The first week of the course introduces you to what exactly OpenFOAM is. OpenFOAM is developed primarily for the LINUX operating system. We will also cover the basics of the Linux operating system for anybody who is not acquainted with Linux. We will be covering in detail on the following topics: 

• Introduction to OpenFOAM 
• Users, Future opportunities
• OS and Version Selection
• Windows Subsystem for Linux
• Basics of Linux
• Test case
• Installing opt and debug modes

The course is targeted towards the development of a CFD solver using OpenFOAM. OpenFOAM is primarily a C++ library. Hence, a good understanding of the basics of C++ is quintessential. In this week, we will cover in detail the following topics:

• Setting up environment: Visual Studio Code
• Namespaces
• Data Structures
• Pointers
• Static and dynamic arrays
• STL - std::array and std::vector
• Declarations and definitions
• Passing by reference/value 
• Function Parameters and overloading

Object Oriented Programming brings a plethora of features to improve usability of any C++ code that you generate. In this week, we will cover:

• OOP – Classes and objects
• Inheritance 
• Smart Pointers – auto, unique, and shared  
• Template programming
• Polymorphism
• Operator overloading
• Abstract classes, Virtual functions

C++ is a high level language that let’s users create independent programs that are easier to interpret than assembly level codes. Here we will delve into the building blocks of it’s code organization by covering the following topics :

• Introduction to parallel programming MPI 
• Make files and Cmake 
• Library and class organization
• Compiling a solver

In this week, we further explore the various dictionaries available in OpenFOAM and try to understand the different C++ concepts used to achieve a particular task. We will be looking into : 

• 5 OpenFOAM Classes : Constructor/Destructor,Overloading,Inheritance & Polymorphism 
• Time dictionary 
• IOObject and objectRegistry
• Fields dictionary 
• Scalars, Vectors, and Tensors
• Implicit & Explicit namespaces (FVM & FVC)

Finite Volume Method (FVM) is one of the most commonly used methods of converting PDE’s to ALE’s. In this week, Upon introducing the basic principles of FVM, we dive deep into the way in which openFOAM handles individual terms of the governing equations. The following concepts are covered in this week:

• General conservation equation
• Navier-Stokes equations 
• Gauss Divergence Theorem 
• Discretization of the source term
• Discretization of the convective term 
• Upwind
• Linear Upwind
• Flux Limiter (TVD)
• Stability criterion – CFL condition 

FVM in openFOAM is implemented in 3 parts. 1) Surface interpolation 2) fvc and 3) fvm using the mentioned finite volume techniques covered in the previous week. In this week, we will look into the multiple algorithmic choices of gradient operators and discretization schemes that can be employed by covering the following topics :

• Gradient schemes
• Green-Gauss Cell Based
• Green- Gauss Node Based
• Discretization of the diffusion term 
• Laplacian schemes
• Non orthogonal meshes and solution
• N-S Equations revisited
• Collocated vs Staggered grids
• SIMPLE algorithm 

If we consider the discretized form of the Navier-Stokes system, the form of the equations shows linear dependence of velocity on pressure and vice-versa. This inter-equation coupling is called velocity pressure coupling and often calls for a special treatment in order to decouple the terms. This week, we will look at some of the standard techniques used in CFD to achieve the same. Topics include :

• SIMPLE algorithm - Need for Under Relaxation 
• SIMPLEC algorithm - Consistent SIMPLE
• PISO algorithm 
• PIMPLE algorithm

Linear systems in numerical methods often reduce to a sparse system (matrix having many zero elements) which can be computationally expensive to solve using standard algebraic methods. This week we will look into the working of some of the linear solvers used in openFOAM. Topics include : 

• Non-orthogonal correctors

• From mesh to matrix 

• Linear solvers 

• Jacobi

• Gauss Seidel

• Newton-Kyrlov family 

• Preconditioners 

• Smoothers 

• Solver tolerances

The concept of turbulence is something that has not been understood vividly till date although turbulent flows are commonplace in most real life scenarios. Considered as the cornerstone of fluid dynamics, Turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. This week, we will look into the basic types of turbulence models used in CFD.  

• Basics of turbulence 
• RANS averaging 
• The k-epsilon model
• The k-omega model 

This week is an extension of the concepts covered in the previous week where different turbulence models are weighed in against each other for specific applications. This week we further our understanding of the boundary layer theory by introducing ‘Wall functions’ which  are used to bridge the inner region between the wall and the fully developed turbulent layer to customizing a user defined turbulence model. Topics include :

• The k-omega SST model 
• Wall modelling and wall functions
• Creating a turbulence model

Time discretization is a mathematical technique applied to transient problems which require solutions in which position varies as a function of time. Temporal discretization involves the integration of every term in different equations over a time step (Δt). Topics include :

• Discretization of the time term 
• Forward and backward Euler 
• Crank-Nicholson 
• Function Objects 
• Latex for Report Writing