Physics

In this paper, we propose a hybrid lattice Boltzmann method (HLBM) for solving fluid-structure interaction problems. The proposed numerical approach is applied to model the flow induced by a vibrating thin lamina submerged in a viscous quiescent fluid. The hydrodynamic force exerted by the fluid on the solid body is described by means of a complex hydrodynamic function, whose real and imaginary parts are determined via parametric analysis. Numerical results are validated by comparison with those from other numerical as well as experimental works available in the literature. The proposed hybrid approach enhances the capability of lattice Boltzmann methods to solve fluid dynamic problems involving moving geometries.

We propose a multi-component discrete Boltzmann model (DBM) for premixed, nonpremixed, or partially premixed nonequilibrium reactive flows. This model is suitable for both subsonic and supersonic flows with or without chemical reaction and/or external force. A two-dimensional sixteen-velocity model is constructed for the DBM. In the hydrodynamic limit, the DBM recovers the modified Navier-Stokes equations for reacting species in a force field. Compared to standard lattice Boltzmann models, the DBM presents not only more accurate hydrodynamic quantities, but also detailed nonequilibrium effects that are essential yet long-neglected by traditional fluid dynamics. Apart from nonequilibrium terms (viscous stress and heat flux) in conventional models, specific hydrodynamic and thermodynamic nonequilibrium quantities (high order kinetic moments and their departure from equilibrium) are dynamically obtained from the DBM in a straightforward way. Due to its generality, the developed methodology is applicable to a wide range of phenomena across many energy technologies, emissions reduction, environmental protection, mining accident prevention, chemical and process industry.

Algorithms based on deep neural networks (DNNs) have attracted increasing attention from the scientific computing community. DNN based algorithms are easy to implement, natural for nonlinear problems, and have shown great potential to overcome the curse of dimensionality. In this work, we utilize the multi-scale DNN-based algorithm (MscaleDNN) proposed by Liu, Cai and Xu (2020) to solve multi-scale elliptic problems with possible nonlinearity, for example, the p-Laplacian problem. We improve the MscaleDNN algorithm by a smooth and localized activation function. Several numerical examples of multi-scale elliptic problems with separable or non-separable scales in low-dimensional and high-dimensional Euclidean spaces are used to demonstrate the effectiveness and accuracy of the MscaleDNN numerical scheme.

The numerical simulation of fluid flow through a complex geometry with heat transfer is of strong interest for many applications, such as oil-filled power transformers. A fundamental challenge here is that high resolution is necessary to resolve the fluid flow phenomena, but this makes simulation of the full geometry very expensive in terms of computational power. In this work, we develop a simulation methodology that combines a porous-medium approach for simulating some regions of the domain, coupled with fully resolved simulations in those regions which are deemed most interesting to study in detail. As one does not resolve flow features like thermal boundary layers in the regions modeled with the porous approach, the resolution in these parts can be orders of magnitude coarser. This multiscale approach is validated against the use of fully resolved simulations in the whole domain, as well as against analytical solutions to the extended Graetz problem. We then apply the approach to the study of oil flow and heat transfer in large electric power transformers and demonstrate a significant reduction in computational cost compared to a fully resolved approach.

We present a deep neural network multigrid solver (DNN-MG) that we develop for the instationary Navier-Stokes equations. DNN-MG improves computational efficiency using a judicious combination of a geometric multigrid solver and a recurrent neural network with memory. The multigrid method is used in DNN-MG to solve on coarse levels while the neural network corrects interpolated solutions on fine ones, thus avoiding the increasingly expensive computations that would have to be performed on there. A reduction in computation time is thereby achieved through DNN-MG's highly compact neural network. The compactness results from its design for local patches and the available coarse multigrid solutions that provides a "guide" for the corrections. A compact neural network with a small number of parameters also reduces training time and data. Furthermore, the network's locality facilitates generalizability and allows one to use DNN-MG trained on one mesh domain also on an entirely different one. We demonstrate the efficacy of DNN-MG for variations of the 2D laminar flow around an obstacle. For these, our method significantly improves the solutions as well as lift and drag functionals while requiring only about half the computation time of a full multigrid solution. We also show that DNN-MG trained for the configuration with one obstacle can be generalized to other time dependent problems that can be solved efficiently using a geometric multigrid method.

To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of the classical Fast Multipole Method, result in a cost per Metropolis-Hastings step which grows in proportion to some positive power of the number of particles N in the system. This prohibitively large cost prevents accurate simulations of systems with a sizeable number of particles. Currently, large systems are often simulated by truncating the Coulomb potential which introduces uncontrollable systematic errors. In this paper we present a new multilevel method which reduces the computational complexity to O(log(N)) per Metropolis-Hastings step, while maintaining errors which are comparable to direct Ewald summation. We show that compared to related previous work, our approach reduces the overall cost by better balancing time spent in the proposal- and acceptance- stages of each Metropolis-Hastings step. By simulating large systems with up to N= 10 5 particles we demonstrate that our implementation is competitive with state-of-the-art MC packages and allows the simulation of very large systems of charged particles with accurate electrostatics.

The high-Tc superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing HTS dynamos and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark problem has been implemented using several different methods, including H-formulation-based methods, coupled H-A and T-A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. A critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom (DOFs), tolerance settings and the approximate time taken per cycle for each model.

This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal distribution functions. An iterative algorithm is proposed to match the simulated covariance function of stochastic samples to the target covariance function, and only a few times iterations can converge to a required accuracy. Several explicit representations, based on Karhunen-Loève expansion and Polynomial Chaos expansion, are further developed to represent the obtained stochastic samples in series forms. Proposed methods can be applied to non-gaussian and non-stationary stochastic processes, and three examples illustrate their accuracies and efficiencies.

The scale-resolving simulation of high speed compressible flow through direct numerical simulation (DNS) or large eddy simulation (LES) requires shock-capturing schemes to be more accurate for resolving broadband turbulence and robust for capturing strong shock waves. In this work, we develop a new paradigm of dissipation-controllable, shock capturing scheme to resolve multi-scale flow structures in high speed compressible flow. This novel paradigm of shock-capturing scheme is named as PnTm-BVD-CD. The proposed PnTm-BVD-CD scheme has following desirable properties. First, it can capture large-scale discontinuous structures such as strong shock waves without obvious non-physical oscillations while resolving sharp contact, material interface and shear layer. Secondly, the numerical dissipation property of PnTm-BVD-CD can be effectively controlled between n+1 order upwind-biased scheme and non-dissipative n+2 order central scheme through a simple tunable parameter λ . Thirdly, with λ=0.5 the scheme can recover to n+2 order non-dissipative central interpolation for smooth solution over all wavenumber, which is preferable for solving small-scale structures in DNS as well as resolvable-scale in explicit LES. Finally, the under-resolved small-scale can be solved with dissipation controllable algorithm through so-called implicit LES (ILES) approach.

Extensive set of tests on different platforms indicated that there is a performance drop of current standard de facto software library for the Discrete Fourier Transform (DFT) in case of large 2D array sizes (larger than 16384x16384). Parallel performance for Symmetric Multi Processor (SMP) systems was seriously affected. The remedy for this problem was proposed and implemented as a software library for 2D out of place complex to complex DFTs. Proposed library was thoroughly tested on different available architectures and hardware configurations and demonstrated significant (38-94%) performance boost on vast majority of them. The new library together with the testing suite and results of all tests is published as a project on this http URL platform under free software license (GNU GPL v3). Comprehensive description of programming interface as well as provided testing programs is given.