4,628 research outputs found
A Unique "Nonnegative" Solution to an Underdetermined System: from Vectors to Matrices
This paper investigates the uniqueness of a nonnegative vector solution and
the uniqueness of a positive semidefinite matrix solution to underdetermined
linear systems. A vector solution is the unique solution to an underdetermined
linear system only if the measurement matrix has a row-span intersecting the
positive orthant. Focusing on two types of binary measurement matrices,
Bernoulli 0-1 matrices and adjacency matrices of general expander graphs, we
show that, in both cases, the support size of a unique nonnegative solution can
grow linearly, namely O(n), with the problem dimension n. We also provide
closed-form characterizations of the ratio of this support size to the signal
dimension. For the matrix case, we show that under a necessary and sufficient
condition for the linear compressed observations operator, there will be a
unique positive semidefinite matrix solution to the compressed linear
observations. We further show that a randomly generated Gaussian linear
compressed observations operator will satisfy this condition with
overwhelmingly high probability
Particle-resolved thermal lattice Boltzmann simulation using OpenACC on multi-GPUs
We utilize the Open Accelerator (OpenACC) approach for graphics processing
unit (GPU) accelerated particle-resolved thermal lattice Boltzmann (LB)
simulation. We adopt the momentum-exchange method to calculate fluid-particle
interactions to preserve the simplicity of the LB method. To address load
imbalance issues, we extend the indirect addressing method to collect
fluid-particle link information at each timestep and store indices of
fluid-particle link in a fixed index array. We simulate the sedimentation of
4,800 hot particles in cold fluids with a domain size of , and the
simulation achieves 1750 million lattice updates per second (MLUPS) on a single
GPU. Furthermore, we implement a hybrid OpenACC and message passing interface
(MPI) approach for multi-GPU accelerated simulation. This approach incorporates
four optimization strategies, including building domain lists, utilizing
request-answer communication, overlapping communications with computations, and
executing computation tasks concurrently. By reducing data communication
between GPUs, hiding communication latency through overlapping computation, and
increasing the utilization of GPU resources, we achieve improved performance,
reaching 10846 MLUPS using 8 GPUs. Our results demonstrate that the
OpenACC-based GPU acceleration is promising for particle-resolved thermal
lattice Boltzmann simulation.Comment: 45 pages, 18 figure
Wall-sheared thermal convection: heat transfer enhancement and turbulence relaminarization
We studied the flow organization and heat transfer properties in
two-dimensional and three-dimensional Rayleigh-B\'enard cells that are imposed
with different types of wall shear. The external wall shear is added with the
motivation of manipulating flow mode to control heat transfer efficiency. We
imposed three types of wall shear that may facilitate the single-roll, the
horizontally stacked double-roll, and the vertically stacked double-roll flow
modes, respectively. Direct numerical simulations are performed for fixed
Rayleigh number and fixed Prandtl number , while the
wall-shear Reynolds number () is in the range .
Generally, we found enhanced heat transfer efficiency and global flow strength
with the increase of . However, even with the same magnitude of global
flow strength, the heat transfer efficiency varies significantly when the cells
are under different types of wall shear. An interesting finding is that by
increasing the wall-shear strength, the thermal turbulence is relaminarized,
and more surprisingly, the heat transfer efficiency in the laminar state is
higher than that in the turbulent state. We found that the enhanced heat
transfer efficiency at the laminar regime is due to the formation of more
stable and stronger convection channels. We propose that the origin of thermal
turbulence laminarization is the reduced amount of thermal plumes. Because
plumes are mainly responsible for turbulent kinetic energy production, when the
detached plumes are swept away by the wall shear, the reduced number of plumes
leads to weaker turbulent kinetic energy production. We also quantify the
efficiency of facilitating heat transport via external shearing, and find that
for larger , the enhanced heat transfer efficiency comes at a price of
a larger expenditure of mechanical energy.Comment: 27 pages, 16 figure
- β¦