Simulation Scheme Research Articles

High-order adaptive multi-domain time integration scheme for microscale lithium-ion batteries simulations

We investigate the modeling and simulation of ionic transport and charge conservation in lithium-ion batteries (LIBs) at the microscale. It is a multiphysics problem that involves a wide range of time scales. The associated computational challenges motivate the investigation of numerical techniques that can decouple the time integration of the governing equations in the liquid electrolyte and the solid phase (active materials and current collectors). First, it is shown that semi-discretization in space of the non-dimensionalized governing equations leads to a system of index-1 semi-explicit differential algebraic equations (DAEs). Then, a new generation of strategies for multi-domain integration is presented, enabling high-order adaptive coupling of both domains in time, with efficient and potentially different domain integrators. They reach a high level of flexibility for real applications, beyond the limitations of multirate methods. A simple 1D LIB half-cell code is implemented as a demonstrator of the new strategy for the simulation of different modes of cell operation. The integration of the decoupled subsystems is performed with high-order accurate implicit nonlinear solvers. The accuracy of the space discretization is assessed by comparing the numerical results to the analytical solutions. Then, temporal convergence studies demonstrate the accuracy of the new multi-domain coupling approach. Finally, the accuracy and computational efficiency of the adaptive coupling strategy are discussed in the light of the conditioning of the decoupled subproblems compared to the one of the fully-coupled problem. This new approach will constitute a key ingredient for the high-fidelity 3D LIB simulations based on actual electrode microstructures.

A positivity-preserving approach for implicit dual-time stepping schemes in multi-component flow simulations

A positivity-preserving approach for implicit dual-time stepping schemes in multi-component flow simulations

Alternative dissolution-rate controlled model and time adaptive, high resolution scheme for site-scale subsurface carbon sequestration simulation

Performance assessment and field-development planning for carbon geo-sequestration relies on reservoir simulation. The standard approach is to use regular (corner-point) grids in space and a fully implicit discretisation in time, solving for all primary unknowns at once using Newton’s method. While the former limits the physical realism of the simulation model built from the geomodel, the latter leads to a large ill-conditioned system of equations that is inefficient to solve. We overcome the regularisation issue via a hierarchy of fully unstructured, geobody-conforming, finite element meshes which can be refined until mesh convergence is achieved. To address the time discretisation issue we employ, for the first time, the linearly implicit extrapolation scheme (LIMEX) to solve the highly non-linear coupled two-phase flow and reactive transport equations. To solve the arising large sparse systems of linear equations, we apply the geometric multigrid (GMG) method that demonstrates optimal, linear complexity and allows an efficient parallelization on supercomputers. Another novel feature of our formulation is the consideration of the kinetics of mass transfer between the carbonic and aqueous phases. This approach removes the first-order dependence on mesh refinement of CO2 that is dissolved, a characteristic feature of standard equilibrium models. We demonstrate the parallel scalability of our simulation framework with an implementation based on the UG4 platform. Proof-of-concept results accurately capture key features of CO2 migration including filtration by capillary barriers and convective dissolution of CO2 at the base of the plume.

REGULARITY OF THE ASYMPTOTIC BLOW-UP FOR A NONLINEAR PARABOLIC EQUATION WITH CRITICAL ENERGY

We consider the behaviour of the critical energy for the nonlinear heat equation. We focus on the analysis of critical solutions for a class of nonlinear heat equations in a bounded domain. In order to study the construction of suitable approximate solutions, and then the more precisely, we show that the solution of a semi-discrete form of (P) becomes zero when t goes to infinity and we give to infinity and give its asymptotic behaviour. Using some non-standard schemes, we also prove certain estimates for discrete forms of the problem that the numerical approximation of the explosion time where is an increasing function, . We derive some criteria for the initial data that guarantee the explosion of the solution of in a finite time. More general non-linearities will be briefly considered. We will always assume that belongs to a space of functions in which the problem is well posed and we denote by the maximum existence time of the solution of . We start with a simple criterion. In the case of a bounded domain, it is based on Kaplan's eigenfunction method, see [9]. We show that the solution of a semi-discrete form of becomes zero when tends to infinity and give its asymptotic behaviour. Using non-standard schemes, we also prove some estimates for discrete forms of . Finally, the heat equation in has been solved numerically by testing the convergence and stability of explicit and implicit schemes in simulation using finite difference methods. The examples show that the implemented schemes are consistent with the theoretical predictions and that the truncation errors depend on the mesh size, spacing and time step. Some numerical examples are given to illustrate all these results.

Repeated interaction scheme for the quantum simulation of non-Markovian electron transfer dynamics.

Quantum algorithms have the potential to revolutionize our understanding of open quantum systems in chemistry. In this work, we demonstrate that a repeated interaction model, which could serve as the foundation for a digital quantum algorithm, can effectively reproduce non-Markovian electron transfer dynamics under four different donor-acceptor parameter regimes and for a donor-bridge-acceptor system. We systematically explore how the model scales for the regimes. Notably, our approach exhibits favorable scaling in the required repeated interaction duration as the electronic coupling, temperature, damping rate, and system size increase. Furthermore, a single Trotter step per repeated interaction leads to an acceptably small error, and high-fidelity initial states can be prepared with a short time evolution. This efficiency highlights the potential of the model for tackling increasingly complex systems. When fault-tolerant quantum hardware becomes available, algorithms based on this model could be extended to incorporate structured baths, additional energy levels, or more intricate coupling schemes, enabling the simulation of real-world open quantum systems that remain beyond the reach of classical computation.

Meshless Numerical Simulation on Dry Shrinkage Cracking of Concrete Piles for Offshore Wind Power Turbine

Against the backdrop of the global energy transition, offshore wind power has undergone rapid development. As a vital component of offshore wind power infrastructure, dry shrinkage cracking in concrete piles poses a significant threat to the safe and stable operation of offshore wind power systems. However, the fundamental mechanism of concrete pile cracking during dry shrinkage—particularly the coupled effects of moisture diffusion, meso-structural heterogeneity, and stress evolution—remains poorly understood, lacking a unified theoretical framework. This knowledge gap hinders the development of targeted anti-cracking strategies for offshore concrete structures. Hence, investigating the mechanism of dry shrinkage cracking is of substantial importance. This paper employs numerical simulation to explore the patterns and influencing factors of dry shrinkage cracking in concrete piles for offshore wind turbines, aiming to provide theoretical support for enhancing pile performance. A meshless numerical simulation method based on the smoothed particle hydrodynamics (SPH) framework is developed, which generates concrete meso-structures via a specific algorithm, discretizes the moisture diffusion equation, defines dry shrinkage stress terms, and introduces a fracture coefficient to characterize particle failure, enabling the simulation of concrete dry shrinkage cracking processes. Simulation schemes are designed for varying aggregate percentages, aggregate particle sizes, dry shrinkage coefficients, and moisture diffusion coefficients, using a 100 mm-diameter circular concrete model. Qualitative results reveal the following: Increased aggregate percentages lead to more uniform moisture diffusion, with dry shrinkage crack number and length first increasing and then decreasing; larger aggregate particle sizes exacerbate moisture diffusion non-uniformity and intensify dry shrinkage cracking; higher dry shrinkage coefficients correlate with increased crack number and length; elevated moisture diffusion coefficients accelerate surface water loss, with cracking severity first increasing and then decreasing. The proposed SPH-based meshless method effectively simulates dry shrinkage cracking in offshore wind turbine concrete piles, demonstrating the significant impact of different factors on moisture diffusion and cracking patterns. This study offers insights for applying the SPH method in related fields, deepens the understanding of concrete dry shrinkage cracking mechanisms, and provides a theoretical foundation for the design and optimization of offshore wind power concrete piles.

Simulation of the 1d XY model on a quantum computer

The field of quantum computing has grown fast in recent years, both in theoretical advancements and the practical construction of quantum computers. These computers were initially proposed, among other reasons, to efficiently simulate and comprehend the complexities of quantum physics. In this paper, we present a comprehensive scheme for the exact simulation of the 1-D XY model on a quantum computer. We successfully diagonalize the proposed Hamiltonian, enabling access to the complete energy spectrum. Furthermore, we propose a novel approach to design a quantum circuit to perform exact time evolution. Among all the possibilities this opens, we compute the ground and excited state energies for the symmetric XY model with spin chains of n=4n=4 and n=8n=8 spins. Further, we calculate the expected value of transverse magnetization for the ground state in the transverse Ising model. Both studies allow the observation of a quantum phase transition from an antiferromagnetic to a paramagnetic state. Additionally, we have simulated the time evolution of the state all spins up in the transverse Ising model. The scalability and high performance of our algorithm make it an ideal candidate for benchmarking purposes, while also laying the foundation for simulating other integrable models on quantum computers.

ESMAC Best Paper 2024: Defining exoskeleton aim matters: Simulating optimal assistive moments with explicit objectives using bilevel optimization.

ESMAC Best Paper 2024: Defining exoskeleton aim matters: Simulating optimal assistive moments with explicit objectives using bilevel optimization.

Urban Flood Model-Driven Optimization of Flood Control and Drainage Engineering Solutions

With the rapid advances of global climate change and urbanization, urban flooding is causing greater losses. Existing urban flood control and drainage engineering design standards are often applied to single projects. This paper proposes a set of urban flood model-driven optimization of flood control and drainage engineering solutions. Applied to Shenzhen’s Shawan interception project, the preferred option demonstrates significant improvements, such as the following: a 25% reduction ratio of the maximum designed water depth at key points of the Shawan River main stream, a 0.26% reduction in the maximum submerged area of the urban surface, a 3.27% reduction in the full pipe rate of drainage pipe, and a 10.81% reduction in the overflow rate of inspection wells. The comprehensive flood control and drainage benefits are the best, and they achieve the solution of problems within the basin. Aiming at the shortage of comprehensive consideration of project scale, combination mode, and control scheme in urban flood control planning and design, this simulation scheme proposes a set of detailed design technologies of urban flood control engineering based on a flood numerical model. The analysis results show that the ideas proposed in this paper can provide a reference for the design of urban flood control and drainage engineering.

A Novel Stream Network Upscaling Scheme for Accurate Local Streamflow Simulations in Gridded Global Hydrological Models

Abstract Large‐scale hydrological models are progressing toward sub‐kilometer resolutions to achieve “locally relevant hydrological simulations.” However, grid‐based domain representations introduce significant errors in streamflow within small catchments, a challenge that remains unresolved by state‐of‐the‐art modeling schemes, such as 8‐directional gridded routing (D8). Here, we introduce the Subgrid Catchment Conservation (SCC) scheme to enhance streamflow estimation at any location within the domain using a coarse resolution (i.e., 1 km or more), continental scale, grid‐based hydrological model (HM). Gridded HMs not preserving the DEM‐reference (or subgrid) catchment area is usually referred as the catchment size problem. SCC allows multiple outflow from grid cells, a key feature that preserves the subgrid catchment area of all points of interest across scales. SCC is a general concept; however, for demonstration purposes, it has been implemented in the mesoscale hydrological model, mHM. We employ a global setup with 62 large‐scale domains encompassing 5,256 streamflow gauging stations, and a regional setup encompassing 187 stations in the Rhine river basin. We found that the widely used D8 scheme's efficacy diminishes drastically for catchments under 30 times the grid size. SCC demonstrates remarkable consistency in streamflow in the regional experiment with nine out of 10 stations exceeding the mean flow benchmark (KGE −0.41) across 1–100 km model resolutions. In addition, SCC's ability to resolve multiple points of interests in a grid leads to greater modeling flexibility. By addressing the catchment size problem, SCC marks a significant advancement for global‐scale simulations producing locally relevant streamflow.

Full engine 3D simulation scheme considering rotor motion for turbojet engine under crosswind conditions

Full engine 3D simulation scheme considering rotor motion for turbojet engine under crosswind conditions

Evaluation of Turbulence Parameterization in Gray Zone Simulations of Real-Case Precipitation Events

Abstract In practice, the deep convection parameterization schemes are often switched off in convection-permitting simulations, which enables the turbulence parameterization scheme to be solely responsible for the representation of subgrid-scale (SGS) turbulent fluxes inside convective clouds. However, traditional 3D turbulence schemes or 1D planetary boundary layer (PBL) schemes in convection-permitting simulations adopt the eddy-diffusivity formulation to represent SGS turbulent fluxes in the free atmosphere, leading to insufficient mixing inside convective clouds above the PBL, which further results in the overestimation of heavy precipitation in convection-permitting simulations. In this study, we applied a nonlinear horizontal gradient (H-gradient) term, which is capable of representing countergradient SGS turbulent transports inside convective clouds, to a 3D turbulent kinetic energy–based turbulence scheme. The results of two heavy precipitation case studies showed that the new 3D turbulence scheme, modified by the H-gradient term, produces satisfactory results that agree well with observations in terms of the magnitude and distribution of precipitation. A two-month experiment further showed that the modified scheme can reduce the systematic bias of overestimated heavy and extreme precipitation in convection-permitting simulations.

An efficient structured grid generation scheme for seismic wave simulation in regions with extreme topography

Using curvilinear structured grids, the finite difference method (FDM) can effectively simulate seismic wave propagation in regions with irregular topography. However, generating high-quality curvilinear structured grids in regions with extreme topography, such as mountains or nearly vertical reservoir dams, is not an easy task and limits the application of FDM in seismic wave simulation. Grid quality is crucial for finite difference simulations, as it directly affects the accuracy, stability, and efficiency of the simulation. Therefore, achieving an efficient and automatic generation of high-quality structured grids is essential for applying FDM to seismic wave simulation in regions with topography. The grids used for seismic wave simulation have a special feature compared to other computational problems: only the shape of the free surface is fixed, while the shapes of the other boundaries are free to be set. Based on this feature, we propose an efficient and automatic grid generation scheme that integrates the hyperbolic grid generation method and the algebraic interpolation method. Initially, the grids are generated using the hyperbolic method, starting from the given free surface and expanding layer by layer along the depth direction. However, when dealing with extreme topographies, the resulting grids exhibit poor smoothness in the depth direction. To enhance the grid quality, we redistribute the grid points using an interpolation approach along the depth direction. We designed two models with extreme topography and used the Foothills model to test the grid generation scheme and its application in seismic wave simulation. The results of the grid quality assessment indicate that the scheme can efficiently generate high-quality grids. Seismic wave propagation simulations reveal that these high-quality grids significantly improve computational efficiency with sufficient simulation accuracy.

High Order Approximations and Simulation Schemes for the Log-Heston Process

High Order Approximations and Simulation Schemes for the Log-Heston Process

GPU-enabled high-order gas-kinetic scheme for actuator line model simulations of wind turbine wakes

Abstract For the first time, we integrate the actuator line model (ALM) into a fourth-order gas-kinetic scheme (GKS) to accurately simulate wind turbine wakes. We first extend the GKS to the simulation of weakly compressible flows within a well-developed two-stage fourth-order framework. The ALM is included as an external body force term in the momentum equation for the GKS. The in-house second-order and fourth-order GKS with ALM is implemented on Graphics Processing Units (GPU) to leverage their parallel computing capabilities for wake turbulence simulation. The NREL 5 MW reference wind turbine is simulated using the GPU-enabled second-order and fourth-order GKS with ALM. The normal and tangential forces acting on the turbine blades agree well between the second-order and fourth-order GKS, indicating that the numerical discretization error has a very limited impact on the blade force predictions. For the wind turbine wake, the instantaneous wake turbulent structures, the time-averaged velocity and turbulent kinetic energy from the second-order GKS with locally-refined grids converge to those from the fourth-order GKS with uniform grids, demonstrating that the high-order numerical scheme improves the resolution of the vortex-dominated wake turbulence. In addition, the fourth-order GKS with uniform grid is more efficient than the second-order GKS with locally-refined grid.

Issues of Effective Integration of Solar Power Plant with Local Power Grid

The article studies the possibility of improving the most efficient integration of solar power plants (SPP) with the electric grid by analyzing foreign scientific literature. The reasons for the inefficient integration of SPP and the power system are identified based on the results of scientific theoretical and experimental works by leading experts from developed countries. The issues of variability of weather conditions, the influence of external and internal factors on the operation of the network, the use of the most advanced technologies for managing the network, the method of accumulating the generated energy by batteries and their impact on the distortion of the energy parameters of the network are considered. The issues of introducing the technology of modern converters, anti-islanding, protection, forecasting the "sun-grid" system and smart grid are described. The methods of various scientists used in the integration of solar photovoltaic plants to electric grids and their results are discussed. Attention is paid to the development of control algorithms, the creation of simulation schemes of models. The main directions of methods for efficient connection of SPP to electric grids are indicated. Possible cases of failure of power plants, power lines and the safety of the entire system are taken into account. The technical and economic aspects of the problem of the issue under consideration in the construction of integrated systems in hard-to-reach areas of the planet are considered. It is recommended, as an important step, to optimize the implementation of Internet of Things (IoT) technology, smart monitoring of the generation of electrical power received from solar power plants, accumulation and consumption of energy by consumers.

Research on impact resistance of CF/UHMWPE fiber interlayer hybrid composite target plate

Abstract The effectiveness of the numerical simulation scheme was verified by setting up an impact experimental platform for ultra-high molecular weight polyethylene (UHMWPE) fiber laminates penetrated by 7.62mm ordinary projectiles, and the finite element model of impact resistance of CF/UHMWPE fiber laminates was established to further explore the effects of ply angle and ply sequence on impact resistance of hybrid laminates. When CF laminates are in the front, UHMWPE fiber laminates are in the rear, and UHMWPE fiber laminates account for a high proportion, the target plate has higher impact resistance.

Exact simulation scheme for the Ornstein–Uhlenbeck driven stochastic volatility model with the Karhunen–Loève expansions

Exact simulation scheme for the Ornstein–Uhlenbeck driven stochastic volatility model with the Karhunen–Loève expansions

Study on Influencing Factors of Roadway Surrounding Rock Stability of Extremely Weak Coal Seam In Wangxingzhuang Coal Mine

The Er1 coal seam in Wangxingzhuang Coal Mine is an extremely weak coal seam. In order to explore the influence degree of geological conditions such as tunnel burial depth, seam thickness, mining influence, and support parameters such as bolt cable row spacing and U-shaped steel row spacing on the stability of roadway surrounding rock, this paper adopts the orthogonal test design numerical simulation scheme and evaluates the influence degree of each factor on the test index through range analysis. The results provide the parameter basis for roadway support of extremely weak coal seam in Wangxingzhuang Coal Mine. The research results of this paper have certain theoretical significance and engineering practice value.

Fractional modeling and numerical investigations of COVID-19 epidemic model with non-singular fractional derivatives: a case study

This paper focuses on the pivotal challenge of representing fractional dynamics in the context of computational biology, presenting an innovative approach. We utilize a non-singular kernel-type derivative to reformulate a fractional-order epidemic model. Our research focuses on several key aspects. First, we determine the reproductive number, represented as , which is crucial for predicting and understanding the dynamics of the disease being studied. To assess the stability of the system, we employ the Routh-Hurwitz stability criteria. Additionally, we employ the Lasale invariant principle to gain insights into the dynamical behavior of the equilibria. In order to validate our model’s accuracy, we conduct data fitting exercises and subsequently perform numerical experiments to corroborate our theoretical findings. Furthermore, we leverage the Banach and Leary Schauder alternative theorem to establish the existence of solutions with unique characteristics, enhancing the robustness of our approach. To facilitate practical implementation, we utilize the Toufit-Atangana scheme for numerical simulations of the proposed fractional model. Our findings show that the model performs well across the entire density spectrum. Specifically, we note that stability decreases with higher scheme orders but improves with lower fractional-order derivatives.