20,825 research outputs found
Stochastic collocation on unstructured multivariate meshes
Collocation has become a standard tool for approximation of parameterized
systems in the uncertainty quantification (UQ) community. Techniques for
least-squares regularization, compressive sampling recovery, and interpolatory
reconstruction are becoming standard tools used in a variety of applications.
Selection of a collocation mesh is frequently a challenge, but methods that
construct geometrically "unstructured" collocation meshes have shown great
potential due to attractive theoretical properties and direct, simple
generation and implementation. We investigate properties of these meshes,
presenting stability and accuracy results that can be used as guides for
generating stochastic collocation grids in multiple dimensions.Comment: 29 pages, 6 figure
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is computationally demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reactiondiffusion equations. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is show-cased by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models,together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator
A fast, low-memory, and stable algorithm for implementing multicomponent transport in direct numerical simulations
Implementing multicomponent diffusion models in reacting-flow simulations is
computationally expensive due to the challenges involved in calculating
diffusion coefficients. Instead, mixture-averaged diffusion treatments are
typically used to avoid these costs. However, to our knowledge, the accuracy
and appropriateness of the mixture-averaged diffusion models has not been
verified for three-dimensional turbulent premixed flames. In this study we
propose a fast,efficient, low-memory algorithm and use that to evaluate the
role of multicomponent mass diffusion in reacting-flow simulations. Direct
numerical simulation of these flames is performed by implementing the
Stefan-Maxwell equations in NGA. A semi-implicit algorithm decreases the
computational expense of inverting the full multicomponent ordinary diffusion
array while maintaining accuracy and fidelity. We first verify the method by
performing one-dimensional simulations of premixed hydrogen flames and compare
with matching cases in Cantera. We demonstrate the algorithm to be stable, and
its performance scales approximately with the number of species squared. Then,
as an initial study of multicomponent diffusion, we simulate premixed,
three-dimensional turbulent hydrogen flames, neglecting secondary Soret and
Dufour effects. Simulation conditions are carefully selected to match
previously published results and ensure valid comparison. Our results show that
using the mixture-averaged diffusion assumption leads to a 15% under-prediction
of the normalized turbulent flame speed for a premixed hydrogen-air flame. This
difference in the turbulent flame speed motivates further study into using the
mixture-averaged diffusion assumption for DNS of moderate-to-high Karlovitz
number flames.Comment: 36 pages, 14 figure
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