4,613 research outputs found
An introduction to uncertainty quantification for kinetic equations and related problems
We overview some recent results in the field of uncertainty quantification
for kinetic equations and related problems with random inputs. Uncertainties
may be due to various reasons, such as lack of knowledge on the microscopic
interaction details or incomplete information at the boundaries or on the
initial data. These uncertainties contribute to the curse of dimensionality and
the development of efficient numerical methods is a challenge. After a brief
introduction on the main numerical techniques for uncertainty quantification in
partial differential equations, we focus our survey on some of the recent
progress on multi-fidelity methods and stochastic Galerkin methods for kinetic
equations
Error estimates of a bi-fidelity method for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with random inputs
Uniform error estimates of a bi-fidelity method for a kinetic-fluid coupled
model with random initial inputs in the fine particle regime are proved in this
paper. Such a model is a system coupling the incompressible Navier-Stokes
equations to the Vlasov-Fokker-Planck equations for a mixture of the flows with
distinct particle sizes. The main analytic tool is the hypocoercivity analysis
for the multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with
uncertainties, considering solutions in a perturbative setting near the global
equilibrium. This allows us to obtain the error estimates in both kinetic and
hydrodynamic regimes
Accelerating moderately stiff chemical kinetics in reactive-flow simulations using GPUs
The chemical kinetics ODEs arising from operator-split reactive-flow
simulations were solved on GPUs using explicit integration algorithms. Nonstiff
chemical kinetics of a hydrogen oxidation mechanism (9 species and 38
irreversible reactions) were computed using the explicit fifth-order
Runge-Kutta-Cash-Karp method, and the GPU-accelerated version performed faster
than single- and six-core CPU versions by factors of 126 and 25, respectively,
for 524,288 ODEs. Moderately stiff kinetics, represented with mechanisms for
hydrogen/carbon-monoxide (13 species and 54 irreversible reactions) and methane
(53 species and 634 irreversible reactions) oxidation, were computed using the
stabilized explicit second-order Runge-Kutta-Chebyshev (RKC) algorithm. The
GPU-based RKC implementation demonstrated an increase in performance of nearly
59 and 10 times, for problem sizes consisting of 262,144 ODEs and larger, than
the single- and six-core CPU-based RKC algorithms using the
hydrogen/carbon-monoxide mechanism. With the methane mechanism, RKC-GPU
performed more than 65 and 11 times faster, for problem sizes consisting of
131,072 ODEs and larger, than the single- and six-core RKC-CPU versions, and up
to 57 times faster than the six-core CPU-based implicit VODE algorithm on
65,536 ODEs. In the presence of more severe stiffness, such as ethylene
oxidation (111 species and 1566 irreversible reactions), RKC-GPU performed more
than 17 times faster than RKC-CPU on six cores for 32,768 ODEs and larger, and
at best 4.5 times faster than VODE on six CPU cores for 65,536 ODEs. With a
larger time step size, RKC-GPU performed at best 2.5 times slower than six-core
VODE for 8192 ODEs and larger. Therefore, the need for developing new
strategies for integrating stiff chemistry on GPUs was discussed.Comment: 27 pages, LaTeX; corrected typos in Appendix equations A.10 and A.1
An efficient surrogate model for emulation and physics extraction of large eddy simulations
In the quest for advanced propulsion and power-generation systems,
high-fidelity simulations are too computationally expensive to survey the
desired design space, and a new design methodology is needed that combines
engineering physics, computer simulations and statistical modeling. In this
paper, we propose a new surrogate model that provides efficient prediction and
uncertainty quantification of turbulent flows in swirl injectors with varying
geometries, devices commonly used in many engineering applications. The novelty
of the proposed method lies in the incorporation of known physical properties
of the fluid flow as {simplifying assumptions} for the statistical model. In
view of the massive simulation data at hand, which is on the order of hundreds
of gigabytes, these assumptions allow for accurate flow predictions in around
an hour of computation time. To contrast, existing flow emulators which forgo
such simplications may require more computation time for training and
prediction than is needed for conducting the simulation itself. Moreover, by
accounting for coupling mechanisms between flow variables, the proposed model
can jointly reduce prediction uncertainty and extract useful flow physics,
which can then be used to guide further investigations.Comment: Submitted to JASA A&C
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