Discontinuous Galerkin Methods for Convection Diffusion Equations with Random Coefficients

2019-09-11
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.
Citation Formats
P. Çiloğlu and H. Yücel, “Discontinuous Galerkin Methods for Convection Diffusion Equations with Random Coefficients,” presented at the BEYOND 2019: Computational Science and Engineering Conference (9 - 11 Eylül 2019), Ankara, Türkiye, 2019, Accessed: 00, 2021. [Online]. Available: http://files.iam.metu.edu.tr/beyond2019/booksofabstract_beyond2019.pdf.