write technical reports where computational results are presented and explained
· Communicate results and conclusions in a clear way.

Content

· Finite difference and related techniques.
· Spectral methods.
· Examples of continuum systems. 
· Practice in using Python, C and elements of  C++ as programming tools.

Organisation

Basic theory and methods are covered by a series of lectures. The students get training by applying the theory and methods in exercises and homework problems. An important part consists of practical training of carrying out computations using a set of given problems within projects throughout the course. The projects are accounted for in a written report. It is expected that the projects normally are performed in teams of two.

Literature

The main course literature is provided through the course lecture notes.
Further recommended material includes:

Programming practice:

  • Introduction to Numerical Programming, A Practical Guide for Scientists and Engineers Using Python and C/C++, Titus Adrian Beu
  • A Primer on Scientific Programming with Python by Langtangen, Hans Petter
  • The C Programming Language, by Brian W. Kernighan and Dennis M. Ritchie
  • C++ Primer by Stanley B. Lippman  (Author), Josée Lajoie  (Author), Barbara E. Moo

Finite difference methods:

  • Computational physics, Richard Fitzpatrick
  • Computational Physics, Mark Newman

Spectral methods:

  • Spectral methods and their applications, Guo Ben-Yu
  • Chebyshev and Fourier Spectral Methods, John P. Boyd

Advanced methods for continuum systems:

  • Computational physics, J. M. Thijssen
  • Plasma Physics via computer simulation, C. K. Birdsall, A. B. Langdon
  • Computational physics, Richard Fitzpatrick

Examination including compulsory elements

The course contains coding assignments, computing-lab assignments, theory assignments contained within projects worked on throughout the course. The examination is through reports to be submitted for assessment throughout the course. All examination parts will be graded in order to achieve the final grade.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.