Azzera filtri
Azzera filtri

Need help with this MATLAB HW

1 visualizzazione (ultimi 30 giorni)
Dhinesh Nagarajan
Dhinesh Nagarajan il 20 Apr 2021
Commentato: Walter Roberson il 20 Apr 2021
%% Steady-state diffusion equation
%% PDE and boundary conditions
% The transient diffusion equation reads
%
% $$\alpha\frac{\partial c}{\partial t}+\nabla.\left(-D\nabla c\right)=0,$$
%
% where $c$ is the independent variable (concentration, temperature, etc)
% , $D$ is the diffusion coefficient, and $\alpha$ is a constant.
clc; clear;
%% add paths
addpath('FVTool');
FVToolStartUp
%% Define the domain and create a mesh structure
L = 1; % domain length
Nx = 20; % number of cells
dx = L/Nx;
m = createMesh2D(Nx,Nx, L,L);
x = m.cellcenters.x;
y = m.cellcenters.y;
%% Create the boundary condition structure
BC = createBC(m); % all Neumann boundary condition structure
BC.left.a(:) = 0; BC.left.b(:)=1; BC.left.c(:)=10; % left boundary
BC.right.a(:) = 0; BC.right.b(:)=1; BC.right.c(:)=0; % right boundary
BC.top.a(:) = 1; BC.top.b(:)=0; BC.top.c(:)=bc(x,1); % top boundary
BC.bottom.a(:) = 1; BC.bottom.b(:)=0; BC.bottom.c(:)=bc(x,0); % bottom boundary
%% define the transfer coeffs
D_x = 1;
D_y = 1;
D = createFaceVariable(m, [D_x, D_y]);
Mdiff = diffusionTerm(D);
%% define source term
[X, Y] = ndgrid(x, y);
S = @(X,Y)(6*X.*Y.*(1-Y)-2*X.^3)
s1 = constantSourceTerm(createCellVariable(m,S(X,Y)));
%s1 = 0*s1;
[Mbc, RHSbc] = boundaryCondition(BC);
M = Mdiff+Mbc;
RHS = -s1+RHSbc;
c = solvePDE(m,M, RHS);
figure(1);visualizeCells(c);caxis([0,10]);drawnow;
% view 3D plot
% add ghost points to x and y
x = [-0.5*dx; x; L+0.5*dx];
y = [-0.5*dx; y; L+0.5*dx];
[X, Y] = ndgrid(x, y);
% fix corner points as ghost point
u = c.value;
u(1,1) = u(1,2);
u(1,end) = u(1,end-1);
u(end,1) = u(end,2);
u(end,end) = u(end,end-1);
figure(2); surf(X, Y, u);
%axis([0 L 0 L 0 10]);
function g = bc(x,y)
g = -sin(10*pi*x);
end
  1 Commento
Walter Roberson
Walter Roberson il 20 Apr 2021
What difficulty are you asking for assistance with?

Accedi per commentare.

Risposte (0)

Tag

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by