International Journal for Uncertainty Quantification, 2015
Plasma modelers often change the ion-to-electron mass ratio and speed of light to Alfvén speed ra... more Plasma modelers often change the ion-to-electron mass ratio and speed of light to Alfvén speed ratio to decrease computational cost. Changing these parameters may affect the outcome of simulation and uncertainty in the results. This work aims to quantify the uncertainty of varying the ion-to-electron mass ratio, speed of light to Alfvén speed ratio, and the initial magnetic flux perturbation on the reconnected flux to provide a confidence limit. In this study, the multilevel Monte Carlo (MMC) method is employed to estimate the mean and variance, and the results are compared with the standard Monte Carlo (MC) and the probabilistic collocation (PC) methods. The plasma model used here is the twofluid plasma where ions and electrons are treated as two separate fluids. Numerical simulations are presented showing the effectiveness of the MMC method when applied to the quasi-neutral ion cyclotron waves and the Geospace Environment Modeling (GEM) magnetic reconnection challenge problems. The mean reconnected flux with error bars provides a reconnection flux variation envelope, which can help numerical modelers to evaluate whether their reconnection flux lies inside the envelope for different plasma models. The results of the MMC mean and variance are comparable to the MC method but at a much lower computational cost.
In this paper, we present an adaptive, analysis of variance (ANOVA)-based data-driven stochastic ... more In this paper, we present an adaptive, analysis of variance (ANOVA)-based data-driven stochastic method (ANOVA-DSM) to study the stochastic partial differential equations (SPDEs) in the multi-query setting. Our new method integrates the advantages of both the adaptive ANOVA decomposition technique and the data-driven stochastic method. To handle high-dimensional stochastic problems, we investigate the use of adaptive ANOVA decomposition in the stochastic space as an effective dimension-reduction technique. To improve the slow convergence of the generalized polynomial chaos (gPC) method or stochastic collocation (SC) method, we adopt the data-driven stochastic method (DSM) for speed up. An essential ingredient of the DSM is to construct a set of stochastic basis under which the stochastic solutions enjoy a compact representation for a broad range of forcing functions and/or boundary conditions.
Sickle cell disease (SCD) is an inherited blood disorder characterized by rigid, sickle-shaped re... more Sickle cell disease (SCD) is an inherited blood disorder characterized by rigid, sickle-shaped red blood cells (RBCs). Because of their rigidity and shape, sickle cells can get stuck in smaller blood vessels, causing blockages and depriving oxygen to tissues. This study develops and applies mathematical models to better understand the mechanism of SCD. Two-dimensional models of RBCs and blood vessels have been constructed by representing them as discrete particles interacting with different forces. The nonlinear, elastic property of healthy RBCs could be adequately reproduced using a cosine angle bending force and a wormlike chain spring force. With the ability to deform, RBCs can squeeze through narrow blood vessels. In modeling sickle cells as rigid bodies and applying repelling and friction forces from the blood vessel, this study shows that geometrical factors (dimensions of the sickle cell and blood vessels) as well as rigidity and adhesiveness of the sickle cell all play an important role in determining how, and if, sickle cells become trapped within narrow blood capillaries. With lack of data to validate the model, this study primarily provides a sensitivity analysis of factors influencing sickle cell occlusion and identified critical data to support future modeling.
This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow comp... more This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors. We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.
2012 IEEE Power and Energy Society General Meeting, 2012
Neighboring regional transmission organizations (RTO) and independent system operators (ISOs) exc... more Neighboring regional transmission organizations (RTO) and independent system operators (ISOs) exchange electric power to enable efficient and reliable operation of the grid. Net interchange (NI) schedule is the sum of the transactions (in MW) between an RTO/ISO and its neighbors. Effective forecasting of the amount of actual NI can improve grid operation efficiency and avoid the volatility of the energy markets due to changes of NI schedules. This paper presents results of a preliminary investigation into various methods of prediction that may result in improved prediction accuracy. The methods studied are linear regression, forward regression, stepwise regression, and support vector machine (SVM) regression. The effectiveness of these methods is compared using the 64 weeks of field measurement data from PJM. The objective is to explore the effectiveness of the prediction methods under different scenarios.
UNCERTAINTY QUANTIFICATION IN DYNAMIC SIMULATIONS OF LARGE-SCALE POWER SYSTEM MODELS USING THE HIGH-ORDER PROBABILISTIC COLLOCATION METHOD ON SPARSE GRIDS
International Journal for Uncertainty Quantification, 2014
In this study, we present a new numerical model for crystal growth in a vertical solidification s... more In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.
The hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM '07] has been successfull... more The hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM '07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential non-oscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.
ABSTRACT The Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program operates ... more ABSTRACT The Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program operates observation sites with numerous instruments to simultaneously quantify surface meteorological conditions, vertical profiles of clouds and other atmospheric constituents, and radiative parameters. In this study, uncertainties are placed on observations taken at the DOE ARM Southern Great Plains (SGP) site in Oklahoma in order to use this suite of observations to calibrate climate model parameters impacting the hydrological cycle. Instrument specifications, field conditions, quality control screening, and missing data are used to assign uncertainties to data streams and propagate them through to averages of interest. The additional uncertainty of comparing measurements between a point observation and a model grid box is investigated using observations from the SGP extended facilities. Preliminary investigations are done using surface meteorology variables like relative humidity and precipitation with plans to extend the analysis to additional variables in the future.
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