Discontinuous Galerkin Methods for Unsteady Convection Diffusion Equation with Random Coefficients

Date

2018-10-21

Author

Çiloğlu, Pelin
Yücel, Hamdullah

Metadata

Show full item record

Item Usage Stats

303
views

0
downloads

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 cause high level of uncertainty in approximating the solution to these problems. To identify the random coefficients, the well–known technique Karhunen Loeve ` (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 covariance. To address the limitations of the standard K–L expansion, we propose Kernel Principal Component Analysis (PCA). In this talk, we investigate the numerical solution of unsteady convection diffusion eqution with random input data by using stochastic Galerkin method. Since the local mass conservation play a crucial role in reservoir simulation and transport problem, we use discontinuous Galerkin method for the spatial discretization. On the other hand the dG(0) is performed for the temporal discretization. We provide some numerical results to illustrate the efficiency of the proposed approach.

URI

http://files.iam.metu.edu.tr/workshop_cse/booksofabstract_beyond.pdf
https://hdl.handle.net/11511/79954
http://files.iam.metu.edu.tr/workshop_cse/abstracts/pelin_ciloglu.pdf

Conference Name

BEYOND: Workshop on Computational Science and Engineering, 20 - 21 October 2018

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Discontinuous Galerkin Methods for Convection Diffusion Equations with Random Coefficients Çiloğlu, Pelin; Yücel, Hamdullah (null; 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 system...
Local improvements to reduced-order approximations of PDE-constrained optimization problems Akman, Tuğba; Karasözen, Bülent; Department of Scientific Computing (2015) Optimal control problems (OCPs) governed partial differential equations (PDEs) arise in environmental control problems, optimal control of fluid flow, petroleum reservoir simulation, laser surface hardening of steel, parameter estimation and in many other applications. Although the OCPs governed by elliptic and parabolic problems are investigated theoretically and numerically in several papers, the studies concerning the optimal control of evolutionary diffusion-convection-reaction (DCR) equation and Burger...
Dynamic Simulation of the Filtration Process Based on the Streamline Technology, Monitoring and Prediction of EOR and Stimulation Methods Jamalbayov, Mehemmed A.; Hasanov, Ilyas R.; Valiyev, Nazim A.; Doğan, Mehmet Onur; Jamalbayli, Tayfun M. (2022-11-03) The purpose of the work is to model the filtration processes in gas condensate and oil (including volatile oil) reservoirs operated by production and injection wells of an arbitrary number on any coordinates, on the basis of which the creation of a computer simulator for visualization and predicting the process and evaluating the effectiveness of EOR and stimulation methods. The solution was obtained on the basis of streamline technology, taking into account reservoir rock deformations, PVT prope...
Singularly perturbed diffusion-advection-reaction processes on extremely large three-dimensional curvilinear networks with a periodic microstructure -- efficient solution strategies based on homogenization theory Kropat, Erik; Meyer-Nieberg, Silja; Weber, Gerhard-Wilhelm (American Institute of Mathematical Sciences (AIMS), 2016-8) Boundary value problems on large periodic networks arise in many applications such as soil mechanics in geophysics or the analysis of photonic crystals in nanotechnology. As a model example, singularly perturbed elliptic differential equations of second order are addressed. Typically, the length of periodicity is very small compared to the size of the covered region. The overall complexity of the networks raises serious problems on the computational side. The high density of the graph, the huge number of ed...
Incompressible flow simulations using least squares spectral element method on adaptively refined triangular grids Akdağ, Osman; Sert, Cüneyt; Department of Mechanical Engineering (2012) The main purpose of this study is to develop a flow solver that employs triangular grids to solve two-dimensional, viscous, laminar, steady, incompressible flows. The flow solver is based on Least Squares Spectral Element Method (LSSEM). It has p-type adaptive mesh refinement/coarsening capability and supports p-type nonconforming element interfaces. To validate the developed flow solver several benchmark problems are studied and successful results are obtained. The performances of two different triangular ...

Citation Formats

P. Çiloğlu and H. Yücel, “Discontinuous Galerkin Methods for Unsteady Convection Diffusion Equation with Random Coefficients,” presented at the BEYOND: Workshop on Computational Science and Engineering, 20 - 21 October 2018, Ankara, Türkiye, 2018, Accessed: 00, 2021. [Online]. Available: http://files.iam.metu.edu.tr/workshop_cse/booksofabstract_beyond.pdf.