We consider modeling of single phase fluid flow in heterogeneous porous media governed by elliptic partial differential equations (PDEs) with random field coefficients. Our target application is biotransport in tumors with uncertain heterogeneous material properties. We numerically explore dimension reduction of the input parameter and model output. In the present work, the permeability field is modeled as a log-Gaussian random field, and its covariance function is specified. Uncertainties in permeability are then propagated into the pressure field through the elliptic PDE governing porous media flow. The covariance matrix of pressure is constructed via Monte Carlo sampling. The truncated Karhunen–Loève (KL) expansion technique is used to decompose the log-permeability field, as well as the random pressure field resulting from random permeability. We find that although very high-dimensional representation is needed to recover the permeability field when the correlation length is small, the pressure field is not sensitive to high-oder KL terms of input parameter, and itself can be modeled using a low-dimensional model. Thus a low-rank representation of the pressure field in a low-dimensional parameter space is constructed using the truncated KL expansion technique.
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ASME 2018 International Mechanical Engineering Congress and Exposition
November 9–15, 2018
Pittsburgh, Pennsylvania, USA
Conference Sponsors:
- ASME
ISBN:
978-0-7918-5202-6
PROCEEDINGS PAPER
Efficient Uncertainty Quantification for Biotransport in Tumors With Uncertain Material Properties
Alen Alexanderian,
Alen Alexanderian
North Carolina State University, Raleigh, NC
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William Reese,
William Reese
North Carolina State University, Raleigh, NC
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Ralph C. Smith,
Ralph C. Smith
North Carolina State University, Raleigh, NC
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Meilin Yu
Meilin Yu
University of Maryland Baltimore County, Baltimore, MD
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Alen Alexanderian
North Carolina State University, Raleigh, NC
William Reese
North Carolina State University, Raleigh, NC
Ralph C. Smith
North Carolina State University, Raleigh, NC
Meilin Yu
University of Maryland Baltimore County, Baltimore, MD
Paper No:
IMECE2018-86216, V003T04A033; 9 pages
Published Online:
January 15, 2019
Citation
Alexanderian, A, Reese, W, Smith, RC, & Yu, M. "Efficient Uncertainty Quantification for Biotransport in Tumors With Uncertain Material Properties." Proceedings of the ASME 2018 International Mechanical Engineering Congress and Exposition. Volume 3: Biomedical and Biotechnology Engineering. Pittsburgh, Pennsylvania, USA. November 9–15, 2018. V003T04A033. ASME. https://doi.org/10.1115/IMECE2018-86216
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