Dear @Mr. Saheria and Colleagues,

Good Day,

Here are what you need, pick up the exact one among the attachments list!!!

I have put the websites too for you as references.

http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf

http://www.quickersim.com/blog/matlab-navier-stokes-solver-in-3d.html

https://people.sc.fsu.edu/~jburkardt/m_src/ns3d_fem/ns3d_fem.html

http://www3.nd.edu/~gtryggva/CFD-Course/2013-Lecture-6.pdf

http://cfd2012.com/matlab-navier-stokes-equations.html

https://www.kth.se/social/upload/4f6130d4f2765431a7000003/project.pdf

https://web.stanford.edu/class/me469b/handouts/incompressible.pdf

I am not conviced you may compute any 3D NS using matlab - may be some limited sections of a general full 3D solver. You need to Watch carefully in the archival literature ! Define the type of 3D NS problem, consider geometry; refer to former works and adapted methods FV, FEM, spectral, LBM, ... A lot of works already done since the 70 ties to be studied.

I am trying to solve it as a 3d one element cube using matlab, Can you suggest some books??

Dear @Mr. Saheria and Colleagues,

Good Day,

Here are what you need, pick up the exact one among the attachments list!!!

I have put the websites too for you as references.

http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf

http://www.quickersim.com/blog/matlab-navier-stokes-solver-in-3d.html

https://people.sc.fsu.edu/~jburkardt/m_src/ns3d_fem/ns3d_fem.html

http://www3.nd.edu/~gtryggva/CFD-Course/2013-Lecture-6.pdf

http://cfd2012.com/matlab-navier-stokes-equations.html

https://www.kth.se/social/upload/4f6130d4f2765431a7000003/project.pdf

https://web.stanford.edu/class/me469b/handouts/incompressible.pdf

The Matlab programming language was used by numerous researchers to solve the systems of partial differential equations including the Navier Stokes equations both in 2d and 3d configurations. The main "trade trick" in all these applications is the clever representation of the "space terms" (discretization of gradient, divergence and Laplace operators) using the formalism of sparse matrices. The majority of the number crunching in this setting is reduced to sparse matrix/vector multiplications which are very fast in Matlab.

The time stepping is usually accomplished with the Runge Kutta method or with the exponential propagators.

Based on my experience, even small vintage computers (like Mac book pro 2007) can handle problems with 10^5 nodes. Modern personal computers can easily accept the Matlab PDEs codes with at least ten times bigger mesh systems.

All the above remarks are based on my experiments with the PDEs on structured and unstructured meshes mainly on the surface of the sphere discretized using the triangular meshes (shallow water system and reaction/advection/diffusion Equation). In the recent months I have started working on generalizations of my codes to 3D setting and I will gladly share my specific experiences in this field if you are interested.

Probably this educational Matlab code is useful.

http://cfd2012.com/index.html

You can check out the QuickerSim CFD Toolbox for MATLAB:

https://quickersim.com/cfdtoolbox/

It is a commercial plug-in but it also has an open-source freeware part. Hence 2d laminar NS implementation is available with the entire code.

http://www.gidropraktikum.narod.ru/Moukalled-et-al-FVM-OpenFOAM-Matlab.pdf

Dear Dr. Saheria,

Have a look on this simple article to solve 3D-NS equations with MATLAB.

Best regards,