**inbox**33731

What's the difference between the Navier stocks equations that describe laminar flow and the navier- stocks equations that solve in DNS (direct numerical simulation) ? : CFD

14 days ago by goajunior

I have asked this question before but I guess I didn't voice it correctly. As the title implies, given the NS equations what are the terms that are causing all the turbulent instabilities? What are the assumptions that we force the original NS equation to solve it without those instabilities (laminar) ? I just want to know the difference between ANSYS's laminar and DNS model via /r/CFD

inbox
14 days ago by goajunior

[October] Shock Capturing Methods : CFD

26 days ago by goajunior

As per the [discussion topic vote](https://ift.tt/2R36cX6), October's monthly topic is Shock Capturing MethodsPrevious discussions: https://ift.tt/2q5USxT via /r/CFD

inbox
26 days ago by goajunior

Approximation in lattice Boltzmann method : CFD

26 days ago by goajunior

Hi everyone,I am currently learning LBM. I have derived the approximated distribution formula from scratch, this:f_i=w_i rho (1+x_j u_j+1/2(u_j u_k+(sigma^2-1)d_ij)(x_i x_j-d_ij)During the derivation, the first step is to approximate a Gaussian distribution with Hermite polynomials. The formula above, uses Hermite polynomials up to degree 2.One question is, is this a good approximation? I plotted the original function and the function approximated by 2 degree of Hermite polynomials. This is what it looks like:https://ift.tt/2R3E4mA my perspective, this is a really poor approximation. The value is so wrong at x=0.Sure we can approximate it with more terms, but given the formula derived from it is widely used, I have doubt on the accuracy of this formula.Anyone familiar with LBM can help me?EDIT:Please confirm my expansion is done correctly:Gaussian: Exp(-x^2/2)/Sqrt(2 Pi)Approximated 2nd order: Exp(-x^2) (1+2x^2)/(2 Sqrt(Pi))(Original function have miu and sigma which are substituted with 0 and 1 respectively)EDIT 2:u/wstrncdn ask me to provide image of higher order approximations, here is the result:https://ift.tt/2q39Pk4 looks like even 3rd order approximation wasn't that good, but it's better with 6th and 9th terms added.9th Appro: exp(-x^2) (321-312x^2+552x^4-160x^6+16x^8)/(384 sqrt(Pi))EDIT 3:Some people pointed out that it's the moment integral that's important. So let's see how accurate it is:(Ordered from 1st to 9th approximation)0th moment: {1., 1., 1., 1., 1., 1., 1., 1., 1.}2nd moment: {0.5, 1., 1., 1., 1., 1., 1., 1., 1.}4th moment: {0.75, 2.25, 2.25, 3., 3., 3., 3., 3., 3.}1st, 3rd moments are all zero (obviously because of symmetry)So 2nd order approximation will get the wrong 4th moment, but the 0th and 2nd are correct. Not sure about asymmetric distributions though.EDIT 4:The discussion have went a long way but I think we can conclude now: 2nd order approximation LBM is actually accurate up to 2nd moments for integrals only, and that's all we want so nothing to be surprised here. via /r/CFD

inbox
26 days ago by goajunior

Introduction to CFD Lectures : CFD

28 days ago by goajunior

NASA Ames hosted a great lecture series introducing CFD and numerical methods. I thought some on this subreddit might find these useful: https://ift.tt/2yMnFeM never tried accessing these from outside the NASA network but I think these are public, let me know if I'm wrong. via /r/CFD

inbox
28 days ago by goajunior

**related tags**

Copy this bookmark: