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Chaojie Mo
The program solves the nonlinear lubrication equation.
const double rho = 6; const double mu = 5; const double lambda = 7.2; const double R = 6.0; const double pi = 3.1415926;
t
h v
h = R-0.01*R*cos(pi*z/60.0); v = 0;
100
hv
Lz
Lz = i*kz;
Lzzz
Lzzz = -i*kz*kz*kz;
Lzz
Lzz = -kz*kz;
dh_dt = -v*Lz[h] - h*Lz[v]/2.0; dv_dt = -v*Lz[v] + 3.0*mu/rho/h/h*(2.0*h*Lz[h]*Lz[v]+h*h*Lzz[v]) - lambda/rho*((-Lz[h]*sqrt(1+Lz[h]*Lz[h]) - h*Lz[h]*Lzz[h]/sqrt(1+Lz[h]*Lz[h]))/(h*h*(1+Lz[h]*Lz[h])) - (Lzzz[h]*pow(1+Lz[h]*Lz[h],3.0/2.0)-3.0*Lz[h]*Lzz[h]*Lzz[h]*sqrt(1+Lz[h]*Lz[h]))/pow(1+Lz[h]*Lz[h],3.0));

hR hI vR vI
hv
hR = h.Re(); hI = h.Im(); vR = v.Re(); vI = v.Im();