Implicit Method Research Articles

Optimization of coupling phase-change materials and thermal screens in façade-integrated hybrid photovoltaic collectors for optimal energy production and thermal comfort in buildings

The operation of building-integrated photovoltaic (BIPV) systems gives rise to a significant proportion of the solar radiation absorbed by the cells being unable to be converted into electricity. This phenomenon consequently increases the temperature. This temperature increase impacts the cells' electrical efficiency, leading to a reduction in their performance and accelerating their degradation. The combination of phase-change materials with insulating fluid blades, situated behind photovoltaic cells, represents a passive cooling solution that optimizes the performance of hybrid photovoltaic systems when incorporated into facades. The present study assesses a system that incorporates paraffin as a PCM and an argon layer in a PV-PCM-argon layer physical model (PVT/ArPCM), in comparison with a PV-PCM system (PVT/PCM), to enhance the thermoelectric performance of photovoltaic systems mounted on façades while ensuring optimal thermal comfort within buildings. The discrete heat transfer equations were solved using the Thomas algorithm and the iterative Gauss-Seidel method in conjunction with the implicit finite difference method. The findings illustrate that the electrical efficiency experienced only a slight increase, estimated at 0.01%, while there was a notable enhancement in the indoor thermal comfort experienced by occupants, with a 65% improvement observed due to the incorporation of an argon-filled thermal screen. The incorporation of an argon layer led to a minor reduction in temperature of 0.01°C in the photovoltaic cells, resulting in a minimal improvement of 0.014% in electrical power production. The phase-changing material incorporated into PVT/ArPCM demonstrated superior thermal management capabilities in comparison to the same material employed in PVT/PCM.

Blast-Resistant Design of Reinforced Concrete Slabs with Auxetic-Shaped Reinforcement Layout

This paper presents a numerical study of a blast-resistant design of reinforced concrete panels with a novel auxetic reinforcement layout inspired by auxetic materials, which have a negative Poisson’s ratio, i.e., shrink under compression and expand under tension. A series of two-way supported panels reinforced with re-entrant auxetic-shaped rebars were numerically tested under a TNT explosion. The high-fidelity multi-physics explicit solver of LS-DYNA was utilized to analyze the efficiency of the proposed design. Firstly, the incident pressure of a TNT explosion data and the structural response of a conventional reinforced concrete panel under a TNT explosion were successfully validated by comparing with the experimental and empirical results. Secondly, the blast-resistant capacity of the proposed model was evaluated in comparison to two different conventional designs. Moreover, a parametric study was carried out to reveal the driving parameters of the newly proposed auxetic-shaped reinforcement design. It has been proved that the proposed auxetic reinforcement layout significantly reduces the spalling radius and increases the energy absorption capacity of panels. As a result of the parametric study, the increased reinforcement volume ratio was ineffective on the spalling radius, although the cell size of auxetic reinforcement was found to be quite effective for the blast-resistant design of concrete panels. Overall, the proposed re-entrant auxetic reinforced panel performed far better than conventional designs under blast load. With the recent developments in 3D printing technology, the proposed auxetic reinforcement layout is a strong candidate to deal with blast-resistant designs of concrete panels.

Transforming chaotic and stiff systems to improve numerical accuracy

AbstractSystems of differential equations can exhibit chaotic or stiff behavior under specific conditions, posing challenges for time-stepping numerical methods. For explicit methods, the required time step resolution significantly exceeds the resolution associated with the smoothness of the exact solution for specified accuracy. In order to improve efficiency, the question arises whether transformation to asymptotically stable solutions can be performed, for which neighbouring solutions converge towards each other at a controlled rate. Employing the concept of local Lyapunov exponents, it is shown that chaotic differential equations can indeed be transformed to obtain high accuracy, whereas stiff equations cannot. For instance, the accuracy of explicit fourth order Runge–Kutta solution of the Lorenz chaotic equations can be increased by several orders of magnitude. Alternatively, the time step can be significantly extended with retained accuracy. The transform method applies broadly to chaotic systems, including weather prediction and turbulence.

Particle Virtual Element Method (PVEM): an agglomeration technique for mesh optimization in explicit Lagrangian free-surface fluid modelling

Explicit solvers are commonly used for simulating fast dynamic and highly nonlinear engineering problems. However, these solvers are only conditionally stable, requiring very small time-step increments determined by the characteristic length of the smallest, and often most distorted, element in the mesh. In the Lagrangian description of fluid motion, the computational mesh quickly deteriorates. To circumvent this problem, the Particle Finite Element Method (PFEM) creates a new mesh (e.g., through a Delaunay tessellation, based on node positions) when the current one becomes overly distorted. A fast and efficient remeshing technique is therefore of pivotal importance for an effective PFEM implementation in explicit dynamics. Unfortunately, the 3D Delaunay tessellation does not guarantee well-shaped elements, often generating zero- or near-zero-volume elements (slivers), which drastically reduce the stable time-step size. Available mesh optimization techniques have limited applicability due to their high computational cost when runtime remeshing is required. An innovative possibility to overcome this problem is the use of the Virtual Element Method (VEM), a variant of the finite element method that can make use of polyhedral elements of arbitrary shapes and number of nodes. This paper presents the formulation of a 3D first-order Particle Virtual Element Method (PVEM) for weakly compressible flows. Starting from a tetrahedral mesh, poorly shaped elements, such as slivers, are agglomerated to form polyhedral Virtual Elements (VEs) with a controlled characteristic length. This approach ensures full control over the minimum time-step size in explicit dynamics simulations, maintaining stability throughout the entire analysis.

Computational analysis of wildland fire resistance for transmission line tower

Finite element (FE) analysis of the transmission towers under a fire event and the accompanying wind is presented. Several key aspects (including temperature-dependent non-linear material properties, geometric non-linearity, member eccentricity due to the single-leg bolted connection, and the temperature-dependent connection behaviour in both the axial and the rotational directions) are considered. A quasi-static analysis is also employed in the FE model using the explicit solver available in Abaqus. The member temperature variation during a realistic fire event is derived analytically based on the fire intensity and the resultant vertical gas temperature distribution so that the effect of the realistic wildland fire can be input as a member temperature profile. First, fire design guidance in terms of the most critical heating and wind pattern, as well as the effect of fire-affected heights are provided based on the case study results. Then, further fire analysis is carried out to investigate the most critical fire scenario and to evaluate the vulnerability of the tower during a realistic fire event. Lastly, an evaluation of a commonly used spray-on thermal insulation and its effectiveness in reducing the member temperature and preserving ultimate strength during a catastrophic wildland fire event are presented. The FE simulations revealed that a 45-degree wind associated with partial side heating leads to a more critical degradation of the overall strength, whereas the effect of fire height is less obvious. In terms of the fire scenario, a longer fire duration associated with a slower wind is more critical for the fire resistance/rating.

An elasto-visco-plastic constitutive model for snow: Theory and finite element implementation

Snow exhibits unique mechanical behaviour due to its evolving properties influenced by temperature, stress conditions, and viscous effects. This paper introduces a nonlinear constitutive model for snow, featuring new formulations for the yield function and strain rate potential, and incorporating viscosity, sintering, and degradation effects. The model is numerically integrated into the Abaqus/Standard FEM software using a fully implicit backward Euler method for time integration and Powell’s hybrid method for linearizing the nonlinear system of equations. The robustness and stability of the numerical scheme ensure accurate simulation of snow behaviour under various loading conditions. The model is finally validated against experimental data available in the literature, demonstrating its effectiveness and reliability in capturing the complex mechanical response of snow.

TaNSR:Efficient 3D Reconstruction with Tetrahedral Difference and Feature Aggregation

AbstractNeural surface reconstruction methods have demonstrated their ability to recover 3D surfaces from multiple images. However, current approaches struggle to rapidly achieve high‐fidelity surface reconstructions. In this work, we propose TaNSR, which inherits the speed advantages of multi‐resolution hash encodings and extends its representation capabilities. To reduce training time, we propose an efficient numerical gradient computation method that significantly reduces additional memory access overhead. To further improve reconstruction quality and expedite training, we propose a feature aggregation strategy in volume rendering. Building on this, we introduce an adaptively weighted aggregation function to ensure the network can accurately reconstruct the surface of objects and recover more geometric details. Experiments on multiple datasets indicate that TaNSR significantly reduces training time while achieving better reconstruction accuracy compared to state‐of‐the‐art nerual implicit methods.

An explicit time integration method for Boussinesq approximation

AbstractThis paper presents a novel approach to the discretization of the Boussinesq equation using finite elements, coupled with an explicit pressure correction scheme. The entire numerical scheme is formulated exclusively in terms of matrix‐vector products, enabling a highly efficient numerical solution. The key advantage of this approach lies in its suitability for fast computations and seamless parallelization on graphics processing units (GPUs). We present the numerical scheme and discuss different computational examples.

Definition, Fabrication, and Compression Testing of Sandwich Structures with Novel TPMS-Based Cores

Triply periodic minimal surfaces (TPMSs) constitute a type of metamaterial, deriving their unique characteristics from their microstructure topology. They exhibit wide parameterization possibilities, but their behavior is hard to predict. This study focuses on using an implicit modeling method that can effectively generate novel thin-walled metamaterials, proposing eight shell-based TPMS topologies and one stochastic structure, along with the gyroid acting as a reference. After insights into the printability and design parameters of the proposed samples are presented, a cell homogeneity analysis is conducted, indicating the level of anisotropy of each cellular structure. For each of the designed metamaterials, multiple samples were printed using a stereolithography (SLA) method, using a constant 0.3 relative density and 50 µm resolution. To provide an understanding of their behavior, compression tests of sandwich-type specimens were performed and specific deformation modes were identified. Furthermore, the study estimates the general mechanical behavior of the novel TPMS cores at different relative densities using an open cell mathematical model. Alterations of the uniform topologies are then suggested and the way these modifications affect the compressive response are presented. Thus, this paper demonstrates that an implicit modeling method could easily generate novel thin-walled TPMSs and stochastic structures, which led to identifying an artificially designed structure with superior properties to already mature topologies, such as the gyroid.

Explicit Group Iterative Method with Semi-Approximate Implicit Approach for Solving One-Dimensional Burgers’ Equation

This paper is considering a semi-approximate approach in investigating the Burgers’ problem. The process of the discretization of Burgers’ problem has taken place which it starts with the second-order finite difference in the discretize process together with the linearization part by using the semi-approximate implicit scheme in a way to achieve the approximation equation, thus generating the corresponding linear system equations. Besides, the Gauss-Seidel (GS), Successive Over-Relaxation (SOR) and explicit group (EG) iterative method has combined together with the SOR iterative method, namely as 4-point EGSOR (4EGSOR) has been introduced in this study for resolving the linear system. To assess the proficiency of the suggested methods on the approximation equation, the numerical test has been conducted by considering three parameters, which are computational time, iteration number and maximum absolute error. The findings indicate that the 4EGSOR method outperforms both SOR and GS iterative methods.

High-order accurate implicit-explicit time-stepping schemes for wave equations on overset grids

New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step, three levels in time, and based on the modified equation approach. Second and fourth-order accurate schemes are developed and they incorporate upwind dissipation for stability on overset grids. The fully implicit schemes are useful for certain applications such as the WaveHoltz algorithm for solving Helmholtz problems where very large time-steps are desired. Some wave propagation problems are geometrically stiff due to localized regions of small grid cells, such as grids needed to resolve fine geometric features, and for these situations the implicit time-stepping scheme is combined with an explicit scheme: the implicit scheme is used for component grids containing small cells while the explicit scheme is used on the other grids such as background Cartesian grids. The resulting partitioned implicit-explicit scheme can be many times faster than using an explicit scheme everywhere. The accuracy and stability of the schemes are studied through analysis and numerical computations.

Implementation of thermal conduction energy transfer models in the Bifrost solar atmosphere MHD code

Thermal conductivity provides important contributions to the energy evolution of the upper solar atmosphere, behaving as a non-linear concentration-dependent diffusion equation. Recently, different methods have been offered as best-fit solutions to these problems in specific situations, but their effectiveness and limitations are rarely discussed. We have rigorously tested the different implementations of solving the conductivity flux, in the massively parallel magnetohydrodynamics code, Bifrost, with the aim of specifying the best scenarios for the use of each method. We compared the differences and limitations of explicit versus implicit methods, and analyse the convergence of a hyperbolic approximation. Among the tests, we used a newly derived first-order self-similar approximation to compare the efficacy of each method analytically in a 1D pure-thermal test scenario. We find that although the hyperbolic approximation proves the most accurate and the fastest to compute in long-running simulations, there is no optimal method to calculate the mid-term conductivity with both accuracy and efficiency. We also find that the solution of this approximation is sensitive to the initial conditions, and can lead to faster convergence if used correctly. Hyper-diffusivity is particularly useful in aiding the methods to perform optimally. We discuss recommendations for the use of each method within more complex simulations, whilst acknowledging the areas where there are opportunities for new methods to be developed.

A homogenized constitutive model for 2D woven composites under finite deformation: Considering fiber reorientation

Two-dimensional (2D) woven composites exhibit excellent mechanical properties along the fiber directions. The mechanical behaviors demonstrate nonlinearity in specific applications. Although plasticity methods can be applied to predict complex behaviors, however, fiber reorientation has been observed during finite deformation, indicating that the fiber directions are no longer along orthotropic material axes when the angle between fibers changes. The angular bisectors of two fiber directions can serve as the orthotropic material axes due to the rotational symmetries even in finite deformation scenarios. This study reports a homogenized nonlinear constitutive model based on the rotational symmetry axes, incorporating plasticity and fiber reorientation phenomena. The plasticity model contains a two-parameter flow potential and power function. Plastic deformations are computed using an explicit method. Fiber reorientation angles are computed both theoretically and numerically. The relationship between mechanical properties and fiber reorientation angles is studied using finite element method (FEM). Due to introduce of a novel approach to determining the strain and stress of 2D woven composites undergoing finite deformation, the proposed model should have potential in engineering predictions.

Coupled filtration–consolidation model for vacuum-preloaded soft ground

The widespread utilisation of vacuum-assisted prefabricated vertical drains for managing clayey soft ground has led to the development of numerous consolidation models. However, these models have limitations when describing the filtration behaviour of soil under conditions of high water content, without the formation of a particle network. To address this issue effectively, in this work, based on the compressional rheology theory, a two-dimensional axisymmetric model incorporating the compressive yield stress Py(ϕ) and a hindered setting factor r(ϕ) was developed to couple the filtration and consolidation of soil under vacuum preloading. A novel approach for determining the unified ϕ–Py–r relationships was introduced. The equation governing such fluid/solid and solid/solid interactions was solved using the alternative direction implicit method, and the numerical solutions were validated against the one-dimensional filtration cases, three-dimensional laboratory model tests and large-scale field trials. Further parametric analysis suggests that the radius of the representative unit and r(ϕ) exclusively affect the dewatering rate of the clayey slurry, while the gel point and Py(ϕ) influence both the dewatering rate and the final deformation.

Jacobian vs. disturbance method for UMATs in ABAQUS: An application to isotropic damage mechanics

This paper compares the computational efficiency of different methodologies to estimate the tangent stiffness applied to ABAQUS standard UMAT user-subroutine, using implicit formulation with predictor corrector methodology. It uses two new methodologies to estimate the stiffness matrix for the predictor-corrector iterative process, named Disturbance Method and Implicit to Explicit Method. With the Disturbance Method, it is enough to build UMATs using only a secant matrix, since an approximate tangential material matrix is automatically computed, promoting a faster implementation of new material constitutive relations in the ABAQUS standard. It is also studied the possibility of the use of a new algorithm that transforms the UMAT implicit formulation to an explicit formulation using a new secant predictor corrector algorithm. In this study, a new concrete damage model that considers fracture energy regularization for both tensile and compressive behaviour with Mode I Fracture is utilized. Classical and known benchmarks to test damage models in the scientific community are used to compare both methods for the calculation of the Jacobian matrix in terms of time and number of iterations.

A class of explicit second derivative general linear methods for non-stiff ODEs

In this paper, we construct explicit second derivative general linear methods (SGLMs) with quadratic stability and a large region of absolute stability for the numerical solution of non-stiff ODEs. The methods are constructed in two different cases: SGLMs with p = q = r = s and SGLMs with p = q and r = s = 2 in which p, q, r and s are respectively the order, stage order, the number of external stages and the number of internal stages. Examples of the methods up to order five are given. The efficiency of the constructed methods is illustrated by applying them to some well-known non-stiff problems and comparing the obtained results with those of general linear methods of the same order and stage order.

Damage characterization and modelling of FRP laminated composites subjected to external edge-on impact

This paper presents both experimental and numerical investigations into the edge-on impact behavior of T700/YPH307 composite laminates with varying lay-up designs and impact energy levels. Various non-destructive testing techniques, including visual inspection, ultrasonic C-scanning and X-ray computed tomography (CT), were used to detect the post-impact damage status and further reveal its 3D spatial distribution. A continuum damage mechanics (CDM) model, incorporating in-plane shear nonlinearity, fracture plane angle within anisotropic materials, as well as fiber kinking failure in longitudinal compression, was established using an explicit solver. Detailed comparison of the experimental and numerical results was conducted in mechanical response curves and failure mechanisms, where a good agreement was observed. Parameter analyses on the in-situ strengths and the friction coefficient were also performed, offering guidelines for the edge-on impact modelling. Failure mechanisms induced by edge-on impact typically exhibit two distinct features: a highly localized debris wedge, which can be regarded as a trigger in the subsequent occurrence of damage, and the bending fracture of the outer plies resulting from the wedge effect during the oscillating stage of an impact force plateau. Besides, higher impact energy exacerbated internal damage, while the influence of the lay-ups was relatively limited.

Spatially mixed implicit–explicit schemes in hydro-mechanically coupled soil dynamics

Mixed implicit–explicit (IMEX) schemes combine elements of both implicit and explicit time integration methods. This allows to efficiently handle boundary value problems with severe differences in stiffness, such as often encountered in soil dynamics. A spatially mixed IMEX scheme, in which different parts of the computational domain may be treated implicitly or explicitly depending on their behaviour, is discussed in this work. Domain decomposition by means of a mortar contact discretisation is used for this purpose and multiple systems of equations are solved. The merits of the scheme in solving problems of soil dynamics are demonstrated, for which the governing equations are extended to hydro-mechanical coupling.

Application of a reaction-based water quality model to the total dissolved solids concentration of the Pasig River.

With the goal to support effective water resource management, water quality models have gained popularity as tools for evaluating the distributions of pollutants and sediments. This work focuses on the application of the numerical solution of an advection-dispersion-reaction (ADR) water quality model for rivers and streams to a major Philippine waterway, the Pasig River. The water quality constituent is described by a system of reaction and advection-dispersion-reaction equations. The model and method are based on a previously used strategy where Guass-Jordan decomposition is applied to the matrix system and the resulting conservative form of the model is solved numerically using the fully implicit scheme and finite element method. The methodology is demonstrated by a case study in Pasig River involving the concentrations of total dissolved solids (TDS) obtained from the Department of Environment and Natural Resources (DENR) through the Pasig River Unified Monitoring Stations (PRUMS) report. Sensitivity analysis and parameter estimation are also applied to the model to assess which parameters influence the model output the most.

A novel iterative algorithm for nonlinear inelastic dynamic analysis of truss structures; MCB-Spline+Sp time integration method

The focus of this work is on the development of a novel algorithm for the nonlinear dynamic analysis of structures. In the sake of a general and easy-to-implement solution method, the tangential stiffness matrix is calculated by combining the Cauchy-Riemann equations derived from the differentiation of complex functions and using the nodal displacement perturbation vector. An implicit direct time integration method based on a cubic B-Spline is integrated with the incremental-iterative method using a quadrature rule based on the interpolation of spline functions, which is referred to as the MCB-Spline+Sp time integration method. A step-by-step algorithm for developing a computer code to implement this method is provided. The effectiveness of the proposed approach is evaluated through several nonlinear time history analyses, which demonstrate its accuracy and efficiency by observing less computational efforts and fast convergence rate. Moreover, a comparison is made between the developed method and well-established techniques such as the Newmark and Standard-Bathe time integration methods in combination with the iterative Newton-Raphson method.