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Machine Learning Approaches for the Solution of the Riemann Problem in Fluid Dynamics:a Case Study

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Communications on Applied Mathematics and Computation 2024年第3期6卷 1832-1859页

作者： Vitaly Gyrya Mikhail Shashkov Alexei Skurikhin Svetlana Tokareva Los Alamos National Laboratory Applied Mathematics and Plasma Physics(T-5)Los AlamosUSA Los Alamos National Laboratory Continuum Models and Numerical Methods(XCP-4)Los AlamosUSA Los Alamos National Laboratory Space Data Science and Systems(ISR-3)Los AlamosUSA

We present our results by using a machine learning(ML)approach for the solution of the Riemann problem for the Euler equations of fluid *** Riemann problem is an initial-value problem with piecewise-constant initial data and it represents a mathematical model of the shock *** solution of the Riemann problem is the building block for many numerical algorithms in computational fluid dynamics,such as finite-volume or discontinuous Galerkin ***,a fast and accurate approximation of the solution of the Riemann problem and construction of the associated numerical fluxes is of crucial *** exact solution of the shock tube problem is fully described by the intermediate pressure and mathematically reduces to finding a solution of a nonlinear *** to delving into the complexities of ML for the Riemann problem,we consider a much simpler formulation,yet very informative,problem of learning roots of quadratic equations based on their *** compare two approaches:(i)Gaussian process(GP)regressions,and(ii)neural network(NN)*** these approaches,NNs prove to be more robust and efficient,although GP can be appreciably more accurate(about 30\%).We then use our experience with the quadratic equation to apply the GP and NN approaches to learn the exact solution of the Riemann problem from the initial data or coefficients of the gas equation of state(EOS).We compare GP and NN approximations in both regression and classification analysis and discuss the potential benefits and drawbacks of the ML approach.

关键词： Machine learning(ML) Neural network(NN) Gaussian process(GP) Riemann problem numerical fluxes Finite-volume method

Optimization of Artificial Viscosity in Production Codes Based on Gaussian Regression Surrogate models

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Communications on Applied Mathematics and Computation 2024年第3期6卷 1521-1550页

作者： Vitaliy Gyrya Evan Lieberman Mark Kenamond Mikhail Shashkov Applied Mathematics and Plasma Physics Theoretical DivisionMail Stop B284Los Alamos National LaboratoryLos AlamosNM 87545USA continuum models and numerical methods group X-Computational Physics DivisionMail Stop F644Los Alamos National LaboratoryLos AlamosNM 87545USA Lagrangian Codes group X-Computational Physics DivisionMail Stop T086Los Alamos National LaboratoryLos AlamosNM 87545USA

To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, the artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of the artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression (GPR) and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG (Burton in Connectivity structures and differencing techniques for staggered-grid free-Lagrange hydrodynamics, Tech. Rep. UCRL-JC-110555, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1992, in Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids, Tech. Rep. CRL-JC-118788, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, Multidimensional discretization of conservation laws for unstructured polyhedral grids, Tech. Rep. UCRL-JC-118306, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, in FLAG, a multi-dimensional, multiple mesh, adaptive free-Lagrange, hydrodynamics code. In: NECDC, 1992). First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize the viscosity for a one-dimensional (1D) propagating detonation problem based on Zel’dovich-von Neumann-Doring (ZND) (Fickett and Davis in Detonation: theory and experiment. Dover books on physics. Dover Publications, Mineola, 2000) detonation theory using a reactive burn model. We compare re

关键词： Optimization Artificial viscosity Gaussian regression surrigate model

numerical analysis of anisotropic stiffness and strength for geomaterials

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Journal of Rock Mechanics and Geotechnical Engineering 2023年第2期15卷 323-338页

作者： Fei Song Manuel A.González-Fernández Alfonso Rodriguez-Dono Leandro R.Alejano Department of Civil and Environmental Engineering Universitat Politècnica de Catalunya(UPC)Barcelona08034Spain CINTECX GESSMin GroupDepartment of Natural Resources and Environmental EngineeringUniversity of VigoVigo36310Spain International Centre for numerical methods in Engineering(CIMNE) Barcelona08034Spain

In numerical modelling,selection of the constitutive model is a critical factor in predicting the actual response of a *** use of oversimplified or inadequate models may not be sufficient to reproduce the actual geomaterial *** selection is especially relevant in the case of aniso-tropic rocks,and particularly for shales and slates,whose behaviour may be affected,*** stability in geothermal or oil and gas production *** this paper,an alternative anisotropic constitutive model has been implemented in the finite element method software CODE_BRIGHT,which is able to account for the anisotropy of shales and slates in terms of both deformability and *** this purpose,a transversely isotropic version of the generalised Hooke’s law is adopted to represent the stiffness anisotropy,while a nonuniform scaling of the stress tensor is introduced in the plastic model to represent the strength ***,a detailed approach has been proposed to determine the model parameters based on the stressestrain results of laboratory ***,numerical analyses are performed to model uniaxial and triaxial tests on Vaca Muerta shale,Bossier shale and slate from the northwest of Spain(NW Spain slate).The experimental data have been recovered from the literature in the case of the shale and,in the case of the slate,performed by the authors in terms of stress-strain curves and strengths.A good agreement can be generally observed between numerical and experi-mental results,hence showing the potential applicability of the approach to actual case ***,the presented constitutive model may be a promising approach for analysing the anisotropic behaviour of rocks and its impact on well stability or other relevant geomechanical problems in aniso-tropic rocks.

关键词： Rock mechanics Anisotropy numerical modelling CODE_BRIGHT Shale Slate

A Review on Aspects of Climate Simulation Assessment

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Advances in Atmospheric Sciences 2009年第4期26卷 736-747页

作者：王斌谢歆李立娟 State Key Laboratory of numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of Sciences Graduate University of Chinese Academy of Sciences

This paper reviews some aspects of evaluation of climate simulation, including the ITCZ, the surface air temperature （SAT）, and the monsoon. A brief introduction of some recently proposed approaches in weather forecast verification is followed by a discussion on their possible application to evaluation of climate simulation. The authors suggest five strategies to extend the forecast verification methods to climate simulation evaluation regardless significant differences between the forecasts and climate simulations. It is argued that resolution, convection scheme, stratocumulus cloud cover, among other processes in the atmospheric general circulation model （AGCM） and the ocean-atmosphere feedback are the potential causes for the double ITCZ problem in coupled models and AGCM simulations, based on the system- and component-level evaluations as well as the downscaling strategies in some recent research. Evaluations of simulated SAT and monsoons suggest that both coupled models and AGCMs show good performance in representing the SAT evolution and its variability over the past century in terms of correlation and wavelet analysis but poor at reproducing rainfall, and in addition, the AGCM alone is not suitable for monsoon regions due to the lack of air-sea interactions.

关键词： climate simulation evaluation forecast verification ITCZ surface air temperature monsoon

A discrete contact model for complex arbitrary-shaped convex geometries

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Particuology 2023年第9期80卷 180-191页

作者： Jan E.Marquardt Ulrich J.Römer Hermann Nirschl Mathias J.Krause Lattice Boltzmann Research group Karlsruhe Institute of TechnologyStraße am Forum 8Karlsruhe76131Germany Institute for Mechanical Process Engineering and Mechanics Karlsruhe Institute of TechnologyStraße am Forum 8Karlsruhe76131Germany Institute of Engineering Mechanics Karlsruhe Institute of TechnologyKaiserstraße 10Karlsruhe76131Germany Institute for Applied and numerical Mathematics Karlsruhe Institute of TechnologyEnglerstraße 2Karlsruhe76131Germany

The shape of particles has a significant influence on the behavior of suspensions,as the particle-fluid,particle-particle,and particle-wall interactions depend on ***,the simultaneous consideration of complex particle shapes and four-way coupling remains a major *** is mainly due to a lack of suitable contact *** models for complex shapes have been proposed in literature,and most limit the accuracy of the particle-fluid *** this reason,this paper presents a novel contact model for complex convex particle shapes for use with partially saturated methods,in which we propose to obtain necessary contact properties,such as the indentation depth,by a discretization of the contact *** goal of the proposed model is to enable comprehensive and accurate studies of particulate flows,especially with high volume fractions,that lead to new insights and contribute to the improvement of existing industrial *** ensure correctness and sustainability,we validate the model extensively by studying cases with and without *** the latter case,we use the homogenized lattice Boltzmann *** provided investigations show a great agreement of the proposed discrete contact model with analytical solutions and the literature.

关键词： Partially saturated cells method Homogenized lattice Boltzmann method Arbitrarily shaped particle Discrete contact model Particle-resolved simulation OpenLB

An Efficient Multi-Scale Modelling Approach for ssDNA Motion in Fluid Flow

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Journal of Bionic Engineering 2008年第4期5卷 299-307页

作者： M. Benke E. Shapiro D. Drikakis Fluid Mechanics and Computational Science group Department of Aerospace Sciences Cranfield University

The paper presents a multi-scale modelling approach for simulating macromolecules in fluid flows. Macromolecule transport at low number densities is frequently encountered in biomedical devices, such as separators, detection and analysis systems. Accurate modelling of this process is challenging due to the wide range of physical scales involved. The continuum approach is not valid for low solute concentrations, but the large timescales of the fluid flow make purely molecular simulations prohibitively expensive. A promising multi-scale modelling strategy is provided by the meta-modelling approach considered in this paper. Meta-models are based on the coupled solution of fluid flow equations and equations of motion for a simplified mechanical model of macromolecules. The approach enables simulation of individual macromolecules at macroscopic time scales. Meta-models often rely on particle-corrector algorithms, which impose length constraints on the mechanical model. Lack of robustness of the particle-corrector algorithm employed can lead to slow convergence and numerical instability. A new FAst Linear COrrector （FALCO） algorithm is introduced in this paper, which significantly improves computational efficiency in comparison with the widely used SHAKE algorithm. Validation of the new particle corrector against a simple analytic solution is performed and improved convergence is demonstrated for ssDNA motion in a lid-driven micro-cavity.

关键词： multi-scale modelling DNA macromolecule transport meta-modelling particle corrector

Nonlinear analysis of traffic jams in an anisotropic continuum model

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Chinese Physics B 2010年第11期19卷 156-164页

作者： Arvind Kumar Gupta Sapna Sharma Department of Mathematics IIT Ropar-140001India Mathematics group Birla Institute of Technology and SciencePilani-333031India

This paper presents our study of the nonlinear stability of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence. In order to establish traff^c flow stability criterion or to know the critical parameters that lead, on one hand, to a stable response to perturbations or disturbances or, on the other hand, to an unstable response and therefore to a possible congestion, a nonlinear stability criterion is derived by using a wavefront expansion technique. The stability criterion is illustrated by numerical results using the finite difference method for two different values of anisotropic parameter. It is also been observed that the newly derived stability results are consistent with previously reported results obtained using approximate linearisation methods. Moreover, the stability criterion derived in this paper can provide more refined information from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic than previously established methodologies.

关键词： traffic flow non-linear stability wavefront method

numerical evaluation of strength and deformability of fractured rocks

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Journal of Rock Mechanics and Geotechnical Engineering 2013年第6期5卷 419-430页

作者： Majid Noorian Bidgoli Zhihong Zhao Lanru Jing Department of Land and Water Resources Engineering Engineering Geology and Geophysics Research GroupRoyal Institute of Technology (KTH) Department of Geological Sciences Stockholm University

Knowledge of the strength and deformability of fractured rocks is important for design, construction and stability evaluation of slopes, foundations and underground excavations in civil and mining engineering. However, laboratory tests of intact rock samples cannot provide information about the strength and deformation behaviors of fractured rock masses that include many fractures of varying sizes, orientations and locations. On the other hand, large-scale in situ tests of fractured rock masses are economically costly and often not practical in reality at present. Therefore, numerical modeling becomes necessary. numerical predicting using discrete element methods(DEM) is a suitable approach for such modeling because of their advantages of explicit representations of both fractures system geometry and their constitutive behaviors of fractures, besides that of intact rock matrix. In this study, to generically determine the compressive strength of fractured rock masses, a series of numerical experiments were performed on two-dimensional discrete fracture network models based on the realistic geometrical and mechanical data of fracture systems from feld mapping. We used the UDEC code and a numerical servo-controlled program for controlling the progressive compressive loading process to avoid sudden violent failure of the models. The two loading conditions applied are similar to the standard laboratory testing for intact rock samples in order to check possible differences caused by such loading conditions. numerical results show that the strength of fractured rocks increases with the increasing confning pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening. The stresses and strains obtained from these numerical experiments were used to ft the well-known Mohr-Coulomb(MC) and Hoek-Brown(H-B) failure criteria, represented by equivalent material properties defning these two criteria. The results show that bot

关键词： Strength Deformability Fractured rocks Discrete element methods(DEM) Failure criteria

Impacts of major volcanic eruptions over the past two millennia on both global and Chinese climates:A review

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Science China Earth Sciences 2024年第1期67卷 61-78页

作者： Weiyi SUN Deliang CHEN Guonian LÜ Liang NING Chaochao GAO Renhe ZHANG Bin WANG Jian LIU Key Laboratory for Virtual Geographic Environment Ministry of EducationState Key Laboratory Cultivation Base of Geographical Environment Evolution of Jiangsu ProvinceJiangsu Center for Collaborative Innovation in Geographical Information Resource Development and ApplicationSchool of Geography ScienceNanjing Normal UniversityNanjing 210023China Regional Climate group Department of Earth SciencesUniversity of GothenburgGothenburg 40530Sweden College of Environmental and Resource Science Zhejiang UniversityHangzhou 310058China Department of Atmospheric and Oceanic Sciences&Institute of Atmospheric Sciences Fudan UniversityShanghai 200437China Department of Atmospheric Sciences and Atmosphere-Ocean Research Center University of Hawaii at ManoaHonoluluHI 96825USA Jiangsu Provincial Key Laboratory for numerical Simulation of Large Scale Complex Systems School of Mathematical ScienceNanjing Normal UniversityNanjing 210023China Open Studio for the Simulation of Ocean-Climate-Isotope Qingdao National Laboratory for Marine Science and TechnologyQingdao 266237China

Major volcanic eruptions(MVEs)have attracted increasing attention from the scientific *** studies have explored the climatic impact of MVEs over the past two ***,proxy-based reconstructions and climate model simulations indicate divergent responses of global and China’s regional climates to ***,we used multiple data from observations,reconstructions,simulations,and assimilations to summarize the historical facts of MVEs,the characteristics and mechanisms of their climatic impact,and directions for future *** reviewed volcanic datasets and determined intensive MVE periods;these periods corresponded to the years 530–700,1200‒1460,and 1600‒1840 *** tropical MVEs,a substantial cooling effect is observed throughout the globe and China on the interannual-interdecadal time scales but an inconsistent cooling magnitude is detected between reconstructions and *** the first summer after tropical MVEs,a decrease in global and monsoonal precipitation is *** reconstructions and simulations,an increased precipitation is seen for the Yangtze River Basin,while large uncertainties in precipitation changes are present for other regions of *** drought can be induced by frequent eruptions and volcanism superimposed on low solar irradiation and internal *** affect climate directly through the radiative effect and indirectly by modulating internal variability,such as the El Niño‒Southern Oscillation(ENSO)and Atlantic Multidecadal Oscillation(AMO).However,changes in the phase,amplitude,and periodicity of ENSO and AMO after MVEs and the associated mechanisms remain controversial,which could account for model-reconstruction ***,other internal variability,uncertainties in reconstruction methods and aerosol‒climate models,and climate background may also induce model-reconstruction *** gaps and directions for future research are also discussed.

关键词： Major volcanic eruption Climate variability Mechanism Past two millennia Internal variability