Computational Fluid Dynamics-Basics

Numerical Algorithms in Computational Fluid Dynamics

What you'll learn

Understanding the role of numerical algorithms in CFD.

Formulation of tridiagonal systems.

Derivation and mathematical background of the TDMA.

Application to one-dimensional heat conduction problems.

Requirements

No prior knowledge regarding this topic is required. All you can learn on the go

Description

This course is designed to introduce students to the foundational numerical methods used in solving partial differential equations in CFD. Emphasis will be placed on the Tridiagonal Matrix Algorithm (TDMA) and the SIMPLE algorithm for pressure-velocity coupling. Students will gain hands-on experience with algorithm implementation and their applications in fluid dynamics.Learning OutcomesBy the end of this course, students will be able to:Understand and apply TDMA and SIMPLE algorithms to solve CFD problems.Develop numerical solutions for multi-dimensional fluid flow and heat transfer problems.Analyze and optimize the performance of numerical methods in CFD applications.Integrate algorithms to create efficient, robust CFD solvers.This course focuses on Introduction to Numerical Methods in CFD, Overview of computational fluid dynamics, Basics of discretization techniques: finite difference, finite volume, and finite element methods and understanding the role of numerical algorithms in CFD. Students will better understand Formulation of tridiagonal systems, Derivation and mathematical background of the TDMA and Application to one-dimensional heat conduction problems. The challenge of pressure-velocity coupling in CFD, Step-by-step derivation of the SIMPLE algorithm and importance of under-relaxation factors and their tuning are well discussed. Students will select a fluid flow problem, implement numerical methods (TDMA and SIMPLE), and present their findings. The key concepts and algorithms will be reviewed and lead to further learning paths in CFD.

Overview

Section 1: Introduction to CFD

Lecture 1 SIMPLE ALGORITHM IN CFD

Section 2: SIMPLE ALGORITHM -NUMERICALS

Lecture 2 Application of SIMPLE ALGORITHM

Section 3: Tri-Diagonal Matrix Algorithm

Lecture 3 TDMA

Section 4: Applications of TDMA

Lecture 4 Applications of TDMA- Numericals

Lecture 5 TDMA continued

High School/Secondary School Physics Students .Undergraduate Engineers.