Need some guidance to solve this problem for velocity and pressure variables
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Hello all,
In my problem, I need to solve the following equations to calculate the variables velocity (from Eq .(1 and 2)) and pressure (from Eq .(3)).
∇.G=S (1)
∇×G-G×∇(ln(F1+F2*G))=0 (2)
∇^2 (P^2)=-(F1+F2*G)S - G∙∇(F1+F2*G) (3)
where, G, G = mass velocity vector and its magnitude, P = Pressure and S = source term.
Here is my code below and queries to follow:
1) While defining continuity Eq. (1), I'm facing an error,
% ERROR: Array indices must be positive integers or logical values.
2) Without Eq. (1), the velocity and pressure values obtained are not good as expected.
I'm not sure about my approach as how to find the appropriate velocity and pressure.
Someone kindly examine the code and judge my approach and assist me further.
Thank you
clear; clc; close all;
L=0.25; W =5;
Nx=10; Ny=200;
x = linspace(0,L,Nx);
y = linspace(0,W,Ny);
[X, Y] = meshgrid(x,y);
dx = x/Nx; dy = y/Ny;
rhoo = 0.8;
por = 0.3; mu =0.8E-5; dia = 0.003;
P = 101325.*ones(Ny,Nx);
V = zeros(Ny,Nx);
Gvec = zeros(Ny,Nx);
TimeStep =1;
Vx = gradient(X, TimeStep);
Vy = gradient(Y, TimeStep);
Vmag = sqrt(Vx.^2 + Vy.^2);
% Boundary conditions
V(:,1) = 0;
V(Ny,:) = 0;
V(1,:) = V(Ny-1,:);
V(:,Nx) = V(:,Nx-1);
V(Ny,1) = 0;
V(1,1) = 0;
S = [0 0 0.1458 0.2058 0.2161 0.2171 0 0 0 0];
f1 = (300*((1-por).^2)*P*mu)/(rhoo.*(dia.^2)*(por.^3));
f2 = (3.5.*(1-por).*P)/(rhoo.*dia.*(por.^3));
F1 = f1.*ones(Ny,Nx);
F2 = f2.*ones(Ny,Nx);
Gvec =rhoo.*V;
Gmag =rhoo.*Vmag;
%divergence(Gvec) = 0 % Eq. (1)
% ERROR: Array indices must be positive integers or logical values.
d1 = log (F1 + (F2.*Gmag));
d2 = gradient(d1);
A = curl(Gvec,X);
B = curl(d2,Gvec);
V = A - B % Eq. (2)
d3 = F1 + (F2.*Gmag);
d4 = gradient(d3);
P = gradient(gradient((P.^2))) + divergence(d3,Gvec) + d3.*S % Eq. (3)
4 Comments
Torsten
on 29 Aug 2022
Edited: Torsten
on 29 Aug 2022
May I know why you are guiding to use black box tools like ANSYS or COSMOL ?
The laminar Navier Stokes equations need a special treatment because of the velocity-pressure coupling. They are hard to solve for a beginner. Or how much time do you plan to invest in reading before you start programming ?
Is that impossible to solve by MATLAB ?
If it can be done in OPENFOAM, ANSYS and COMSOL, it can also be done in MATLAB. But you will have to program it from scratch if you don't find code somewhere else. So again the question: how much time do you plan to invest ? I would estimate half a year if you have to do all by yourself.
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