Algorithm For Numerical Simulation Research Articles

Numerical study of the porosity-permeability evolution due to chmically-active fluid injection

The paper presents a numerical algorithm for simulation of the reactive transport at the pore scale. The algorithm allows simulating pore space evolution, porosity, absolute permeability, and form factor changes due to core matrix dissolution or precipitation. We also, introduce the topological measure; the persistence diagrams of independent cycles in pore space to classify different dissolution scenarios. Using derived classification, we constructed the statistically reliable porosity-permeability relations for different dissolution scenarios.

Film thickness dependency and refractive index sensing capabilities of lossy mode resonances in metallic indium-rich ITO thin films

Film thickness plays a crucial role in determining the position and depth of lossy mode resonance (LMR). Herein, we explore the overall film thickness dependency of LMR properties of pulsed-laser-deposited metallic indium-rich indium tin oxide (ITO) thin films by employing a simple Kretschmann–Raether geometry. It is observed that the depth of LMR is increased monotonically with increasing film thickness. Extremely high attenuation values of − 20 d B for transverse electric and − 10 d B for transverse magnetic polarizations are achieved for the film with the greatest film thickness. Also, the LMR positions are considerably redshifted with increasing thickness. A numerical simulation algorithm based on the modified transfer matrix method, where surface roughness is taken into account with the application of anisotropic Bruggemann effective medium approximation, is used to simulate the experimental LMR spectra for all vacuum-deposited ITO thin films effectively. As an application of this study, refractive index (RI) sensing is demonstrated in the RI range of 1.3325–1.4459, and highest sensitivity values of 3840 nm/RIU and 2542 nm/RIU are accomplished for transverse electric and transverse magnetic polarizations, respectively. This study will help in attaining a deep level of understanding of the film thickness effect on thin film based LMR and elevate metallic indium-rich ITO as an excellent material template for LMR studies.

The design of an open-source carbonate reservoir model

This work presents a new open-source carbonate reservoir case study, the COSTA model, that uniquely considers significant uncertainties inherent to carbonate reservoirs, providing a far more challenging and realistic benchmarking test for a range of geo-energy applications. The COSTA field is large, with many wells and large associated volumes. The dataset embeds many interacting geological and petrophysical uncertainties in an ensemble of model concepts with realistic geological and model complexity levels and varying production profiles. The resulting number of different models and long run times creates a more demanding computational challenge than current benchmarking models. The COSTA model takes inspiration from the shelf-to-basin geological setting of the Upper Kharaib Member (Early Cretaceous), one of the most prolific aggradational parasequence carbonate formations sets in the world. The dataset is based on 43 wells and the corresponding fully anonymised data from the northeastern part of the Rub Al Khali basin, a sub-basin of the wider Arabian Basin. Our model encapsulates the large-scale geological setting and reservoir heterogeneities found across the shelf-to-basin profile, into one single model, for geological modelling and reservoir simulation studies. The result of this research is a semi-synthetic but geologically realistic suite of carbonate reservoir models that capture a wide range of geological, petrophysical, and geomodelling uncertainties and that can be history-matched against an undisclosed, synthetic ‘truth case’. The models and dataset are made available as open-source to analyse several issues related to testing new numerical algorithms for geological modelling, uncertainty quantification, reservoir simulation, history matching, optimization and machine learning. Supplementary material: supplementary data associated with this article can be found in the data repository for the COSTA model available at https://doi.org/10.17861/6e36e28d-50d9-4e31-9790-18db4bce6e5d and supplementary material is available at https://doi.org/10.6084/m9.figshare.c.5823571

Multiscale analysis of tunnel surrounding rock disturbance: A PFC3D-FLAC3D coupling algorithm with the overlapping domain method

Under the condition of high in-situ stress, the instantaneous excavation disturbs surrounding rocks, which shows different internal mechanisms on the different scales. At present, there still lacks numerical simulation algorithms for multiscale analysis in this field. A PFC3D-FLAC3D coupling algorithm with the overlapping domain method (ODM) was proposed. ODM can optimize the problem of energy reflection between different coupling domains and improve the accuracy of calculation. ODM was verified to a certain extent, including the velocity transmission and the mechanical deformation of models. In addition, the coupling algorithm with ODM was applied to the tunnel excavation under the assumption of the Kastner formula and the Songhua–Changchun diversion tunnel in China. In the tunnel excavation simulation, the simulation results showed that the coupling algorithm can characterize the stress distribution of surrounding rocks on the macro-scale, and reveal the phenomena of crack initiation propagation and large deformation on the micro-scale. By comparing with the empirical formula and the engineering data, it can be found that the coupling algorithm accurately and effectively realized the multiscale simulation of rocks disturbance. This research have some reference value for the multiscale investigation, which is the disturbance of surrounding rock caused by tunnelling.

Consensus of Fractional-Order Double-Integral Multi-Agent System in a Bounded Fluctuating Potential

At present, the consensus problem of fractional complex systems has received more attention. However, there is little literature on the consensus problem of fractional-order complex systems under noise disturbance. In this paper, we present a fractional-order double-integral multi-agent system affected by a common bounded fluctuating potential, where the protocol term consists of both the relative position and velocity information of neighboring agents. The consensus conditions of the presented system in the absence of noise are analytically given and verified by a numerical simulation algorithm. Then, the influences of the system order and other system parameters on the consensus of the presented system in the presence of bounded noise are also analyzed. It is found that when compared with the classical integer-order system, the presented fractional-order system has a larger range of consensus parameters and has more rich dynamic characteristics under the action of random noise. Especially, the bounded noise has a promoting effect on the consensus of the presented fractional-order system, while there is no similar phenomenon in the corresponding integer-order system.

Reacting condensed phase explosives in direct contact

In this article, we present a new formulation and an associated algorithm for the simultaneous numerical simulation of multiple condensed phase explosives in direct contact with each other, which may also be confined by (or interacting with one or more) compliant inert materials. Examples include composite rate-stick (i.e., involving two explosives in contact) problems, interaction of shock waves with chemically active particles in condensed-phase explosives, and devices such as detonators and boosters. There are several formulations that address the compliant or structural response of confiners and particles due to detonations, but the direct interaction of explosives remains a challenge for most formulations and algorithms. The proposed formulation addresses this problem by extending the conservation laws and mixture rules of an existing hybrid formulation (suitable for solving problems involving the coexistence of reactants and products in an explosive mixture and its immiscible interaction with inert materials) to model the interaction of multiple explosive mixtures. An algorithm for the solution of the resulting system of partial differential equations is presented, which includes a new robust method for the retrieval of the densities of the constituents of each explosive mixture. This is achieved by means of a multi-dimensional root-finding algorithm, which employs physical as well as mathematical considerations in order to converge to the correct solution. The algorithm is implemented in a hierarchical adaptive mesh refinement framework and validated against results from problems with known solutions. Additional case studies demonstrate that the method can simulate the interaction of detonation waves produced by military grade and commercial explosives in direct contact, each with its own distinct equation of state and reaction rate law.

Development and Performance Analysis of Pneumatic Soft‐Bodied Bionic Flipper

The sea lion fore flipper has superior underwater movement performance. Its structural characteristics and propulsion mechanism are drawn, combined with the large deformation and hyperelastic properties of silicone, a pneumatic soft‐bodied bionic flipper with strong underwater mobility, good environmental adaptability, and flexible attitude transformation. Based on Yeoh's second‐order constitutive model of silicone, the nonlinear dynamic analysis of the main limb of the bionic flipper is carried out, and the deformation analysis theoretical model is established. Then, the force analysis of infinitesimal and integral of the wing fin of the bionic flipper is analyzed by the blade element theory, to obtain the theoretical model of underwater propulsion dynamic performance. The superiority of the hydrodynamic performance of the bionic flipper is analyzed and confirmed using the bidirectional fluid–structure coupling numerical simulation algorithm. An experimental test platform is built to test the physical model of the bionic flipper. The motion and dynamic characteristics curves of the bionic flipper are obtained and compared with the corresponding numerical simulation results. The results show that the theoretical model and numerical simulation are accurate, and the structure is feasible, which can provide methods and references for the research and implementation of the underwater propeller.

Three-dimensional fractional system with the stability condition and chaos control

A three-dimensional system is introduced in this paper and its local stability is analyzed. Our study establishes the validity and uniqueness of the linear feedback control for the proposed system and proves its existence and uniqueness. The numerical simulation algorithm described by Atanackovic and Stankovic is finally applied. The analytical results are analyzed and the dynamics of the system are explored in more detail.

Development of the Platform for Three-Dimensional Simulation of Additive Layer Manufacturing Processes Characterized by Changes in State of Matter: Melting-Solidification.

A new platform for three-dimensional simulation of Additive Layer Manufacturing (ALM) processes is presented in the paper. The platform is based on homogeneous methods—the Lattice Boltzmann Method (LBM) with elements of Cellular Automata (CA). The platform represents a new computer-based engineering technique primarily focused on Selective Laser Melting (SLM) technology. Innovative computational strategies and numerical algorithms for simulation and analysis of entire powder bed-based technology with changes in state of matter (melting-solidification) are presented in the paper. The models deal mainly with heat transfer, melting and solidification, and free-surface flow. Linking LBM and CA into a complex holistic model allows for complete full-scale simulations avoiding complicated interfaces. The approach is generic and can be applied to different multi-material powder bed-based SLM processes. A methodology for the adaptation of the model to the real material (Ti-6Al-4V alloy) and processing parameters is presented. The paper presents the first quantitative results obtained on the platform and shows the ability of the model to simulate and analyze a very complex technology, entirely without a complicated interface between the sub-models. It solves the large-scale problem connected with computer-aided design and analysis of new multi-passes and multi-materials processes.

Symmetrically partitioned isotropic model for quantitative equivalent simulation of circumferential anisotropy

Abstract Simulation wells with known parameters are vital in the study of anisotropic methods and logging equipment development. We propose a symmetrically partitioned isotropic (SPI) model, which can quantitatively control the parameters of equivalent circumferential anisotropy. First, the circumferential anisotropy of the flexural wave dispersion in the SPI model is analysed using a perturbation method, and the azimuth characteristics of the flexural wave and the wave velocity in the model are evaluated using a numerical simulation algorithm. Next, the circumferential anisotropy characteristics of the model are verified. Finally, the linear relationship between the fast and slow shear-wave velocities of the model and the model parameters is obtained through multiple linear regression analyses, and then, the equivalent circumferential anisotropy is predicted. The feasibility of the quantitative equivalent simulation of circumferential anisotropy media using the SPI model is verified.

Optimization of energy tunnel heat extraction section design based on simulated annealing algorithm

Energy tunnel is an alternative energy-saving technology of ground source heat pump （GSHP）， which has been applied in China in recent years. However， the current engineering practice still lacks the mature design method， and the heat extraction section design of the energy tunnel usually depends on engineering analogy. It is necessary to develop a convenient and reliable method to assist energy tunnel design. To address this problem，an optimization framework is developed to guide the heat extraction section design of energy tunnel in the severe cold region based on numerical simulation and simulated annealing algorithm. With this framework， the location of the heat extraction section can be automatically selected based on the in-site geological and meteorological conditions. Then， sensitivity analysis in terms of different design parameters of the heat extraction section is conducted to investigate their influence on heat transfer efficiency and heat extraction section design. The results show that smaller pipe spacing， lower inlet water temperature， and higher flow rate of circulating medium in pipes will benefit the higher heat exchange efficiency， shorter design length of heat extraction section， and the resultant lower cost. In addition， the deviation of the starting position within several meters will not affect the total heat extraction capability for a certain length of the heat extraction section. The proposed methodology will provide important support for the energy tunnel design in engineering practice.

Wave propagation characteristics in porous medium containing a solid in pores

Aiming at the propagation characteristics of acoustic waves in a porous medium containing a solid in pores, the equations of motion and constitutive relation are deducted in the case of two-solid porous media. The frequency dispersion and attenuation characteristics of wave modes are analyzed by a plane wave analysis. In addition, based on the first-order velocity-stress equations, the time-splitting high-order staggered-grid finite-difference algorithm is proposed and constructed for understanding wave propagation mechanisms in such a medium, where the time-splitting method is used to solve the stiffness problem in the first-order velocity-stress equations. The generation mechanisms and energy distributions of different kinds of waves are investigated in detail. In particular, the influences of the friction coefficient between solid grains and pore solid as well as frequency on wave propagation are analyzed. It can be known from the results of plane wave analysis that there are two compression waves (P1 and P2) and two shear waves (S1 and S2) in a porous medium containing a solid in pores. The attenuations of P2 wave and S2 wave are much larger than those of P1 wave and S1 wave. This is due to the friction between the solid grains and the pore solid. The results show that our proposed numerical simulation algorithm can effectively solve the problem of stiffness in the velocity-stress equations, with high accuracy. The excitation mechanisms of the four wave modes are clearly revealed by the simulation results. The P1 wave and S1 wave propagate primarily in the solid grain frame, while P2 wave and S2 wave are concentrated mainly in the pore solid, which are caused by the relative motion between the solid grains and the pore solid. Besides, it should be pointed out that the wave diffusions of the P2 wave and S2 wave are influenced by the friction coefficient between solid grains and pore solid. The existence of friction coefficient between two solids makes P2 wave and S2 wave attenuate to a certain extent at high frequency, but the attenuation is much smaller than that at low frequency. This is the reason why it is difficult to observe the slow waves in practice. However, because the slow waves also carry some energy, it may not be ignored in the studying of the energy attenuation of acoustic waves in porous media.

An Improved Parameter Dimensionality Reduction Approach Based on a Fast Marching Method for Automatic History Matching

History matching is a critical step in reservoir numerical simulation algorithms. It is typically hindered by difficulties associated with the high-dimensionality of the problem and the gradient calculation approach. Here, a multi-step solving method is proposed by which, first, a Fast marching method (FMM) is used to calculate the pressure propagation time and determine the single-well sensitive area. Second, a mathematical model for history matching is implemented using a Bayesian framework. Third, an effective decomposition strategy is adopted for parameter dimensionality reduction. Finally, a localization matrix is constructed based on the single-well sensitive area data to modify the gradient of the objective function. This method has been verified through a water drive conceptual example and a real field case. The results have shown that the proposed method can generate more accurate gradient information and predictions compared to the traditional analytical gradient methods and other gradient-free algorithms.

Investigation of error in evaluation of spectral statistical characteristics of numerical solution of stochastic dynamic system

In this paper, an algorithm for numerical simulations is developed for calculating a discrete dynamic system with a stochastic perturbation and an analysis of the quality of numerical solutions is carried out. For this, an algorithm for the numerical solution of a second-order differential equation with a stochastic right-hand side was developed and this algorithm was implemented as a program. The next step was to carry out a set of computational studies by varying the parameters of numerical integration with the subsequent assessment of their impact on the error and accuracy of simulations. To estimate the spectral density, the Welch periodogram method was used. To check the quality of simulations and assess the accuracy of solutions, it is proposed to compare the results of numerical integration and subsequent digital processing with analytical solutions that are known for the linear problem, given by the equation. As a result of the work, a comparative analysis of the dispersion of displacements relative to the lengths of signals from a different number of blocks was carried out, into which the signal is divided for the Welch method; the confidence interval of the error at different signal lengths and the confidence interval of the error with a different number of blocks at a certain signal length. Comparison of the variance with a different number of blocks showed that with a signal length of 30 s and from 90 s, there is a slight scatter of the variance values within an error of ± 5%.

A Real-Time Matrix Iterative Optimization Algorithm of Booking Elevator Group and Numerical Simulation Formed by Multi-Sensor Combination

Elevators are an essential indoor transportation tool in high-rise buildings. The world is advocating the design concept of safety, energy-saving, and intelligence. We focus on improving operation speed and utilization efficiency of the elevator group. This paper proposed a real-time reservation elevator groups optimization algorithm, and a dynamic matrix iterative model has been established. The indoor navigation technology UWB is applied, which can help users to quickly find elevators. The manned equilibrium efficiency and running time equilibrium efficiency of elevator group are given. Moreover, the data filtering criterion formulas for user waiting time and elevator remaining space are defined. In this paper, three numerical examples are given. Example 1 is a single elevator in n-storey building. Example 2 is compared with different scheduling algorithms, such as FCFS, SSTF, LOOK, and SCAN algorithms, and the results show that our method has the advantages of short total running time and less round-trip frequency. At last, the matrix of numerical iteration results are visualized, and the data movement status of people on each floor can be observed. Example 3 introduced elevator group algorithms. For high-rise buildings, this paper adopts a high, medium, and low hierarchical management model; this model has high coordination, as well as fast response, batch process, and adaptive function. Finally, we also discussed and compared the complexity of single elevator and elevator group algorithms. Therefore, this method has great development potential and practical application value, which deserves further study.

Numerical Simulation Algorithm Design of Influence on Existing Tunnel by Underpass Construction of New Tunnel

Simulation is a powerful tool that can be used for systematic planning, analysis, and decision-making. Proper designing is preliminary required to construct a new tunnel over an existing tunnel to ensure safety and durability. Once an underpass tunnel completes, the interaction between the tunnel structure and the nearby soil gains a stable state and the stress of the tunnel is balanced. However, the stability of an existing tunnel is affected if the construction in the nearby area is not properly analyzed. This article proposes a numerical simulation model to empirically analyze lining force and surface settlement in order to ensure safety in engineering practice. The existing tunnel structure working condition is simulated under the new tunnel. The artificial honeybee colony algorithm is used to extract the parameter fusion characteristic value of tunnel influence and the model of estimating the bending moment of group piles. The structural mechanics of existing tunnels under new tunnels are analyzed using the triple bend model to improve the bearing capacity of existing tunnels under new tunnels. Based on the above analysis, numerical simulation experiments are designed. The proposed method has high accuracy and strong fitting ability and can effectively reduce the displacement of existing tunnels. Moreover, the method can improve the bearing capacity of tunnels. For tunneling operation, the results of the simulation may be used as a recommendation.

Numerical Algorithms for Simulation of a Fluid-Filed Fracture Evolution in a Poroelastic Medium

The paper deals with the computational framework for the numerical simulation of the three dimensional fluid-filled fracture evolution in a poroelastic medium. The model consists of several groups of equations including the Biot poroelastic model to describe a bulk medium behavior, Reynold’s lubrication equations to describe a flow inside fracture and corresponding bulk/fracture interface conditions. The geometric model of the fracture assumes that it is described as an arbitrary sufficiently smooth surface with a boundary. Main attention is paid to describing numerical algorithms for particular problems (poroelasticity, fracture fluid flow, fracture evolution) as well as an algorithm for the coupled problem solution. An implicit fracture mid-surface representation approach based on the closest point projection operator is a particular feature of the proposed algorithms. Such a representation is used to describe the fracture mid-surface in the poroelastic solver, Reynold’s lubrication equation solver and for simulation of fracture evolutions. The poroelastic solver is based on a special variant of X-FEM algorithms, which uses the closest point representation of the fracture. To solve Reynold’s lubrication equations, which model the fluid flow in fracture, a finite element version of the closet point projection method for PDEs surface is used. As a result, the algorithm for the coupled problem is purely Eulerian and uses the same finite element mesh to solve equations defined in the bulk and on the fracture mid-surface. Finally, we present results of the numerical simulations which demonstrate possibilities of the proposed numerical techniques, in particular, a problem in a media with a heterogeneous distribution of transport, elastic and toughness properties.

Optimization and decision-making of novel laser-induced thermal therapy for deep-lying tumor based on multi-objective genetic algorithm and three-way decisions method

In this paper, we develop novel laser-induced thermal therapy (LITT) schemes, multiple and single rotating laser irradiation, for deep-lying breast tumor to maximize tumor killing while minimizing normal tissue damage and preventing the surface overheating without the aid of external media such as nanoparticles and photosensitizers. Combined with numerical simulation and multi-objective genetic algorithm (MOGA), the incident angle, radius, intensity and exposure time of the multiple laser irradiation, as well as the rotational period and exposure time of the single rotating laser irradiation are optimized based on the surface response model, and a series of Pareto-optimal solutions are obtained. The three-way decisions method is utilized to effectively manage the Pareto-optimal solutions and select the ideal solution with a comprehensive consideration of the risk preferences (aversion, proneness and neutralness) of the surgeon. Compared with the traditional LITT, the ideal solution selected by the operator with risk neutralness attitude makes the surface temperature maintain at an acceptable level, and the killing volume of normal tissue is reduced by 80.4% for the multiple laser irradiation and 99.74% for the single rotating laser irradiation in the case of complete tumor killing. Results obtained can be employed as a guideline for the selection of LITT regimens for deep-lying breast tumor under consideration of the surgeon’s risk preferences.

A new seasonal frozen soil water-thermal coupled migration model and its numerical simulation.

In this paper, a mathematical model based on spherical differential unit cell is proposed as a model for studying seasonal freeze-thaw soil space infinitesimal differential unit cell. From this model, the basic equations of permafrost moisture and heat flow motion are directly derived, then the linked equations form the permafrost water-heat coupled transport model. On this basis, the one-dimensional seasonal permafrost water-heat transport equation is derived. The model reduces the original spatial three-variable coordinate system (parallel hexahedron) into a coupled equation with a single spherical radius (R) as the independent variable, so the iterations of the numerical simulation algorithm is greatly reduced and the complexity is decreased. Finally, the model is used to simulate the seasonal freeze-thaw soil in the ShiHeZi region of Xinjiang, China. The principle of the simulation is to collect the soil temperature and humidity values of the region in layers and fixed-points using a homemade freeze-thaw soil sensor, after that we solve it by numerical calculation using MATLAB. The analysis results show that the maximum relative error of the model we proposed is 4.36, the minimum error is 0.98, and the average error is 2.515. The numerical simulation results are basically consistent with the measured data, then the proposed model is consistent with the matching states of permafrost moisture content and soil temperature in the region at different times. In addition, the experiments also demonstrate the reliability and accuracy of the model.

Numerical simulation of deflagration in hydrogen-air gas mixes

Verification of validity of different manifolds of chemical reactions and coefficients in Arrhenius formulae was made for numerical simulation of deflagration appearing in hydrogen-air gas mixes. Kinetic model of branching chain reaction was tested for initial stage of detonation of this kind of mixes. One dimensional numerical simulations of deflagration initiation where provided for small closed heat isolated region. The next problem was solved numerically:in small closed volume, initially filled by hydrogen-air mix with atmospheric meanings of gas dynamics parameters at moment t=0 temperature rising till meaning, at which reaction of deflagration should begin. Numerical experiment consist of calculation of thermodynamics parameters of gas mix in small isolated volume. Meanings of molar concentration of components of gas mix where calculated by implicit numerical method of Gir for numerical decision. Calculation where provided till zero concentration of hydrogen or not appearing of deflagration at all. Characteristic feature of hydrogen-air gas mix deflagration is appearance of sudden explosion after long period of induction. In this induction period grows of radicals H, O and OH appears. Mass of radicals, nevertheless stay small, and one radical component transverse to the others. This explosion mechanism is branching chain reaction introduced by N.N.Semenov. In agreement with branching chain reaction theory during process of branching chain reaction radicals H, O, OH many times initiates reaction with other components of the mix. Nevertheless mass of radical components preserve small during the reaction, them almost fully disappeared in every time of the process. That’s why method of “quasi - stationary concentration” is treated to components O, OH (velocity of changing of this components concentration is equal to zero). For concentration of component H one simplified differential equation is treated. Speed of changing H essentially grater then speed of changing “slow” components H2, O2, H2O, that’s why equation for H should be solved separately. Algorithm was developed for numerical simulation of hydrogen-air mixes on the basis of theory branching chain reactions. Calculations provided demonstrate applicability of developed algorithm for numerical simulations of initial stage of deflagration of hydrogen-air mixes.