Computer Simulations in Physics

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Three Fluid Solvers, compared.	Visualization Description
	Simple stream line tracking particle, I used some my own improvements here to get better view of particle movements.
	U horizontal velocity component (absolute value of U), darker means slower in U direction here
	V velocity component (absolute value of U), darker means slower in U direction here.
	both U and V velocity sketch, where absolute value of U is placed as RED component of RGB colour pixel, and V is placed as GREEN velocity component
There you can download Animations of fluid flow trough different geometries. These two examples have been done for my friend Jakub Kominiarczuk. Firs example animation is a fluid flow trough 0 degree frisbee with Re=400. Second example is also a frisbee but it was made with Re=10000 and for freesbee angle 45 degree. If you are interested, I can do for you animations of geometries which you are interested in. Just drop me an Email. If I will have some time, I will do it for you.

SIMPLE, SIMPLER, Vorticity - Stream Fluid Solvers
Some time ago I took a course TMM53 Computational Fluid Mechanics. It was taken during my exchange studies in Sweden (Linkopings University). During the course I haven't been on any lecture (because lectures were provided in Swedish) but I made three projects, and the final one I am presenting on that web page. My task was to implement one (or two) of Navier-Stokes solution methods. I will not describe it very carefully there, because they are described in my paper which is listed below. I had to implement three different solution methods: 1. SIMPLE - Semi Implicit Method for Pressure Linked Equations 2. SIMPLER - Semi Implicit Method for Pressure Linked Equations Revised 3. Vorticity-Stream Functions approach for 2D NS equations There I will show some results from three solvers. Three of them gives me the same result (ohh! maybe it is good test case of my solvers?) so there is no different between the results. First of all let us consider Driven Cavity problem for Reynolds Number Re=400: I have got good quality pictures with well known vortices in the corners: Re=400, Classical Driven Cavity problem, Ratio 1:1 Re=400, Classical Driven-Cavity Problem, Ratio 1:2 Flow over rectangular obstacle, Re=100, SIMPLE Method (Only in SIMPLE Solver Boundary conditions have been implemented). Pictures have been generated with particle tracking method, and I add there some my ideas. . I also developed some other kinds of visualization, most of them you can find in my report which can be downloaded from main page or there: "Solution to two-dimensional Incompressible Navier-Stokes Equations with SIMPLE, SIMPLER and Vorticity-Stream Function Approaches. Driven-Lid Cavity Problem: Solution and Visualization.", Maciej Matyka , University of Linkoping, CFD Project Report #3, 6.V.2003 (.ps.zip ~1.2 Mb) PDF (~300 kb) On that page you can also find some examples of animations which are made with SIMPLE solver. In that solver I have implemented boundary conditions which allow me to make for example some kind of wind tunnel, to see how air is going trough different geometries.

SIMPLE, SIMPLER, Vorticity - Stream Fluid Solvers

Some time ago I took a course TMM53 Computational Fluid Mechanics. It was taken during my exchange studies in Sweden (Linkopings University). During the course I haven't been on any lecture (because lectures were provided in Swedish) but I made three projects, and the final one I am presenting on that web page.

My task was to implement one (or two) of Navier-Stokes solution methods. I will not describe it very carefully there, because they are described in my paper which is listed below. I had to implement three different solution methods:

1. SIMPLE - Semi Implicit Method for Pressure Linked Equations
2. SIMPLER - Semi Implicit Method for Pressure Linked Equations Revised
3. Vorticity-Stream Functions approach for 2D NS equations

There I will show some results from three solvers. Three of them gives me the same result (ohh! maybe it is good test case of my solvers?) so there is no different between the results. First of all let us consider Driven Cavity problem for Reynolds Number Re=400: I have got good quality pictures with well known vortices in the corners:

Re=400, Classical Driven Cavity problem, Ratio 1:1

Re=400, Classical Driven-Cavity Problem, Ratio 1:2

box

Flow over rectangular obstacle, Re=100, SIMPLE Method (Only in SIMPLE Solver Boundary conditions have been implemented).

Pictures have been generated with particle tracking method, and I add there some my ideas. . I also developed some other kinds of visualization, most of them you can find in my report which can be downloaded from main page or there:

"Solution to two-dimensional Incompressible Navier-Stokes Equations with SIMPLE, SIMPLER and Vorticity-Stream Function Approaches. Driven-Lid Cavity Problem: Solution and Visualization.", Maciej Matyka , University of Linkoping, CFD Project Report #3, 6.V.2003 (.ps.zip ~1.2 Mb) PDF (~300 kb)

On that page you can also find some examples of animations which are made with SIMPLE solver. In that solver I have implemented boundary conditions which allow me to make for example some kind of wind tunnel, to see how air is going trough different geometries.

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