BEYOND 2019: Computational Science and Engineering Conference, Ankara, Turkey, 9 - 11 September 2019
Partial differential equations (PDEs) with random input data is one of the most powerful tools to model
oil and gas production as well as groundwater pollution control. However, the information available
on the input data is very limited, which causes high level of uncertainty in approximating the solution
to these problems. To identify the random coefficients, the well–known technique Karhunen Loéve
(K–L) expansion has some limitations. K–L expansion approach leads to extremely high dimensional
systems with Kronecker product structure and only preserves two–point statistics, i.e., mean and variance. To address the limitations of the standard K–L expansion, we propose principal component
analysis (PCA), i.e., linear and kernel PCA.
This talk concerns a numerical investigation of convection diffusion equation with random input data
by using stochastic Galerkin method. Since the local mass conservation plays a crucial role in reservoir simulations, we use discontinuous Galerkin method for the spatial discretization. To illustrate
the efficiency of the proposed approach, we provide some numerical experiments with Gaussian and
uniform distributed coefficients.