Staggered Pressure Method

In this method, the pressure can be approximated using equation 4.8 as following:

Substituting equation 4.24 into equation 4.8, there is obtained:

[G]{p}i+1 = [G]{pK+1 - p[Q]t{U}i+1 - 7At[C]{p}i+1 - pAt2[K']{p}m

([G] + pAt2[K] + yAt[C"]){P}i+1 = [G]{P}*+1 - p[Q]T{U}i+1 (4.26)

Substituting equation 4.26 into equation 4.7 with [H] = [G] + PAt2[K'] + YAt[C], gives:

([M] + pP At2[Q][H]-1[Q]T ){U }i+i + [C]{U }i+i + [K]{U }i+i = (4.27)

Using equation 4.27, the variable {U}i+1can be calculated. Substituting {U}i+1 into equation 4.7 gives {p}i+1 and its derivatives.

Therefore, the procedure of the staggered pressure method can be summarized by the following steps: ..

1. Solving equation 4.24 to calculate {p}*+1.

2. Substituting {p}*+1in equation 4.27 to calculate {U}i+1.

3. Substituting {U}i+1in equation 4.26 to calculate {p}i+1 and its derivatives.

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