Discretization of a system of ODEs with two variables.

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Andrian Mirza
Andrian Mirza 2021-5-9
评论： Tanmay Das 2021-8-5
I try to solve this system:
I have trouble trying to discretize the system. As you see above the system has two variables, t and n. n is the length of the pipe (better saying it is a segment of the pipe)
t is the time. I need n to be discrete though. Can you help solving this?
The code I came up with so far:
syms C_bulk(t) C_stag(t) SC(t) t Y
i = 0;
while i < n
% Differential Equations
A_pipe = pi*d_pipe^2/4;
V_bulk = i*A_pipe;
%C_bulk0 = P_in*y0/(R*T)*M_Hg;
C_bulk0 = 5000*10^(-12);
N_max = 1.2140*10^19;
Fug = 0.144992321;
s_0 = 1;
A_bulk = (d_pipe - 4.25*10^(-5))^2*pi/4;
A_stag = A_pipe - A_bulk;
V_stag = (d_pipe^2/4*i - V_bulk/n);
SSA = 1;
Z = 0.61;
v = 10^(17);
q_max = N_max*M_Hg/NA;
ode1 = diff(C_bulk,t) == F_vol/V_bulk*(C_bulk0 - C_bulk) + k_m/V_bulk*A_stag*(C_stag - C_bulk);
ode2 = diff(C_stag,t) == k_m/V_stag*A_stag*(-C_stag + C_bulk)-(Fug*C_stag*R*T1*NA/(M_Hg*sqrt(2*pi*M_Hg*R*T1))*s_0*(1-SC)/(V_stag*N_max)*A_pipe*q_max*SSA - v*SC*exp(-(126-28.82*SC)/(R*T1)))*A_pipe*q_max*SSA/V_stag;
ode3 = diff(SC,t) == (C_stag*Fug*Z*R*T1*NA/(M_Hg*sqrt(2*pi*M_Hg*R*T1))*s_0*(1-SC)/N_max - v*SC*exp(-1000*(151-28.82*SC)/(R*T1)));
odes = [ode1, ode2 ode3];
[VF,Subs] = odeToVectorField(odes);
odefcn = matlabFunction(VF, 'Vars',{t,Y});
i = i + L/n;
end

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