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A new algorithm for numerical modelling of impurity transport in the frame of statistically homogeneous sharply contrasting media

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RUSSIAN JOURNAL OF numerical ANALYSIS AND MATHEMATICAL MODELLING 2019年第6期34卷 339-351页

作者： Kondratenko, Petr S. Matveev, Leonid V. Vasiliev, Alexander D. Russian Acad Sci Nucl Safety Inst Bolshaya Tulskaya St 52 Moscow 115191 Russia State Univ Moscow Inst Phys & Technol 9 Inst Per Dolgoprudnyi 141700 Moscow Region Russia

A new method is developed to calculate characteristics of contaminant transport (including non-classical regimes) in statistically homogeneous sharply contrasting media. A transport integro-differential equation in the space-time representation is formulated on the basis of the model earlier proposed by one of the authors (L. M.). Analytical expressions for transport characteristics in limiting time intervals in the one-dimensional case are derived. An interpolation form is proposed for the integral kernel of the transport equation. On a basis of this expression, an algorithm is developed for numerical modelling the contaminant transport in statistically homogeneous sharply contrasting media. Trial numerical 1D calculations are performed based on this algorithm. Good agreement was found between the numerical simulation results and the asymptotic analytical expressions.

关键词： Non-equilibrium transport model non-classical transport quasi-diffusion sub-diffusion concentration asymptotics numerical algorithm

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numerical study of the process of unsteady flow in a three-layer porous medium

MAGAZINE OF CIVIL ENGINEERING

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MAGAZINE OF CIVIL ENGINEERING 2023年第3期119卷

作者： Ravshanov, R. Abdullaev, Z. S. Kotov, E. V. Turkmanova, Sh. N. Res Inst Dev Digital Technol & Artificial Intellig Tashkent Uzbekistan Tashkent Inst Irrigat & Agr Mechanizat Engineers Tashkent Uzbekistan Peter Great St Petersburg Polytech Univ St Petersburg Russia

The unsteady fluid flow in a three-layer porous medium is numerically investigated and is an important and topical problem. An analytical solution of the equation for the pressure fluid layer is obtained on the basis of the theory of elastic regime, taking into account the overflow from the coating and the low -permeability layer into the low-permeability bulkhead and external sources that greatly affect the liquid level change. In the main bounded aquifer only horizontal liquid migrations prevail, and in the cover and low -conductive layers only vertical migrations prevail, allowing for horizontal components of the flow rate to be omitted here. Evaporation from the surface of a liquid in a porous medium is considered. Evaporation from the surface of a liquid in a porous medium significantly affects the distribution of overflows in the layers and the distribution of the liquid level in a porous medium. Therefore, when designing vertical drains for enhanced oil recovery in multilayer reservoirs and designing fluid flows in reservoirs, evaporation must be taken into account. The computational experiments have established that the dynamics of changes in the liquid level in a porous medium depends significantly on the evaporation parameter. With an increase in its value, the liquid level in a porous medium decreases proportionally over time. The accuracy of the numerical solution using the balance equation showed that the error does not exceed 1.3%.

关键词： mathematical model groundwater filtration analytical solution numerical algorithm

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A Novel Fractional Plastic Damage Model for Quasi-brittle Materials

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Acta Mechanica Solida Sinica 2021年第5期34卷 706-717页

作者： Peng-Fei Qu Qi-Zhi Zhu Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering Hohai UniversityNanjing210098China College of Civil and Transportation Engineering Hohai UniversityNanjing210098China

In this work,a novel constitutive model is developed within the framework of fractional plasticity to delineate the coupling between inelastic deformation and damage of quasi-brittle *** with the common challenge of determining plastic flow direction,we resort herein to the Riemann–Liouville definition of fractional derivatives,instead of introducing an additional plastic *** pre-peak hardening behavior is described using an exponential function,while the post-peak softening response is viewed as the consequence of material *** describing damage evolution,a damage criterion is constructed in terms of plastic volume dilation related to micro-crack *** is conducive to supply a new insight for describing the complex influence of the non-orthogonality of plastic flow on damage *** numerical applications,a semi-implicit return mapping algorithm is *** predictive performance of the model is evaluated by comparing numerical simulations with experimental data under various loading paths.

关键词： Quasi-brittle materials Fractional plasticity Damage Dilatancy numerical algorithm

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algorithms for Stochastically Rounded Elementary Arithmetic Operations in IEEE 754 Floating-Point Arithmetic

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTING 2021年第3期9卷 1451-1466页

作者： Fasi, Massimiliano Mikaitis, Mantas Orebro Univ Sch Sci & Technol S-70182 Orebro Sweden Univ Manchester Dept Math Manchester M13 9PL Lancs England

We present algorithms for performing the five elementary arithmetic operations (+, -, x, divided by, and root) in floating point arithmetic with stochastic rounding, and demonstrate the value of these algorithms by discussing various applications where stochastic rounding is beneficial. The algorithms require that the hardware be compliant with the IEEE 754 floating-point standard and that a floating-point pseudorandom number generator be available. The goal of these techniques is to emulate stochastic rounding when the underlying hardware does not support this rounding mode, as is the case for most existing CPUs and GPUs. By simulating stochastic rounding in software, one has the possibility to explore the behavior of this rounding mode and develop new algorithms even without having access to hardware implementing stochastic rounding- once such hardware becomes available, it suffices to replace the proposed algorithms by calls to the corresponding hardware routines. When stochastically rounding double precision operations, the algorithms we propose are between 7.3 and 19 times faster than the implementations that use the GNU MPFR library to simulate extended precision. We test our algorithms on various tasks, including summation algorithms and solvers for ordinary differential equations, where stochastic rounding is expected to bring advantages.

关键词： Stochastic processes Hardware Standards Tools Software Libraries Monte Carlo methods Floating-point arithmetic error-free transformation stochastic rounding numerical analysis numerical algorithm IEEE 754

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Regret-based budgeted decision rules under severe uncertainty

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INFORMATION SCIENCES 2024年 665卷

作者： Nakharutai, Nawapon Destercke, Sebastien Troffaes, Matthias C. M. Chiang Mai Univ Fac Sci Dept Stat Chiang Mai 50200 Thailand Univ Technol Compiegne Sorbonne Univ CNRS UMR Heudiasyc 7253 F-60200 Compiegne France Univ Durham Dept Math Sci Durham DH1 3LE England

One way to make decisions under uncertainty is to select an optimal option from a possible range of options, by maximizing the expected utilities derived from a probability model. However, under severe uncertainty, identifying precise probabilities is hard. For this reason, imprecise probability models uncertainty through convex sets of probabilities, and considers decision rules that can return multiple options to reflect insufficient information. Many well-founded decision rules have been studied in the past, but none of those standard rules are able to control the number of returned alternatives. This can be a problem for large decision problems, due to the cognitive burden decision makers have to face when presented with a large number of alternatives. Our contribution proposes regret-based ideas to construct new decision rules which return a bounded number of options, where the limit on the number of options is set in advance by the decision maker as an expression of their cognitive limitation. We also study their consistency and numerical behaviour.

关键词： Decision Regret Minimax Maximin Imprecise probability Optimization numerical algorithm

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Free Rocking of a Rigid Block on a Flexible Structure with Non-Smooth Contact Dynamics

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APPLIED SCIENCES-BASEL 2024年第15期14卷 6483页

作者： Mudric, Teo Ceh, Nina Hante, Stefan Arnold, Martin Univ Rijeka Fac Civil Engn Radmile Matejcic 3 Rijeka 51000 Croatia Martin Luther Univ Halle Wittenberg Inst Math Theodor Lieser St 5 D-06120 Halle Halle Germany

When structures are subjected to dynamic loading, such as that caused by an earthquake or working machinery, the rocking behavior of objects located on parts of the loaded structure plays an important role in addressing the protection and stability of non-structural components. In this work, the free rocking of a rigid block on a flexible beam and rigid base was investigated using numerical simulations. To this end, a numerical code based on the non-smooth contact dynamics method was developed for this particular problem, and numerical simulations are compared to experimental tests when a rigid base is considered. The purpose of the study was to investigate the predictive capabilities and limitations of the numerical model and address the effect of introducing beam flexibility on the rocking response. The investigated flexibilities were such that the beam deflection under the static weight of the block remains within the common limit of 1/250 of the beam span. For a rigid base, qualitatively good correlation with the experiments was obtained, and good convergence in terms of the time-step is displayed. With the increase in beam base flexibility, it was observed that the simulation results tend to become more sensitive to mesh density and time-step size. Furthermore, we identify a limited flexibility with respect to which unreliable predictions of the overall free rocking are obtained, which corresponds to the stiffness resulting in the beam deflection under the block weight of beam-span/2500. For stiffnesses higher than that, no significant effect of beam flexibility in comparison to the rigid base was noticed in terms of tilt angle and rocking duration, which indicates the adequacy of a rigid base approximation for beams with low flexibility.

关键词： non-smooth contact dynamics rocking numerical algorithm experimental validation

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A Coupled Model of Controlled Synthesis, of a Composite on a Substrate

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2022年第7期43卷 1878-1893页

作者： Knyazeva, A. G. Kryukova, O. N. Russian Acad Sci Siberian Branch Inst Strength Phys & Mat Sci Tomsk 634055 Russia

A mathematical model of the process of composite synthesis from a mixture of powders is formulated. It is assumed that the synthesis is performed on a substrate and is controlled by a scanning laser beam. The stress-strain state is described in quasi-static approximation. The model takes into account two phenomena that are neglected in traditional surface treatment and 3D models: the mutual influence of the heat transfer process and deformation and the heat sources and sinks that result from chemical reactions. The formation of the composition is described by a total reaction scheme that includes a strengthening particle formation stage and a matrix formation stage. The nonlinear model is reduced to a dimensionless form and investigated numerically using an implicit difference scheme for the thermal conductivity equation, the semi-implicit Euler method for the kinetic equations, and the iteration procedure for the mechanical equilibrium problem. As a result of the calculations, we have the fields of temperature, concentrations, stresses, and strains at an arbitrary moment of time, as well as the final composition of the composite. It is shown that the coupling of processes of different physical nature is important both for determining the composition of the composite and for estimating the residual stresses and strains.

关键词： coupled model composite synthesis reaction rates residual stresses controlled mode numerical algorithm

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Novel Analytical Thermal Performance Rate Analysis in ZnO-SAE50 Nanolubricant: Nonlinear Mathematical Model

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Computers, Materials & Continua 2021年第4期67卷 477-489页

作者： Adnan Abbasi Umar Khan Naveed Ahmed Syed Tauseef Mohyud-Din Ilyas Khan El-Sayed M.Sherif Department of Mathematics Mohi-ud-Din Islamic UniversityNerian SharifAJ&K12080Pakistan Department of Mathematics and Statistics Hazara UniversityMansehra21120Pakistan Department of Mathematics HITEC UniversityTaxilaCantt47070Pakistan University of Multan Multan66000Pakistan Department of Mathematics and Statistics Ton Duc Thang UniversityHo Chi Minh City72915Vietnam Department of Mechanical Engineering College of EngineeringKing Saud UniversityAl-Riyadh11421Saudi Arabia Department of Physical Chemistry Electrochemistry and Corrosion LaboratoryNational Research CentreCairo12622Egypt

The investigation of local thermal transport rate in the nanolubricants is *** lubricants are broadly used in environmental pollution,mechanical engineering and in the paint industry due to high thermal performance ***,thermal transport in ZnO-SAE50 nanolubricant under the impacts of heat generation/absorption is *** colloidal suspension is flowing between parallel stretching disks in which the lower disk is positioned at z=0 and upper disk apart from distance *** problem is transformed in dimensionless version via described similarity *** the next stage,an analytical technique(VPM)is implemented for the solution *** graphical results against multiple flow parameters were furnished over the region of interest and explained *** is imperative to mention that the results are plotted for ZnO-SAE50 and conventional liquid as ***,rapid motion of the fluid is perceived against high Reynolds andγ*** wall shear stresses at the upper end rises for multiple Reynolds andγwhile;decrement is detected at the lower *** significant contribution of an internal heat source is noted for thermal performance rate at the upper ***,the local heat transport rate declines at the lower *** altering Reynolds number,prompt heat transfer rate is gained at the upper disk and increasing behavior of the local heat transport rate is slow at the lower *** the study,it is concluded that the nanolubricants have high thermal ***,such fluids are reliable to use in above stated areas.

关键词： Zno-SAE50 nanolubricant thermal performance local heat transport numerical algorithm skin friction

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An algorithm for accurate modeling and simulating reactor cores with involute-shaped fuel plates by Monte Carlo

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INTERNATIONAL JOURNAL OF ENERGY RESEARCH 2021年第8期45卷 12449-12463页

作者： Zhang, Shen Gui, Nan Kai, Tan Yang, Xingtuan Tu, Jiyuan Jiang, Shengyao Tsinghua Univ Inst Nucl & New Energy Technol Collaborat Innovat Ctr Adv Nucl Energy Technol Key Lab Adv Reactor Engn & SafetyMinist Educ Beijing 100084 Peoples R China RMIT Univ Sch Engn Melbourne Vic Australia

A real three-dimensional representation of reactor core with involute fuel plates via Monte Carlo method is still lacking at the present, and usually equivalent homogeneous models of water coolants and simplified fuel plate shapes have been used. This work proposed an algorithm to simulate the reactor core composed of involute fuel plates with an explicit accurate description of its involute surfaces. The description of involute surfaces is through its governing equations. The mathematical function methods to depict the involute curves and the schemes to compute the distance between any neutron particle and an involute surface along a ray are presented and demonstrated step-by-step. The algorithm is realized in the Monte Carlo code and validated by the published data of a high flux isotope reactor. This study definitively provides a method to model the involute fuel plates in the Monte Carlo simulation.

关键词： fuel plate involute shape Monte Carlo method numerical algorithm reactor core

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On the Simultaneous Identification of the Volumetric Heat Capacity and the Thermal Conductivity of a Substance 13th

On the Simultaneous Identification of the Volumetric Heat Ca...

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13th International Conference on Optimization and Applications (OPTIMA)

作者： Albu, Alla Gorchakov, Andrei Zubov, Vladimir Russian Acad Sci Fed Res Ctr Comp Sci & Control Moscow Russia

ISBN: (纸本)9783031225420;9783031225437

The study of nonlinear problems associated with heat transfer in the substance is very important for practice. Previously, we proposed an efficient algorithm for identifying the thermal conductivity of a substance based on the results of experimental observation of the dynamics of the temperature field in an object. In this paper, we investigate the possibility of extending the application of the proposed algorithm to obtain a numerical solution to the problem of simultaneous identification of the temperature-dependent the thermal conductivity and the volumetric heat capacity of the substance under study. The consideration is carried out on the basis of the first initial-boundary value problem for the one-dimensional non-stationary heat equation. The considered inverse coefficient problem is reduced to a variational problem, which is solved by gradient methods based on the application of the Fast Automatic Differentiation technique.

关键词： Nonlinear problems Inverse coefficient problems Heat equation numerical algorithm Fast Automatic Differentiation

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