
[Sponsors] 
November 12, 1998, 20:55 
Gradient Matrix in FEM

#1 
Guest
Posts: n/a

At the moment I am developing a FEM code to solve the Navier Stokes equations splitting the equation in three. The equations are: one for convection, one for diffusion and one for pressure. In the pressure equation I am obtaining an antisimetric matrix. I would like to know if someone has had such experience and any idea of where could be the bug. I really would be glad to have some sugestions......!


November 18, 1998, 20:25 
Re: Gradient Matrix in FEM

#2 
Guest
Posts: n/a

Hello ThoLi,
I have tried working with two equations also: Burger's eq. for velocity and Poisson eq. for pressure, using the projection method (Chorin), and also I was using analitycal integration for the Galerkin integrals. Some strange things were hapenning, the solution started converging to a very good solution and instead of converging (small variations in velocity) it continued incrementing, diverging from the desired solution. * And so I did the splitting in three eqs., in a way that I could verify the evolution of each one, and I also used Gauss Quadrature to do the integration. The simetric matrices are OK, mass: Ni Nj and grad: dNi/dx dNj/dx, x = x, y, but the other ones become antissimetric, for example, the divergent: Ni dNj/dx, x = x,y, and the nonlinear convective term has a similar problem: Ni dNj/dx Nk. * For example, if I have flow over a plate, it is ok, if I have flow in a duct, one side will be the opposite to the other. * If you could send me na example of a divergent matrix, it would be very usefull for me to find my error, because I haven't found this matrix in any literature or papers. * Thanking you very much for your interest and help, Sincerely yours, Astrid * P.S. *My equations: term1: viscosity (second order derivatives of velocity)  Equation 3 term2: convection (first order derivates)  Equation 1 term3: gradient of pressure Equation 2: two steps: grad(P) = div(v) / dt term4: divergence of velocity dv =  div(p) * dt 

November 23, 1998, 13:25 
Re: Gradient Matrix in FEM

#3 
Guest
Posts: n/a

Hello Astrid,
please send me (or post) also the following informations: which finite elements do you use (shape: triangular/rectangular; linear,quadratic,... polynomials; integration gaussian (how many points?); ) What variables are involved? (v: velocity?; p: pressure? P: also pressure? t: time? are there more? ) How big is your Reynoldsnumber? Have you tried zero convection (= zero Reynolds)? Describe your timediscretization scheme! (What have you done with dv/dt? with div(v)/dt?) give me some sketches of your geometry! and of the flow directions, you expect! you can send me a fax at +49 89  63812515 (it's a shared fax, so send also a page it's for me!)  I used: rectangles with biquadratic polynomials, i.e. x^2 * y^2 was included; integration with a fourpointgaussian in x and ydirection (resulting in 16 = 4*4 points) v: velocity, (x,y) > (vx,vy) ; p: pressure, (x,y) > p (no time, no timediscretization) My ReynoldsNumber was 20; I had an exact solution for the case Reynolds=0 and incremented the Reynoldsnumber (the influence of the convection) in small steps; I tried SIMPLE as solving algorithm, but then used a direct solver, because I didn't find the right parameters for SIMPLE to converge ... I'll send you a matrix, when I know your elements ... greetings ThoLi 

November 30, 1998, 21:09 
Re: Gradient Matrix in FEM

#4 
Guest
Posts: n/a

Hello ThoLi, I am writting the formulation I've been using and as soon as it is ready I'll send it to you. Thank you for your interest, Astrid PS: can I send you a Word97 file? or would it be better to fax it?


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Force can not converge  colopolo  CFX  13  October 4, 2011 22:03 
OpenFOAM version 1.6 details  lakeat  OpenFOAM Running, Solving & CFD  42  August 26, 2009 21:47 
assemble matrix in fem  ztdep  Main CFD Forum  0  September 14, 2008 12:30 
convective stiffness matrix for FEM  Juergen Kertz  Main CFD Forum  5  December 23, 2005 06:55 
comments on FDM, FEM, FVM, SM, SEM, DSEM, BEM  kenn  Main CFD Forum  2  July 18, 2004 18:28 