Lecture 8
Magnetostatics Simulation with the Finite Volume Method
This lecture covers slides 13 .
Reading Material
- Ferziger, J.H., Perić, M., Street, R.L. (2020). Finite Volume Methods. In: Computational Methods for Fluid Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-99693-6_4, Chapter 4.
- Ferziger, J.H., Perić, M., Street, R.L. (2020). Complex Geometries. In: Computational Methods for Fluid Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-99693-6_9, Section 9.6-9.8, 9.10-11.
Finite Volume Basics
In this video, we will cover:
- Introduction to the finite volume method
- The difference between FVM compared to FDM and FEM
- Various verification techniques for FVM
- Covers: slides 13 (pages 1-8)
Finite Volume Toy Example
In this video, we will cover:
- Introducing the finite volume toy example
- Covers: slides 13 (pages 9-10)
Gauss Divergence Theorem
In this video, we will cover:
- Introducing the Gauss Divergence Theorem
- Showcasing its utility for FVM
- Covers: slides 13 (pages 11-15)
Transport and Flux
In this video, we will cover:
- Introducing the concept of transport and flux
- Showcasing its utility for FVM
Finite Volume Traits of the Trade
In this video, we will cover:
- The steps used in the finite volume method
- How to apply the steps on the toy example
- Using the properties of piecewise continuous integrals
- Using the Leibniz rule for differentiation under the integral
- Applying the Midpoint approximation rule
- Covers: slides 13 (pages 16-22)
Finite Volume Mesh Details
In this video, we will cover:
- Which mesh layout to use
- Where to store different physical quantities
- Different control volume types
- Covers: slides 13 (pages 23-25)
Step-by-Step Solution to The Toy Problem
Introduction to the Magnetostatic Problem
In this video, we will cover:
- Introduction to the Maxwell equations
- Definitions used for electric and magnetic fields
- Definition of the magnetostatic problem for this week
- Visualizations for the solution of the magnetostatic problem
- Covers: slides 13 (pages 38-41)
Implementation Details for the Magnetostatic
Problem
In this video, we will cover:
- Problems with discontinuous integrands
- Handling discontinuous integrands
- Covers: slides 13 (pages 47-52)