Electrohydrodynamic lubrication cp PATH AMPL short = 1, := 100; /* grid 0 .. N */ /* half-points go 1 .. N */ param pi := 4 * atan(1); param xa := -3; param xf > xa, := 2; param dx := (xf - xa) / N; param alpha := 2.832; param lambda := 6.057; param k_init := 1.6; param p_init {i in 1..N} := max(0, 1 - abs((xa +1 + i*dx)/2)); param w {i in 0..N} := (if i in {0,N} then 0.5 else 1); var k := k_init; var p {i in 1..N} >= 0, := p_init[i]; var h {j in 0..N} = ( xa + (j+.5)*dx)^2 + k + 1 + 1/pi * (sum {i in 0..N} w[i] * (i-j-0.5)*dx * log(abs(i-j-.5)*dx) * ((if i < N then p[i+1]) - (if i > 1 then p[i-1]) ) ) ; psum : k complements ( 1 - dx*2/pi * sum {i in 1..N} w[i]*p[i] ) = 0; reynolds {i in 1..N}: p[i] >= 0 complements ( (lambda / dx) * (h[i]-h[i-1]) - (1/dx^2) * ( h[i]^3 * ((if i < N then p[i+1])-p[i]) / exp(alpha*((if i < N then p[i+1])+p[i])*.5) - h[i-1]^3 * (p[i]-(if i > 1 then p[i-1])) / exp(alpha*(p[i]+(if i > 1 then p[i-1]))*.5) ) ) >= 0; ]]> solve; printf "Pressure is:\n"; display p;