Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation

Table 1

Stochastic convergence results for KL-MC simulations with in the pressures and fluxes. Convergence ratios are given in parentheses.

	Pressure error	Flux error	Flux error
Results for
100	0.871395160535	0.065990195314	0.028573904583
400	0.364829041492 (2.39)	0.069916447041 (0.94)	0.018699389288 (1.52)
1600	0.055858569054 (6.53)	0.021215209498 (3.29)	0.006586753979 (2.83)
6400	0.054169889340 (1.03)	0.012411413073 (1.71)	0.003615613202 (1.82)
Results for
100	0.254380891374	0.049476177143	0.026290307316
400	0.112240817113 (2.27)	0.024602883474 (2.01)	0.011912256200 (2.21)
1600	0.064059879872 (1.75)	0.011673912035 (2.11)	0.004237191244 (2.81)
6400	0.050133900679 (1.28)	0.008381613088 (1.39)	0.003806688304 (1.11)
Results for
100	0.441427542393	0.047070576489	0.022927539745
400	0.204776531658 (2.16)	0.025904577051 (1.82)	0.014762469928 (1.55)
1600	0.093540699576 (2.19)	0.015060205886 (1.72)	0.006659195033 (2.22)
6400	0.035279177226 (2.65)	0.005514284413 (2.73)	0.002559067034 (2.60)