## of Ramesh Kolluru

### M y understanding of what CFD is

CFD.pdf

I like to develop codes for simulation of fluid flow.I have written some codes in C++ for wave equation, Burger's equation, Heat equation, Euler equation and 3D-NS equations using implicit and methods.

Here are few files that I found on World Wide Web, which would give you a brief introduction on what and why you need to learn CFD.

lecture1.pdf (Document Courtsey WWW)

symp05-Yi.pdf (Document Courtsey WWW)

If you have any further doubts or clarifications you can contact or post your questions on the Blog and I will try to address them to the best of my knowledge.

### Computational Fluid Dynamics

CFD is acronym of Computational Fluid Dynamics, is solving governing partial differential equations of fluid flows using numerical techniques.

The governing equations of fluid flows are

a) Continuity (conservation of mass)

b) Conservation of linear momentum

c) Conservation of energy (First Law of Thermodynamics).

Equations a) and b) along with the equation of state are called Navier-Stokes Equations. These NS equations are non-linear partial differential equations, valid for any kind of fluid flowing in any domain. The behaviour of the equations are strongly dependent on the flow regime like laminar flow, transition and turbulent flow.

There is no general analytical solution to these set of equations (if you can solve its worth while earning Million dollars "http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness"). Since no general analytical solution exists we use numerical methods to solve these NS equations, which is nothing but C- Computation part in CFD.

So good so far, but what's the big deal in solving these equations.

• Highly non-linear.
• Equations characteristics  are based on flow characteristics.
• Also discontinuities like shocks, slip planes occur at higher Mach number flows which also introduces some trouble.
• Challenging tasks include in CFD include predicting turbulence with out any adhoc models, accurate prediction of shock and its interaction with turbulence, numerical accuracy of the solution, low artificial dissipation schemes.
Although, some progress is made in shock capturing, simulating turbulence is next to impossible. Even though researchers all around the world are trying to solve the problem of turbulence with different perspectives but the achievement made so far in mimicking turbulence is meagre.

### Finite Volume Method

In this section a brief introduction of cell centered finite volume method will be described and the code snippets developed by me using this method will be made available in the downloads section. All the codes in this section are developed by me and tested for few test cases. Interested people can use the code and do necessary modifications for their use.