Stability Numerical Simulation Research Articles

Solution of the discrete Boltzmann equation: based on the finite volume method

Mesoscopic methods serve as a pivotal link between the macroscopic and microscopic scales, offering a potent solution to the challenge of balancing physical accuracy with computational efficiency. Over the past decade, significant progress has been made in the application of the discrete Boltzmann method (DBM), which is a mesoscopic method based on a fundamental equation of nonequilibrium statistical physics (i.e., the Boltzmann equations), in the field of nonequilibrium fluid systems. The DBM has gradually become an important tool for describing and predicting the behavior of complex fluid systems. The governing equations comprise a set of straightforward and unified discrete Boltzmann equations, and the choice of their discrete format significantly influences the computational accuracy and stability of numerical simulations. In a bid to bolster the reliability of these simulations, this paper utilizes the finite volume method as a solution for handling the discrete Boltzmann equations. The finite volume method stands out as a widely employed numerical computation technique, known for its robust conservation properties and high level of accuracy. It excels notably in tackling numerical computations associated with high-speed compressible fluids. For the finite volume method, the value of each control volume corresponds to a specific physical quantity, which makes the physical connotation clear and the derivation process intuitive. Moreover, through the adoption of suitable numerical formats, the finite volume method can effectively minimize numerical oscillations and exhibit strong numerical stability, thus ensuring the reliability of computational results. Particularly, the MUSCL format where a flux limiter is introduced to improve the numerical robustness is adopted for the reconstruction in this paper. Ultimately, the DBM utilizing the finite volume method is rigorously validated to assess its proficiency in addressing flow issues characterized by pronounced discontinuities. The numerical experiments encompass scenarios involving shock waves, Lax shock tubes, and acoustic waves. The results demonstrate the method's precise depiction of shock wave evolution, rarefaction waves, acoustic phenomena, and material interfaces. Furthermore, it ensures the conservation of mass, momentum, and energy within the system, as well as accurately measures the hydrodynamic and thermodynamic nonequilibrium effects of the fluid system. Compared with the finite difference method, the finite volume method is also more convenient and flexible in dealing with boundary conditions of different geometries, and can be adapted to a variety of systems with complex boundary conditions. Consequently, the finite volume method further broadens the scope of DBM in practical applications.

A new symplectic integrator for stochastic Hamiltonian systems on manifolds

This paper presents a significant development in the field of geometric numerical stochastic integration schemes. Specifically, the Geometric Symplectic Itô-Taylor 1.0 strong numerical integration scheme, tailored for Hamiltonian systems evolving on 2-sphere or S2 manifold is proposed. The core of this proposed algorithm centers around a new weak symplectic condition. This condition ensures the numerical stability for long duration time integration that can be readily achieved through numerical steps rather than relying solely on analytical satisfaction of the condition. This proposed advancement over the state-of-the-art caters to improved accuracy and stability of numerical simulations in manifold-based dynamical systems for long duration simulations. Through extensive analysis and numerical experiments, the effectiveness and reliability of the proposed scheme and symplectic criterion are validated. The findings of this study promises to offer valuable insights for researchers and practitioners working in the field of symplectic numerical integration methods.

Analysis of Deformation Formation Causes and Reinforcement Disposal Effects in Deep Excavated Expansive Soil Canal Slope: Case Study

Deeply excavated expansive soil canal slopes can have instability risks during operations. The deformation mechanism is analyzed using internal and external factors, such as engineering geology, hydrogeology, rainfall, and groundwater levels in the middle expansive soil canal slope in the central line of the South-to-North Water Diversion Project, Taocha District, Nanyang City, Henan Province, China. The stability of the canal slope and the effect of the reinforcement and disposal measures are evaluated with a geological survey, manual inspection of the defects, safety monitoring data analysis, hidden danger geophysical detection, and stability numerical simulation. The following conclusions are drawn: (1) the surface-refilled cement-treated soil failed to isolate the water vapor exchange between the expansive soil and the atmosphere; and (2) the stagnant water in the upper layer is replenished by precipitation, leading to the increase in the groundwater level during the rainy season and the decrease in the groundwater level during the dry season. Shear creep deformation occurs along the fissure of the second to fourth grade canal slopes. The potential sliding surface consists of a gentle dip angle leading edge and a steep dip angle trailing edge. The arrangement of the antisliding piles on the water-passing section and the crack surface distribution had an effect, and the potential shear outlet is in the first grade berm, the deformed body is still developing, and the trailing edge is not apparent. The potential failure mode of the slope is deep sliding, and the current safety factor is 1.002. A combination of groundwater discharge and micropile reinforcement is required to improve the stability of the canal slope. After the drainage and reinforcement are implemented, the slope’s deep antislide stability safety factor increases to 1.462, which met the safety requirements. The results could provide a reference for the operation management and reinforcement governance of similar projects.

Numerical simulation of stability and responses of dynamic systems under parametric excitation

The stability and responses of dynamic systems under parametric excitation are often encountered in many fields of science and engineering, such as slender columns and thin plates under axial loadings. This paper proposes a novel numerical simulation method to simultaneously construct stability diagrams and predict the responses of multiple degree-of-freedom (DOF) dynamic systems under arbitrary parametric loadings. The method divides an arbitrary load into discrete segments to approximate the variable excitation function by a step function and then accumulates the system responses of each segment using a matrix method. Dynamic stability and response analysis of undamped and damped 1DOF, 2DOF, 3DOF, and multiple DOF systems are conducted, and numerical examples are compared to conventional methods to show the accuracy and advantage of the proposed numerical simulation method. The instability diagrams are also substantiated by vibration response curves obtained from the same method. The method is applied to calibrate the validity and ranges of applicability of the Hill infinite determinants in the Floquet theory of 1DOF Mathieu-Hill equations. The second order approximation of the first instability region from the Hill determinant is acceptable. However, the fourth order approximation of the second instability region must be used to obtain a relatively accurate result. For 2DOF, 3DOF, and multi-parameter linear periodic systems, the method can simultaneously render four types of instability regions in a single procedure: no resonances, simple parametric resonances, combination additive resonances, and combination differential resonances. These results could provide a better understanding of stability and responses of dynamic systems under parametric excitation.

About prestretch in homogenized constrained mixture models simulating growth and remodeling in patient-specific aortic geometries

Evolution of mechanical and structural properties in the Ascending Thoracic Aorta (ATA) is the results of complex mechanobiological processes. In this work, we address some numerical challenges in order to elaborate computational models of these processes. For that, we extend the state of the art of homogenized constrained mixture (hCM) models. In these models, prestretches are assigned to the mixed constituents in order to ensure local mechanical equilibrium macroscopically, and to maintain a homeostatic level of tension in collagen fibers microscopically. Although the initial prestretches were assumed as homogeneous in idealized straight tubes, more elaborate prestretch distributions need to be considered for curved geometrical models such as patient-specific ATA. Therefore, we introduce prestretches having a three-dimensional gradient across the ATA geometry in the homeostatic reference state. We test different schemes with the objective to ensure stable growth and remodeling (G&R) simulations on patient-specific curved vessels. In these simulations, aneurysm progression is triggered by tissue changes in the constituents such as mass degradation of intramural elastin. The results show that the initial prestretches are not only critical for the stability of numerical simulations, but they also affect the G&R response. Eventually, we submit that initial conditions required for G&R simulations need to be identified regionally for ensuring realistic patient-specific predictions of aneurysm progression.

An Overall Uniformity Optimization Method of the Spherical Icosahedral Grid Based on the Optimal Transformation Theory

The improvement of overall uniformity and smoothness of spherical icosahedral grids, the basic framework of atmospheric models, is a key to reducing simulation errors. However, most of the existing grid optimization methods have optimized grid from different aspects and not improved overall uniformity and smoothness of grid at the same time, directly affecting the accuracy and stability of numerical simulation. Although a well-defined grid with more than 12 points cannot be constructed on a sphere, the area uniformity and the interval uniformity of the spherical grid can be traded off to enhance extremely the overall grid uniformity and smoothness. To solve this problem, an overall uniformity and smoothness optimization method of the spherical icosahedral grid is proposed based on the optimal transformation theory. The spherical cell decomposition method has been introduced to iteratively update the grid to minimize the spherical transportation cost, achieving an overall optimization of the spherical icosahedral grid. Experiments on the four optimized grids (the spring dynamics optimized grid, the Heikes and Randall optimized grid, the spherical centroidal Voronoi tessellations optimized grid and XU optimized grid) demonstrate that the grid area uniformity of our method has been raised by 22.60% of SPRG grid, −1.30% of HR grid, 38.30% of SCVT grid and 38.20% of XU grid, and the grid interval uniformity has been improved by 2.50% of SPRG grid, 2.80% of HR grid, 11.10% of SCVT grid and 11.00% of XU grid. Although the grid uniformity of the proposed method is similar with the HR grid, the smoothness of grid deformation has been enhanced by 79.32% of grid area and 24.07% of grid length. To some extent, the proposed method may be viewed as a novel optimization approach of the spherical icosahedral grid which can improve grid overall uniformity and smoothness of grid deformation.

Bioeconomic-Epidemiological Model of Scomber colias Population in the Moroccan Coasts

In this paper, we develop and study a mathematical model for the dynamics of Scomber colias and Thunnus thynnus prey-predator with parasitic helminths. We search to analyze a bioeconomic model in which both susceptible and infected prey populations Scomber colias are exposed to the predator Thunnus thynnus, with varying degrees of exposure. However, the predator feeds preferentially on the most numerous prey types. This implies a kind of switching from the susceptible class to the infected class, and vice versa, as these two types of prey change in numerical superiority. So, the positivity, boundedness, equilibria, stability, and bioeconomic equilibrium are studied. Some numerical simulation of stability is cited. For giving a high yield and keeping the Scomber colias and Thunnus thynnus populations away from extension, we use the Maximum Principle of Pontryagin.

Flux reconstruction using Jacobi correction functions in discontinuous spectral element method

A flux reconstruction approach is implemented in the spectral difference (SD) framework, which we refer to it as discontinuous spectral element method (DSEM), to improve the accuracy and stability of numerical simulations. A new class of correction functions is developed based on a weighted orthogonality condition, which leads to the introduction of Jacobi correction functions. Jacobi correction functions can construct the well-known DSEM and staggered-grid version of nodal discontinuous Galerkin spectral element method (DGSEM) as well as a broad range of other high-order numerical schemes with a variety of numerical characteristics, such as high numerical dissipation to suppress aliasing-driven errors, super accuracy, and solution boundedness in shock prediction. Three single-parameter families of Jacobi correction functions are recognized, and a von Neumann analysis is performed to acquire their wave propagation properties. The order of accuracy and stability criterion of a broad range of schemes are calculated, and the most super-accurate and stable numerical schemes are identified and later validated through a set of numerical experiments on a one-dimensional advection equation. The solution unboundedness issue of the high-order DSEM scheme is discussed through simulating the Burgers equation. An accuracy test performed on the Burgers equation revealed that the new staggered-grid flux reconstruction approach could acquire a higher accuracy than that of the energy stable flux reconstruction framework on a collocated grid. The two-dimensional extension of the new framework is also examined by simulation of a non-linear Euler system of equations for the isentropic vortex in free-stream flow. The staggered-grid flux reconstruction using the Jacobi correction function can precisely reconstruct the DSEM approach for non-linear two-dimensional hyperbolic equations for all polynomial orders.

The Theory and New Unified Formulas of Displacement-Type Local Absorbing Boundary Conditions

ABSTRACTA series of classical absorbing boundary conditions (ABCs), including paraxial-approximation ABCs, Liao’s multi-transmitting formula (MTF), Higdon ABCs, and some other related techniques, have the common feature that the motion of an arbitrary artificial boundary node at each timestep is directly predicted from the motions of some adjacent nodes at several previous timesteps. They are expressed in somewhat equivalent forms, contain similar control parameters, and have comparable accuracy and stability in numerical simulations. This study develops a theoretical framework called displacement-type (a more exact name would be “prediction-type” or “extrapolation-type”) local ABCs to merge these boundary conditions. The idea of this theory mainly originates from the versatility of MTF, which uses a unified formula to approximate the propagation of outgoing waves through each boundary node. This idea can be generalized to other displacement-type local ABCs to unify their expressions and to optimize their applications. These ABCs have two basic control parameters; one is the boundary order, and the other is adjustable computational wave velocities. Considering the poor performance of paraxial ABCs and the slight imperfections in MTF and Higdon ABCs, we propose two new unified formulas to be the starting points of expressing, evaluating, and applying displacement-type local ABCs. One formula is an optimized MTF by introducing various computational wave velocities. The other formula is a generalized Higdon boundary formula, which is established in a unified local coordinate and uses the adjustable computational wave velocities. The rule of choosing boundary parameters for the absorption of acoustic and elastic waves is discussed in detail. Numerical tests validate the proposed theory and formulas. Issues on numerical stability are briefly reviewed and tested in simulation examples. This is still an active research topic related to displacement-type local ABCs.

Application of double-yield model in numerical simulation of stability of mining filling body

Combined with the actual conditions of the middle section of the V# orebody of Xincheng Gold Mine, the criterion, the yield function, and the softening parameter of the double-yield model were studied. And the simulation parameters of the double-yield model were obtained according to the mechanical parameters of the filling body in Xincheng Gold Mine. The FLAC3D numerical simulation method was used to simulate the filling body of first-step mining stage, and the simulation results of the initial and later stages were analyzed. Real-time monitoring equipment was buried in the second layer of the first-step mining stage to get the internal stress-strain law of the filling body. As for double-yield model, the data of the second stratified monitoring, the data of the real-time monitoring, and the data monitored by the Mohr-Coulomb model of the filling body were compared and analyzed. The applicability of the double-yield model in simulating the filling body was verified, which was closer to the results of actual situation. At the same time, the distribution and variation of stress and strain were basically understood. The above analysis results provide a scientific basis for the optimization of deep mining in Xincheng Gold Mine.

Perspective of S−CO2 power cycles

In this perspective paper, the research and development of S-CO2 cycles are analyzed from two aspects: (i) the system design and analysis and (ii) energy transfer/conversion mechanisms and key components development. Based on the analysis, barriers for further promotion of S-CO2 cycles are summarized, including the lack of system design and analysis methodology, not well understood mechanisms of energy transfer/conversion, and technic barriers such as seal, leakage and roto-dynamics stability of key components. To overcome these issues, perspectives on three aspects are proposed. First, S-CO2 cycle adapting to the distinct characteristic of a heat source should be optimized to promote the global system efficiency. Second, new theoretical/numerical works are suggested emphasizing the real gas effect of S-CO2 to improve the accuracy, convergence and stability of numerical simulations, fine experiments should be expanded to verify the correctness of the numerical simulations. Third, the integrated solution strategies for key components such as intermediate heat exchanger, recuperator heat exchanger and turbomachines should be developed and verified in large-scale test loop for reliable and efficient operation. This critical review is hopefully to present readers a clue to promote the development of S-CO2 cycles driven by nuclear energy, renewable energy and fossil energy.

Effect of polymer-stress diffusion in the numerical simulation of elastic turbulence

Elastic turbulence is a chaotic regime that emerges in polymer solutions at low Reynolds numbers. A common way to ensure stability in numerical simulations of polymer solutions is to add artificially large polymer-stress diffusion. In order to assess the accuracy of this approach in the elastic turbulence regime, we compare numerical simulations of the two-dimensional Oldroyd-B and FENE-P models sustained by a cellular force with and without artificial diffusion. We find that artificial diffusion can have a dramatic effect even on the large-scale properties of the flow and we show some of the spurious phenomena that may arise when artificial diffusion is used.

A Lattice Boltzmann Method and Asynchronous Model Coupling for Viscoelastic Fluids

The numerical algorithms of viscoelastic flows can appear a tremendous challenge as the Weissenberg number (Wi) enlarged sufficiently. In this study, we present a generalized technique of time-stably advancing based on the coupled lattice Boltzmann method, in order to improve the numerical stability of simulations at a high Wi number. The mathematical models of viscoelastic fluids include both the equation of the solvent and the Oldroyd-B constitutive equation of the polymer. In the two-dimensional (2D) channel flow, the coupled method shows good agreements between the corresponding exact results and the numerical results obtained by our method. In addition, as the Wi number increased, for the viscoelastic flows through contractions, we show that the prediction of our presented method can reproduce the same numerical results that were reported by previous studies. The main advantage of current method is that it can be applied to simulate the complex phenomena of the viscoelastic fluids.

Stabilization of numerical simulation by modification of combustion reaction models for heavy oil recovery with <i>in-situ</i> combustion method

Stabilization of numerical simulation by modification of combustion reaction models for heavy oil recovery with <i>in-situ</i> combustion method

Validation of accuracy and stability of numerical simulation for 2-D heat transfer system by an entropy production approach

The entropy production in 2-D heat transfer system has been analyzed systematically by using the finite volume method, to develop new criteria for the numerical simulation in case of multidimensional systems, with the aid of the CFD codes. The steady-state heat conduction problem has been investigated for entropy production, and the entropy production profile has been calculated based upon the current approach. From results for 2-D heat conduction, it can be found that the stability of entropy production profile exhibits a better agreement with the exact solution accordingly, and the current approach is effective for measuring the accuracy and stability of numerical simulations for heat transfer problems.

Safety Problem Of Cavity Under Open Pit Bench

Abstract Some open pits in China are severely threatened by hidden cavities under benches which are always inaccessible and unmapped. The first thing to be well considered is safe and precise cavity detection, as the conventional detection methods cannot output a clear cavity vision, a three-dimensional laser measurement system is employed to perform detection, which is deployed from the surface through boreholes. The results from the scanner demonstrated very well the detailed level of information that can be collected in a cavity using this method, with the cavities’ layout under various benches being fully mapped. As detected cavities are always in horizontal and vaulted roof shape, two different theoretical calculation methods are proposed to analyze the cap rock stability for different roof shape. And also, the three-dimensional solid model generated through scanned laser data is used for stability numerical simulation by converting the data format into the one that recognized in corresponding software. Furthermore, acoustic emission technique is adopted to carry out long term real time rupture monitoring in cap rock, and four kinds of typical monitoring results are discussed which represent the rupture behavior in cap rock of unstable cavity, stable cavity, cavity with large working drill above and cavity beside explosion site. Thus, a complete safety evaluation system for such cavity will be established to ensure safe operation above.

Numerical Simulation of Stability Analyzing for Unsaturated Slope with Rainfall Infiltration

Rainfall infiltration exerts great effect on the stability of soil slopes. Based on the actual rainfall data, saturated-unsaturated seepage theory and the mechanical theory of unsaturated porous media, numerical simulations were conducted to examine the seepage field of saturated-unsaturated slope during rainfall infiltration in this paper. The influence of the coefficient with rainfall duration, rainfall patterns, rainfall intensity and soil saturated permeability on seepage field are studied, and the relationship between the factor of safety and the position of sliding surface is obtained. The simulated results show that the saturated hydraulic conductivity has a great effect on slope stability. If the permeability of soil is relatively large, the changing range and the velocity of the factor of safety increase with the rainfall intensity; and if it is relatively in a low degree, the influence of the rainfall intensity on the slope stability is also low

Stability Numerical Simulation of Daping Landslide Group to Sunjiaya Tunnel

The stability of two profile, with No.Ⅲ landslide of Daping landslide group near the tunnel engineering of Sunjiaya, was respectively discussed using limit equilibrium and numerical simulation method at operation one (gravity) and two (gravity+rainstorm) in this paper. The dangerous sliding surface and corresponding safety factors was calculated by limit equilibrium method, to upper and lower parts of No.Ⅲ landslide in two different work conditions. The model of two calculation profiles was established and the dangerous sliding surface and corresponding safety factors was simulated by finite difference software of FLAC3D for upper and lower parts of No.Ⅲ landslide at two operations. Compared with limit equilibrium, FLAC3D is a simple and easy method to analyze the stability of slope.

AN ENTROPY PRODUCTION METHOD TO INVESTIGATE THE ACCURACY AND STABILITY OF NUMERICAL SIMULATION OF ONE-DIMENSIONAL HEAT TRANSFER

In this paper, an approach based on the entropy production theory is applied to investigate the accuracy and stability of numerical simulation of the heat transfer and fluid flow problems, constituting important parts of the simulation procedure. Using the formula of the entropy production of the fluid flow and heat transfer process, the accuracy and stability of numerical simulation are achieved by convergence of the entropy production profile. Various cases, as the one-dimensional steady heat conduction, steady convective heat transfer, and unsteady heat conduction, are evaluated by the current approach, and the approach is proved to be effective.

Numerical Simulation of Stability to Muzhuping Slope Failed by Impoundment in Shuibuya Reservoir

The Shuibuya Dam is the highest concrete faced rockfill dam (the height is 233m) in the world. The dam site is located in Enshi Autonomous Prefecture, Hubei province, china. The reservoir level is a maximum of 400m. When the dam was partially completed, water impoundment was started. On May 10, 2007, when the reservoir level achieved at 289m, a landslide located on the bank of Modao-he River moved rapidly, a tributary of the Qingjiang River. 14 houses collapsed and moved into the river, but nobody was killed due to timely geological prediction. For the purposes of landslide disaster mitigation in the reservoir areas and identification of landslide movement and deformation caused by the change of reservoir level, some researches were conducted, such as geological exploration, some soil tests and numerical simulation and monitoring system. In this paper, the causes of landslides and slope failure mechanism and the stability of slope were simulated by using DDA method and FLAC3D for the different reservoir’s level.