Benchmark problems for subsurface flow uncertainty quantification

• A series of benchmark problems for subsurface flow UQ are designed.
• Three basic flow problems with increasing complexity are selected.
• Different statistical properties for the uncertain model parameter are specified.
• Illustration of the verification of PCM using the benchmark results is given.

SummaryIn this work, we design a series of benchmark problems for subsurface flow uncertainty quantification. Three basic subsurface flow problems with increasing complexity are selected, which are steady state groundwater flow, groundwater contamination, and multi-phase flow. For the steady state groundwater flow, hydraulic conductivity is assumed to be uncertain, and the uncertain model parameter is assumed to be Gaussian random constant, Gaussian random field, and facies field, respectively. For the other two flow problems, the uncertain model parameter is assumed to be Gaussian random field and facies field, respectively. The statistical property of the uncertain model parameter is specified for each problem. The Monte Carlo (MC) method is used to obtain the benchmark results. The results include the first two statistical moments and the probability density function of the quantities of interest. To verify the MC results, we test the convergence of the results and the reliability of the sampling algorithm. For any existing and newly developed uncertainty quantification methods, which are not (fully) verified, the designed benchmark problems in this work can facilitate the verification process of those methods. For illustration, in this work, we provide a verification of the probabilistic collocation method using the benchmark results.