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Pressure poisson equations linear system understanding |
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March 5, 2017, 16:30
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Pressure poisson equations linear system understanding
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#1 |
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Hey, i am still a beginner and i understood the pressure poisson equation and how to derive it but i don't understand how we will put this in a matrix linear system and why is it sparse? I can't imagine what is in the matrix so please if anyone can make a basic figure of some rows and columns to clarify things for me
 Is each row the equation for each fluid cell if we r talking about mac grid solving? Thanks 
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March 5, 2017, 17:15
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#2 | |
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Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
I suggest to start learning from a 1D example. You need to introduce the discretization of the second order derivative, for example using the second order accurate FD formula on structured grid. Each node has a discrete equation that involves surrounding nodes, this way you can see the tridiagonal structure of the matrix. Starting from that, you would go to 2D (matrix with 5 diagonals) and 3D (matrix with 7 diagonals) cases. Of course, if you use formulas of greater accuracy or if you work on unstructured grids, the numbers of entries in the matrix will change. I also suggest to read basic textbooks |
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March 6, 2017, 03:19
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#3 |
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Can you give me sources for what you say
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March 6, 2017, 03:42
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#4 |
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Senior Member
Filippo Maria Denaro
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search on cfd-online, you will find some lists of CFD books
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March 6, 2017, 03:53
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#5 | |
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Quote:
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March 6, 2017, 04:00
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#6 |
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March 6, 2017, 04:02
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#7 | |
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Arjun
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Quote:
Your problem is only simple for people who already understand it. I do not think anyone has that much time to sit down and create a doc for you to understand. Milovan Peric's book in starting chapter (3rd i guess) has that for you where he talks about matrix. This book https://books.google.co.in/books/abo...ir_esc=y&hl=en has simple worked examples of 1 d and 2d that you can learn from. |
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March 6, 2017, 04:18
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#8 |
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Filippo Maria Denaro
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give your email, I have already some pages I have written fro my students, I cannot attach here due to the large dimension of the pdf
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March 6, 2017, 07:43
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#9 |
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March 6, 2017, 10:59
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#10 | |
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Senior Member
Filippo Maria Denaro
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Quote:
ok, just sent |
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