14 research outputs found
The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity
No full textRandom walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backward Îto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000). The latter is best suited to the problems under consideration. It is then applied to two test cases with discontinuous diffusivity, highlighting the advantages of this method.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc
Role of Molecular Diffusion in Contaminant Migration and Recovery in an Alluvial Aquifer System
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Multi-fidelity Design of Porous Microstructures for Thermofluidic Applications
No full textAs modern electronic devices are increasingly miniaturized and integrated,
their performance relies more heavily on effective thermal management.
Two-phase cooling methods enhanced by porous surfaces, which capitalize on
thin-film evaporation atop structured porous surfaces, are emerging as
potential solutions. In such porous structures, the optimum heat dissipation
capacity relies on two competing objectives that depend on mass and heat
transfer. The computational costs of evaluating these objectives, the high
dimensionality of the design space which a voxelated microstructure
representation, and the manufacturability constraints hinder the optimization
process for thermal management. We address these challenges by developing a
data-driven framework for designing optimal porous microstructures for cooling
applications. In our framework we leverage spectral density functions (SDFs) to
encode the design space via a handful of interpretable variables and, in turn,
efficiently search it. We develop physics-based formulas to quantify the
thermofluidic properties and feasibility of candidate designs via offline
simulations. To decrease the reliance on expensive simulations, we generate
multi-fidelity data and build emulators to find Pareto-optimal designs. We
apply our approach to a canonical problem on evaporator wick design and obtain
fin-like topologies in the optimal microstructures which are also
characteristics often observed in industrial applications.Comment: 24 pages, 10 figure
A Modified Gravimetric Method for Measuring Rates of Vapor Adsorption and Desorption on Soils. Kinetics of Toluene Adsorption/Desorption on Bentonite
No full textProbabilistic Neural Data Fusion for Learning from an Arbitrary Number of Multi-fidelity Data Sets
No full textIn many applications in engineering and sciences analysts have simultaneous
access to multiple data sources. In such cases, the overall cost of acquiring
information can be reduced via data fusion or multi-fidelity (MF) modeling
where one leverages inexpensive low-fidelity (LF) sources to reduce the
reliance on expensive high-fidelity (HF) data. In this paper, we employ neural
networks (NNs) for data fusion in scenarios where data is very scarce and
obtained from an arbitrary number of sources with varying levels of fidelity
and cost. We introduce a unique NN architecture that converts MF modeling into
a nonlinear manifold learning problem. Our NN architecture inversely learns
non-trivial (e.g., non-additive and non-hierarchical) biases of the LF sources
in an interpretable and visualizable manifold where each data source is encoded
via a low-dimensional distribution. This probabilistic manifold quantifies
model form uncertainties such that LF sources with small bias are encoded close
to the HF source. Additionally, we endow the output of our NN with a parametric
distribution not only to quantify aleatoric uncertainties, but also to
reformulate the network's loss function based on strictly proper scoring rules
which improve robustness and accuracy on unseen HF data. Through a set of
analytic and engineering examples, we demonstrate that our approach provides a
high predictive power while quantifying various sources uncertainties
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Modeling groundwater contaminant transport in the presence of large heterogeneity: A case study comparing MT3D and RWhet.
No full textA case study is presented that implements two numerical models for simulating a 30-year PAT operation conducted at a large contaminated site for which high-resolution data sets are available. A Markov chain based stochastic method is used to conditionally generate the realizations with random distribution of heterogeneity for the Tucson International Airport Area (TIAA) federal Superfund site. The fields were conditioned to data collected for 245 boreholes drilled at the site. Both MT3DMS and the advanced random walk particle method (RWhet) were used to simulate the PAT-based mass removal process. The results show that both MT3DMS and RWhet represent the measured data reasonably, with Root Mean Square Error (RMSE) less than 0.03. The use of fine grids and the total-variation-diminishing method (TVD) limited the effects of numerical dispersion for MT3DMS. However, the effects of numerical dispersion were observed when compared to the simulations produced with RWhet using a larger number of particles, which provided more accurate results with RMSE diminishing from 0.027 to 0.024 to 0.020 for simulations with 1, 20, and 50 particles. The computational time increased with more particles used in the model, but was still much less than the time required for MT3DMS, which is an advantage of RWhet. By showing the results using both methods, this study provides guidance for simulating long-term PAT systems. This work will lead to improve understanding of contaminant transport and plume persistence, and in turn will enhance site characterization and site management for contaminated sites with large plumes
Modeling groundwater contaminant transport in the presence of large heterogeneity: A case study comparing MT3D and RWhet.
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