longitudinal dispersion in nonuniform isotropic porous media
longitudinal dispersion in nonuniform isotropic porous media
longitudinal dispersion in nonuniform isotropic porous media
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173<br />
times this number. It is possible to <strong>in</strong>crease the sequence length<br />
dramatically at the expense of us<strong>in</strong>g two l<strong>in</strong>ear congruential sequences<br />
simultaneously, which approximately doubles the computation time spent<br />
on generat<strong>in</strong>g random numbers. If the two generators have sequence<br />
lengths which are prime relative to each other (no common factors), the<br />
sequence length of the comb<strong>in</strong>ed generators can be made to produce a<br />
sequence length equal to the product of the two orig<strong>in</strong>al sequence<br />
lengths. The algorithm shown below was first proposed by MacLaren and<br />
Marsaglia, and is discussed <strong>in</strong> Knuth (1969).<br />
Algorithm:<br />
IN+l = AlIN + Bl<br />
I N+1<br />
A2 I N + B2<br />
Generate 100 values from, say, the J sequence and store <strong>in</strong><br />
(A.2)<br />
(A.3)<br />
an array called L(k). Use the I sequence to generate a random<br />
<strong>in</strong>teger value of k, i.e.,<br />
where I 1S the maximum <strong>in</strong>teger that can be represented<br />
max<br />
on the computer. The real random number, R, is<br />
R = L(k)/J max<br />
where J max would typically be equal to Imax.<br />
Use the J sequence to replace the value used, i.e.,
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