Adaptive Grid Method Research Articles

Incorporating numerical method for analyzing the conduction heat transfer during solidification loading nanoparticles

This study examines the freezing within a tank with a curved cold surface, integrating an innovative use of fins. The addition of fins and the careful introduction of nanomaterial knowingly enhance solidification efficiency, with potential applications in areas such as cryopreservation and thermal energy storage. To further optimize the solidification process, various types and concentrations of nano-powders were dispersed into the water, serving as heat transfer enhancers. The mathematical model was refined through specific assumptions, leading to the derivation of two principal equations. These equations were then effectively solved using the Galerkin method, offering a novel optimization approach for solidification. The enhancement in conductivity due to the modifications plays a key role in improving the productivity of the system. Furthermore, the addition of nanoparticles resulted in a notable extension of freezing time around 26.71%. The use of an adaptive grid method during grid generation, coupled with the successful verification of the final model, strengthens the reliability of the research. By increasing the parameter "m" (shape factor) from 4.8 to 8.6, the solidification time was reduced by approximately 6.96%, demonstrating a significant improvement in the system's efficiency.

An adaptive grid method for a two-parameter singularly perturbed problem with non-smooth data

In this paper, a two-parameter singularly perturbed problem with discontinuous source and convection coefficient is studied. This problem is discretized by using a first-order upwind finite difference scheme for which a posteriori error analysis in the maximum norm is derived. Then, based on this a posteriori error estimation, a grid iteration algorithm is designed to generate an adaptive nonuniform mesh. Finally, Numerical experiments are proposed to confirm that our proposed method is first-order uniformly convergent.

Design of information management model based on multiobjective optimization algorithm in intelligent electric financial system

The electric power infrastructure is the cornerstone of contemporary society’s sustenance and advancement. Within the intelligent electric power financial system, substantial inefficiency and waste in information management persist, leading to an escalating depletion of resources. Addressing diverse objectives encompassing economic, environmental, and societal concerns within the power system helps the study to undertake a comprehensive, integrated optimal design and operational scheduling based on a multiobjective optimization algorithm. This article centers on optimizing the power financial system by considering fuel cost, active network loss, and voltage quality as primary objectives. A mathematical model encapsulates these objectives, integrating equations and inequality constraints and subsequently introducing enhancements to the differential evolutionary algorithm. Adaptive variation and dynamic crossover factors within crossover, variation, and selection operations are integrated to optimize algorithm parameters, specifically catering to the multiobjective optimization of the electric power system. An adaptive grid method and cyclic crowding degree ensure population diversity and control the Pareto front distribution. They experimentally validated the approach and the comparisons conducted against AG-MOPSO, INSGA-II, and NSDE algorithms across standard test functions: ZDT1, ZDT2, ZDT3, and DTLZ4. The convergence evaluation indices for this study’s scheme on ZDT1 and ZDT2 are 0.000938 and 0.0034, respectively. Additionally, distribution evaluation indices on ZDT1, ZDT2, ZDT3, and ZDT4 stand at 0.0018, 0.0026, 0.0027, and 0.0009, respectively. These indices indicate a robust convergence and distribution, facilitating the optimization of electric power financial information management and the intelligent handling of the electric power financial system’s information, thereby enhancing the allocation of material and financial resources.

Integrated optimization design of multiphase pump based on adaptive sparse grid method

Multiphase pump play a critical role in natural gas hydrate extraction. However, their stable and efficient operation in complex multiphase flow conditions remains a significant challenge. This study focuses on a “gas-liquid-solid” multiphase mixing pump and uses numerical simulations to analyze its single-stage pressure boosting unit under different conditions. The results revealed a significant decrease in pressure increment and efficiency under high gas content and solid phase content conditions. To address this, the study built an integrated optimization design platform based on an adaptive sparse grid surrogate model. This platform optimized critical hydraulic parameters of the pump through an adaptive sparse grid method and MOGA algorithm. The results show that under water conditions, pressure increment and efficiency can be increased by 12.805 KPa and 1.79%, respectively. Under working conditions of 30% GVF and 25% SVF, the pressure increment can reach 7.889 KPa, and the efficiency can be increased by 2.75%. Verification experiments demonstrated the reliability of the numerical methods utilized. Overall, the integrated optimization design platform saves computational resources, improves optimization efficiency and provides a foundation for ongoing research on the multi-gas co-production of natural gas hydrates.

A330-300 Wake Encounter by ARJ21 Aircraft

Today, aviation has grown significantly in importance. However, the challenge of flight delays has become increasingly severe due to the need for safe separation between aircraft to mitigate wake turbulence effects. The primary emphasis of this investigation resides in elucidating the evolutionary attributes of wake vortices in homogeneous isotropy turbulence. The large eddy simulation (LES) method is used to scrutinize the dynamic evolution of wake vortices engendered by an A333 aircraft in the atmospheric milieu and assess its ramifications on the ARJ21 aircraft. The research endeavor commences by formulating an LES methodology for the evolution of aircraft wake vortices, integrating adaptive grid technology to reduce the necessary grid volume significantly. This approach enables the implementation of axial and non-axial grid adaptive refinement, leading to more accurate simulations of both axial and non-axial vortices. Numerical simulations are conducted using the LES approach to scrutinize three distinct rates of turbulence dissipation amidst the ambient atmospheric turbulence, and the results are juxtaposed with Lidar measurements (Wind3D 6000 LiDAR) of wake vortices acquired at Chengdu Shuangliu International Airport (CTU). Subsequently, the rolling moment of the following aircraft is calculated, and three-dimensional hazard zones are determined for the A333. It is found that during the approach phase, the wake turbulence separation minima for an ARJ21 (CAT-F) following an A333 (CAT-B) is 3.35 NM, which represents a reduction of approximately 33% compared to ICAO RECAT (Wake Turbulence Re-categorization). The findings validate the dependability of the fine-grained mesh used in the vortex core region, engendered through the adaptive grid method, which proficiently captures the Crow instability and the interconnected phenomena of vortices in the numerical examination of aircraft wake. The safety of wake encounters primarily depends on the magnitude of environmental turbulence and the development of structural instability in wake vortices.

Limited sampling strategy and population pharmacokinetic model of mycophenolic acid in pediatric patients with systemic lupus erythematosus: application of a double gamma absorption model with SAEM algorithm.

Mycophenolic acid (MPA), the active metabolite of mycophenolate mofetil (MMF), is widely used in the treatment of systemic lupus erythematosus (SLE). It has been shown that its therapeutic drug monitoring based on the area under the curve (AUC) improves treatment efficacy. MPA exhibits a complex bimodal absorption, and a double gamma distribution model has been already proposed in the past to accurately describe this phenomenon. These previous population pharmacokinetics models (POPPK) have been developed using iterative two stage Bayesian (IT2B) or non-parametric adaptive grid (NPAG) methods. However, non-linear mixed effect (NLME) approaches based on stochastic approximation expectation-maximization (SAEM) algorithms have never been published so far for this particular model. The objectives of this study were (i) to implement the double absorption gamma model in Monolix, (ii) to compare different absorption models to describe the pharmacokinetics of MMF, and (iii) to develop a limited sampling strategy (LSS) to estimate AUC in pediatric SLE patients. A data splitting of full pharmacokinetic profiles sampled in 67 children extracted either from the expert system ISBA (n = 34) or the hospital Saint Louis (n = 33) was performed into train (75%) and test (25%) sets. A POPPK was developed for MPA in the train set using a NLME and the SAEM algorithm and different absorption models were implemented and compared (first order, transit, or simple and double gamma). The best limited sampling strategy was then determined in the test set using a maximum-a-posteriori Bayesian method to estimate individual PK parameters and AUC based on three blood samples compared to the reference AUC calculated using the trapezoidal rule applied on all samples and performances were assessed in the test set. Mean patient age and dose was 13years old (5-18) and 18.1mg/kg (7.9-47.6), respectively. MPA concentrations (764) from 107 occasions were included in the analysis. A double gamma absorption with a first-order elimination from the central compartment best fitted the data. The optimal LSS with samples at 30min, 2h, and 3h post-dose exhibited good performances in the test set (mean bias - 0.32% and RMSE 21.0%). The POPPK developed in this study adequately estimated the MPA AUC in pediatric patients with SLE based on three samples. The double absorption gamma model developed with the SAEM algorithm showed very accurate fit and reduced computation time.

A subgrid model with multiple relaxation time for lattice Boltzmann method based on the Cartesian grid

Purpose The paper aims to expand the scope of application of the lattice Boltzmann method (LBM), especially in the field of aircraft engineering. The traditional LBM is usually applied to incompressible flows at a low Reynolds number, which is not sufficient to satisfy the needs of aircraft engineering. Devoted to tackling the defect, the paper proposes a developed LBM combining the subgrid model and the multiple relaxation time (MRT) approach. A multilayer adaptive Cartesian grid method to improve the computing efficiency of the traditional LBM is also employed.Design/methodology/approach The subgrid model and the multilayer adaptive Cartesian grid are introduced into MRT-LBM for simulations of incompressible flows at a high Reynolds number. Validated by several typical flow simulations, the numerical methods in this paper can efficiently study the flows under high Reynolds numbers.Findings Some numerical simulations for the lid-driven flow of cavity, flow around iced GLC305, LB606b and ONERA-M6 are completed. The paper presents the investigation results, indicating that the methods are accurate and effective for the separated flow after icing.Originality/value LBM is developed with the addition of the subgrid model and the MRT method. A numerical strategy is proposed using a multilayer adaptive Cartesian grid method and its treatment of boundary conditions. The paper refers to innovative algorithm developments and applications to the aircraft engineering, especially for iced wing simulations with flow separations.

A population balance method for simulation of particle-induced droplet breakup in spray flame synthesis and suspension spray combustion

A population balance method based on weighted Monte-Carlo droplets is used to investigate breakup phenomena in single droplet combustion and spray flame synthesis (SFS). Particle shell formation in conjunction with superheating of liquid components is shown to be a plausible cause for droplet breakup. The breakage rate is calculated based on temperature and particle concentration profiles inside individual droplets, whereas the breakage function was determined using shadowgraphy imaging of droplets and image analysis. This enabled the simulation of consecutive breakup events in single droplet combustion and SFS. Furthermore, in the context of population balance simulations, an adaptive grid method is introduced for the calculation of particle accumulation at the droplet surface. This method is applicable to quickly evaporating droplets where particle transport by advection is fast compared to transport by radial diffusion. The new adaptive grid method is evaluated by comparison with seven single droplet combustion experiments from literature. More than that, parallel algorithms for a computationally efficient implementation using graphics processing units (GPUs) are discussed.

SPEA2 based on grid density search and elite guidance for multi-objective operation optimization of wastewater treatment process

It is challenging to introduce an optimization method to improve the operation performance of wastewater treatment process (WWTP) on account of its high energy consumption and poor water quality characteristics. In this paper, an improved Strength Pareto Evolutionary Algorithm 2 (SPEA2) based on grid density search and elite guidance (GDSEG-SPEA2) is proposed for multi-objective operation optimization of WWTP. First, the external archive is divided by an improved adaptive grid method to determine the distribution density of the solutions, and a neighborhood circle strategy as well as a mixed perturbation strategy are designed to search the neighborhood of sparse and crowded solutions, resulting in a more uniformly distributed Pareto front. Then, in order to avoid SPEA2 falling into local optimum after adding the neighborhood search strategies, the crossover and mutation operations based on individual information are proposed to generate new individuals. Finally, an elite guidance strategy, in which the poor-performing individuals of the population learn from the best-performing individuals to update their positions, is introduced into the algorithm to improve convergence. The test function verification shows that the proposed algorithm can obtain the Pareto front with better distribution and convergence than other existing algorithms. The operation optimization control experiment of WWTP shows that the proposed algorithm can better purify water quality and reduce more energy consumption on the premise of ensuring that effluent quality meets the discharge standards, which is better than other optimization algorithms in comparison.

An adaptive divided-difference perturbation method for solving stochastic problems

Most stochastic problems are based on the independent and symmetrically distributed random variables. Using this principle, in this study, we propose an efficient calculation scheme to obtain the statistical moments based on high-order stochastic perturbation (SP) expansion. This solves the long-existing problem of the SP method, namely, the low calculation efficiency of statistical moments using high-order perturbation expansion, and the complexity of the calculation format. The scheme involves adopting the divided-difference method to approximate the partial derivative items of the SP method. The proposed method, which is similar to the collocation point method, only requires the deterministic calculation result for each node in the divided-difference method. In addition, as the adoption of high-order perturbation expansion is limited in multidimensional random problems due to the curse of dimensionality, an adaptive partial derivative items selection method is proposed in this paper to efficiently and reasonably ignore the expansion items that have an insignificant influence on statistical moments. This considerably improves the calculation efficiency of the statistical moments. Finally, the adaptive divided-difference perturbation (ADDP) method proposed in this paper is compared with the quasi-Monte Carlo method and the adaptive sparse grid methods using three numerical examples. The results prove that the ADDP method not only has high efficiency but also leads to significant improvements in the accuracy of statistical moments.

Population pharmacokinetic analysis and dosing optimization of polymyxin B in critically ill patients.

Objectives: Since the global broadcast of multidrug-resistant gram-negative bacteria is accelerating, the use of Polymyxin B is sharply increasing, especially in critically ill patients. Unsatisfactory therapeutic effects were obtained because of the abnormal physiological function in critically ill patients. Therefore, the determination of optimal polymyxin B dosage becomes highly urgent. This study aimed to illustrate the polymyxin B pharmacokinetic characteristics by defining the influencing factors and optimizing the dosing regimens to achieve clinical effectiveness. Methods: Steady-state concentrations of polymyxin B from twenty-two critically ill patients were detected by a verified liquid chromatography-tandem mass spectrometry approach. The information on age, weight, serum creatinine, albumin levels, and Acute Physiology and Chronic Health Evaluation-II (APACHE-II) score was also collected. The population PK parameters were calculated by the non-parametric adaptive grid method in Pmetrics software, and the pharmacokinetic/pharmacodynamics target attainment rate was determined by the Monte Carlo simulation method. Results: The central clearance and apparent volume of distribution for polymyxin B were lower in critically ill patients (1.24 ± 0.38Lh-1 and 16.64 ± 12.74 L, respectively). Moreover, albumin (ALB) levels can be used to explain the variability in clearance, and age can be used to describe the variability in the apparent volume of distribution. For maintaining clinical effectiveness and lowering toxicity, 75mg q12h is the recommended dosing regimen for most patients suffering from severe infections. Conclusion: This study has clearly defined that in critically ill patients, age and ALB levels are potentially important factors for the PK parameters of polymyxin B. Since older critically ill patients tend to have lower ALB levels, so higher dosages of polymyxin B are necessary for efficacy.

Experimental and numerical research of the behavior of 3D internal cracks under uniaxial compression using 3D-ILC technology

Uniaxial compression tests are one of the classic tests of solid mechanics. However, there remain some unsolved problems involving the test methods and numerical simulation. In the present study, in view of the difficulties in the manufacture of real internal cracks, glass, a classical material whose brittleness is quite close to that of natural rock material, is selected to generate pure closed internal cracks using 3D Internal Laser-Engraved Crack (3D-ILC) technology. Through the uniaxial compression test, we observe that the failure of specimens originates from the pre-existing internal crack. First, wing cracks are generated around it, which then propagate. As the load reaches the maximum bearing capacity, the later tensile crack eventually leads to the failure of the specimen. This test method can be used to observe and study the crack propagation process, failure law, failure mode and characteristic load of brittle materials. In the numerical analysis, adaptive grid method is used for grid division and update. The distribution of KI, KII, and KIII at the crack tip is obtained by M-Integral, and the crack propagation is simulated in combination with the maximum tensile stress (MTS) criterion. In terms of numerical simulation, the mode I/II/III propagation simulation of 3D internal crack is successfully realized, which is of great significance. At present, the research of 3D crack propagation and internal crack propagation has encountered bottlenecks in theory, experiment and numerical simulation. It is hoped that the experimental and numerical simulation methods in this paper can provide some reference.

An adaptive grid method for a singularly perturbed convection-diffusion equation with a discontinuous convection coefficient

<abstract><p>In this paper, an adaptive grid method is put forward to solve a singularly perturbed convection-diffusion problem with a discontinuous convection coefficient. First, this problem is discretized by using an upwind finite difference scheme on an arbitrary nonuniform grid except the fixed jump point. Then, a first-order maximum norm a posterior error estimate is derived. Further, based on this a posteriori error estimation and the mesh equidistribution principle, an adaptive grid generation algorithm is constructed. Finally, some numerical experiments are presented that support our theoretical estimate.</p></abstract>

A robust adaptive grid method for first-order nonlinear singularly perturbed Fredholm integro-differential equations

<abstract><p>In this paper, a robust adaptive grid method is developed for solving first-order nonlinear singularly perturbed Fredholm integro-differential equations (SPFIDEs). Firstly such SPFIDEs are discretized by the backward Euler formula for differential part and the composite numerical quadrature rule for integral part. Then both a prior and an a posterior error analysis in the maximum norm are derived. Based on the prior error bound and the mesh equidistribution principle, it is proved that there exists a mesh gives optimal first-order convergence which is robust with respect to the perturbation parameter. Finally, the posterior error bound is used to choose a suitable monitor function and design a corresponding adaptive grid generation algorithm. Numerical results are given to illustrate our theoretical result.</p></abstract>

An Optimal Adaptive Grid Method Based on L1 Scheme for a Nonlinear Caputo Fractional Differential Equation

A nonlinear fractional differential equation with a Caputo derivative of order α is studied. This problem is discretized by using the L1 scheme on an arbitrary nonuniform mesh. By utilizing the Taylor expansion with integral remainder term, an optimal local truncation error estimation of L1 scheme is proved. Based on this truncation error estimation and the mesh equidistribution principle, a new monitor function is constructed to construct an adaptive grid generation algorithm. Numerical experiments are performed to confirm the accuracy of our new adaptive grid algorithm.

A Second-Order Adaptive Grid Method for a Singularly Perturbed Volterra Integrodifferential Equation

In this paper, an adaptive grid method for a singularly perturbed Volterra integro-differential equation is studied. Firstly, this problem is discretized by a new second-order finite difference scheme, for which a truncation error analysis is conducted. Then, based on this truncation error bound and the mesh equidistribution principle, we show that there is a mesh that provides an optimal error bound of O(N−2), which is robust with respect to the perturbation parameter. Finally, based on an approximation monitor function, an adaptive grid generation algorithm is constructed and some numerical results are given to support our theoretical results.

Numerical simulation analysis of symmetric impact of two droplets on a liquid film

Analyzing the impact of a droplet on a liquid film is a typical free-surface problem. However, a few studies have investigated the impact of multiple droplets, and in most cases, the droplet impact direction is assumed to be vertically downward. The effect of the impact angle on the characteristic parameters of the spray remains unknown. In this study, the coupled level set and volume of fluid method is used to analyze the development of the gas–liquid interface when two droplets impact a liquid film, and the grid of the gas–liquid interface is refined using the grid adaptive refinement method. The accuracy of numerical simulation has also been verified. The numerical simulation results showed significant differences in the liquid splash morphology corresponding to the different impact modes. The inward impact of the two droplets promotes splashing, whereas the outward impact inhibits it. The liquid film thickness primarily affects the local splash morphology. The droplet spacing affects the spreading diameter and jet angle. The cylindrical jet formed by the symmetrical inward impact of the droplets is unstable, and the rupture mechanism of the cylindrical jet is elucidated for different impact modes. These results provide reference for the application of droplets impingement.

Complex-valued derivative propagation method with adaptive moving grids for electronic nonadiabatic dynamics

The coupled complex quantum Hamilton–Jacobi equations in the diabatic representation are solved on adaptive moving grids for electronic nonadiabatic dynamics. Substitution of the wave functions in exponential form into the coupled time-dependent Schrödinger equations yields the coupled complex quantum Hamilton–Jacobi equations. Analytic equations of motion are derived for the spatial derivatives of the complex action functions for both surfaces. The equations of motion for the complex actions and their spatial derivatives are converted into the arbitrary Lagrangian–Eulerian frame, allowing us to have many ways to choose the velocities for the moving points. The grid points can be specified to move along with the probability fluid. In contrast, choosing the boundary grid points to follow Lagrangian trajectories and forcing the internal grid points to be equally spaced at each time step, we obtain a moving structured grid of uniform spacing during the wave packet evolution. Several examples are presented to illustrate main features of the adaptive grid method, including a single avoided crossing system, a dual avoided crossing system, an ultrashort laser pulse excitation system, and a three-dimensional nonadiabatic system. Accurate computational results demonstrate that the adaptive grid method provides an alternative way to study electronic nonadiabatic dynamics.

Secure Data Publishing of Private Trajectory in Edge Computing of IoT

Secure data publishing of private trajectory is a typical application scene in the Internet of Things (IoT). Protecting users’ privacy while publishing data has always been a long-term challenge. In recent years, the mainstream method is to combine the Markov model and differential privacy (DP) mechanism to build a private trajectory generation model and publishes the generated synthetic trajectory data instead of the original data. However, Markov cannot effectively model the long-term trajectory data spatio-temporal correlation, and the DP noise results in the low availability of the synthetic data. To protect users’ privacy and improve the availability of synthetic trajectory data, we propose a trajectory generation model with differential privacy and deep learning (DTG). In DTG, we design a private hierarchical adaptive grid method. It divides the geospatial region into several subregions according to the density of positions to realize the discretization of coordinates of the trajectory data. Second, GRU is used to capture the temporal features of the trajectory sequence for good availability, and we generate synthetic trajectory data by predicting the next position. Third, we adopt the optimizer perturbation method in gradient descent to protect the privacy of model parameters. Finally, we experimentally compare DTG with the state-of-the-art approaches in trajectory generation on actual trajectory data T-Drive, Portotaxi, and Swedishtaxi. The result demonstrates that DTG has a better performance in generating synthetic trajectories under four error metrics.

The comparison of adjoint-based grid adaptation and feature-based grid adaptation method

Grid adaption is a popular method to enhance the resolution of flow field and the precision of numerical simulation, which automatically optimizes the grid distribution instead of manual complicated work. There exist usually two grid adaptation methods, the feature based grid adaption and adjoint based grid adaption, the former focuses on shocks, vortexes and other features of flow field, and the latter focuses on lift, drag and other aerodynamic characteristics. The comparison of adjoint based grid adaption and feature based grid adaption method is investigated in this paper. Numerical simulations show that both feature adaption and adjoint adaption could improve the resolution of flow field and the precision of numerical simulation such as lift and drag. As for the flow features, the feature adaptation could capture the obvious shock waves and vortexes in the flow field, the adjoint adaptation, however, only captures the flow features that are contributory to the accuracy of aerodynamic characteristics. As for the aerodynamic characteristics, some shock waves and vortexes have little influences to the forces, so the feature adaptation is not efficient as adjoint adaptation, which could greatly improve the accuracy of aerodynamic characteristics.