Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

You searched for subject:(Locally mass conservation). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters

1. Liu, Kun. Discontinuous Galerkin Methods for Parabolic Partial Differential Equations with Random Input Data.

Degree: PhD, Engineering, 2013, Rice University

This thesis discusses and develops one approach to solve parabolic partial differential equations with random input data. The stochastic problem is firstly transformed into a parametrized one by using finite dimensional noise assumption and the truncated Karhunen-Loeve expansion. The approach, Monte Carlo discontinuous Galerkin (MCDG) method, randomly generates M realizations of uncertain coefficients and approximates the expected value of the solution by averaging M numerical solutions. This approach is applied to two numerical examples. The first example is a two-dimensional parabolic partial differential equation with random convection term and the second example is a benchmark problem coupling flow and transport equations. I first apply polynomial kernel principal component analysis of second order to generate M realizations of random permeability fields. They are used to obtain M realizations of random convection term computed from solving the flow equation. Using this approach, I solve the transport equation M times corresponding to M velocity realizations. The MCDG solution spreads toward the whole domain from the initial location and the contaminant does not leave the initial location completely as time elapses. The results show that MCDG solution is realistic, because it takes the uncertainty in velocity fields into consideration. Besides, in order to correct overshoot and undershoot solutions caused by the high level of oscillation in random velocity realizations, I solve the transport equation on meshes of finer resolution than of the permeability, and use a slope limiter as well as lower and upper bound constraints to address this difficulty. Finally, future work is proposed. Advisors/Committee Members: Riviere, Beatrice M. (advisor), Heinkenschloss, Matthias (committee member), Symes, William W. (committee member), Vannucci, Marina (committee member).

Subjects/Keywords: Parabolic PDEs; Monte Carlo Discontinuous Galerkin; Locally mass conservation; Random input data; Kernel PCA; Random permeability; Darcy's Law; Coupled flow and transport

…combining a random sampling technique and a locally mass conservative method, the uncertainty of… …oscillations in numerical simulations. However, these methods do not possess local mass conservation… …However, it does not satisfy local mass conservation, which is a crucial property in reservoir… …violation of the law of local mass conservation in velocity fields could result in ‚Äúspurious… …attractive advantages of DG methods include: local mass conservation, complex geometrics, high… 

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Liu, K. (2013). Discontinuous Galerkin Methods for Parabolic Partial Differential Equations with Random Input Data. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/71989

Chicago Manual of Style (16th Edition):

Liu, Kun. “Discontinuous Galerkin Methods for Parabolic Partial Differential Equations with Random Input Data.” 2013. Doctoral Dissertation, Rice University. Accessed November 12, 2019. http://hdl.handle.net/1911/71989.

MLA Handbook (7th Edition):

Liu, Kun. “Discontinuous Galerkin Methods for Parabolic Partial Differential Equations with Random Input Data.” 2013. Web. 12 Nov 2019.

Vancouver:

Liu K. Discontinuous Galerkin Methods for Parabolic Partial Differential Equations with Random Input Data. [Internet] [Doctoral dissertation]. Rice University; 2013. [cited 2019 Nov 12]. Available from: http://hdl.handle.net/1911/71989.

Council of Science Editors:

Liu K. Discontinuous Galerkin Methods for Parabolic Partial Differential Equations with Random Input Data. [Doctoral Dissertation]. Rice University; 2013. Available from: http://hdl.handle.net/1911/71989

.