Zeitschriftenartikel: „Explicit numerical simulation“

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Tutueva, Aleksandra, and Denis Butusov. "Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods." Mathematics 9, no. 19 (2021): 2463. http://dx.doi.org/10.3390/math9192463.

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The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

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Azadani, L. N., and A. E. Staples. "Large-Eddy Simulation of Turbulent Barotropic Flows in Spectral Space on a Sphere." Journal of the Atmospheric Sciences 72, no. 5 (2015): 1727–42. http://dx.doi.org/10.1175/jas-d-14-0183.1.

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Abstract Numerical simulations of atmospheric circulation models are limited by their finite spatial resolution, so large-eddy simulation (LES) is a preferred approach to study these models. In LES, a low-pass filter is applied to the flow field to separate the large- and small-scale motions. In implicitly filtered LES, the computational mesh and discretization schemes are considered to be the low-pass filter, while in the explicitly filtered LES approach, the filtering procedure is separated from the grid and discretization operators and allows for better control of the numerical errors. The aim of this paper is to study and compare implicitly filtered and explicitly filtered LES of atmospheric circulation models in spectral space. To achieve this goal, the results of implicitly filtered and explicitly filtered LES of a barotropic atmosphere circulation model on a sphere in spectral space are presented and compared with the results obtained from direct numerical simulation (DNS). Different numerical experiments are performed to investigate the efficiency of explicit filtering over implicit filtering under different dissipation terms and rotation rates. The study shows that explicit filtering increases the accuracy of the computations and improves the results, particularly where the location of coherent structures is concerned, a topic of particular importance in LES of atmospheric flows for climate and weather applications.

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Bannikova, E. Yu, and A. T. Kotvytskiy. "Three Einstein rings: explicit solution and numerical simulation." Monthly Notices of the Royal Astronomical Society 445, no. 4 (2014): 4435–42. http://dx.doi.org/10.1093/mnras/stu2068.

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4

Goel, M. D., KrishnaPrasad Kallada, and I. L. Muthreja. "Numerical Simulation of Bunker Buster Slab under Projectile Impact." Proceedings of the 12th Structural Engineering Convention, SEC 2022: Themes 1-2 1, no. 1 (2022): 1073–79. http://dx.doi.org/10.38208/acp.v1.623.

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In the present investigation, 3-D finite element modelling is carried out to predict the penetration depth and residual velocity of a projectile impacting a target. For the purpose of numerical simulation, target is a concrete slab of planar dimension 5 m × 4 m with an unconfined compressive strength of 50 MPa. This target is considered to be part of protective structure like bunker buster slab. The explicit algorithm of ABAQUS/Explicit® is employed in the simulation of projectile impact. The projectile is modelled as a rigid body and the concrete slab as a deformable body using Lagrangian formulation. The energy dissipation, penetration depth and residual velocities of the projectile impacting at different velocities are compared with the empirical equation as available by simulating a real impact scenario numerically. Investigation is carried out over a wide range of impacting velocities under sub-hydrodynamic range.

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Oleksik, Valentin, Radu Breaz, Gabriel Racz, Paul Dan Brindasu, and Octavian Bologa. "Advanced Techniques used in Numerical Simulation for Deep-drawing Process." MATEC Web of Conferences 290 (2019): 03012. http://dx.doi.org/10.1051/matecconf/201929003012.

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The present paper analyse the main characteristics of the numerical simulation by finite element method of the deep-drawing processes. Also the authors’ highlights the mathematical apparatus and the calculus method used for numerical simulations of metal forming processes in many of the current simulation software. The authors present the capabilities of the inverse analysis, direct analysis, implicit analysis (for springback simulation) and the optimisation analysis applied to explicit formulations.

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Chen, Lei. "Comparisons of Explicit and Implicit Finite Element Methods for Sheet Metal Forming." Advanced Materials Research 936 (June 2014): 1836–39. http://dx.doi.org/10.4028/www.scientific.net/amr.936.1836.

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Sheet metal forming is one of the most commonly practiced fabrication processes in industry. Numerical simulations of the complex parts are possible by finite element method in the past thirty years. The most important problem of the simulation is the reliability of the model. Static implicit method (SI) and dynamic explicit method (DE) were used to simulation sheet metal forming process. It was found that simulation speed in dynamic explicit software has large effect on the simulation results. The best simulation speed is 5~10 m/s. Compared with the simulation and experimental results of thickness, draw-in and CPU time, the DE method is preferred.

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Humby, S. J., M. J. Biggs, and U. Tüzün. "Explicit numerical simulation of fluids in reconstructed porous media." Chemical Engineering Science 57, no. 11 (2002): 1955–68. http://dx.doi.org/10.1016/s0009-2509(02)00103-3.

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Liu, Heng, and Zhenpeng Liao. "An explicit method for numerical simulation of wave equations." Earthquake Engineering and Engineering Vibration 8, no. 1 (2009): 17–28. http://dx.doi.org/10.1007/s11803-009-8132-6.

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Phantu, Suganya, Yupaporn Areepong, and Saowanit Sukparungsee. "Double Moving Average Control Chart for Time Series Data with Poisson INARCH(1)." WSEAS TRANSACTIONS ON BUSINESS AND ECONOMICS 21 (February 23, 2024): 694–707. http://dx.doi.org/10.37394/23207.2024.21.58.

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The objectives of this research are to find the explicit formulas of the average run length (ARL) of a double moving average (DMA) control chart for first-order integer-valued autoregressive conditional heteroscedasticity (INARCH1))) of Poisson count data. In addition, the numerical results obtained from the proposed explicit formulas are compared with those obtained from Monte Carlo simulations (MC) for the Poisson INARCH(1) counting process. An out-of-control ARL (ARL1) is the criteria for measuring the performance of control charts. The numerical results found that the values of both ARL0 and ARL1 obtained from explicit formulas agree with the numerical results obtained from the Monte Carlo simulation (MC), but the latter is very timeconsuming.

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ANDREUCCI, DANIELE, ANTONIO FASANO, MARIO PRIMICERIO, MAURIZIO PAOLINI, and CLAUDIO VERDI. "NUMERICAL SIMULATION OF POLYMER CRYSTALLIZATION." Mathematical Models and Methods in Applied Sciences 04, no. 01 (1994): 135–45. http://dx.doi.org/10.1142/s0218202594000091.

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We consider a mathematical model for solidification of semicrystalline polymers, describing the evolution of temperature, crystalline volume fraction, number and average size of crystals. In turn, the model couples a suitable kinetics of nonisothermal crystallization, taking into account both formation and growth of nuclei, with the thermal energy balance equation. We also present a model of secondary crystallization. The numerical approximation is performed by semiexplicit finite differences in time and finite elements in space. The fully discrete scheme amounts to solve, at any time step, a symmetric positive definite linear system preceded by an elementwise explicit computation. The computed numerical crystal structures match qualitatively the experimental ones.

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Okraschevski, M., N. Buerkle, R. Koch, and H. J. Bauer. "Smoothed particle hydrodynamics physically reconsidered: The relation to explicit large eddy simulation and the issue of particle duality." Physics of Fluids 34, no. 11 (2022): 115108. http://dx.doi.org/10.1063/5.0105104.

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In this work, we will identify a novel relation between Smoothed Particle Hydrodynamics (SPH) and explicit large eddy simulation using a coarse-graining method from non-equilibrium molecular dynamics. While the current literature points at the conclusion that characteristic SPH issues become restrictive for subsonic turbulent flows, we see the potential to mitigate these SPH issues by explicit subfilter stress modeling. We verify our theory by various simulations of homogeneous, isotropic turbulence at [Formula: see text] and compare the results to a direct numerical simulation [T. Dairay et al., “Numerical dissipation vs subgrid-scale modelling for large eddy simulation,” J. Comput. Phys. 337, 252–274 (2017)]. Although the simulations substantiate our theory, we see another issue arising, which is conceptually rooted in the particle itself, termed as particle duality. Finally, we conclude our work by acknowledging SPH as a coarse-graining method for turbulent flows, highlighting its capabilities and limitations.

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Hu, Kai. "Study on Collapse Numerical Simulation Method of Frame Structures Based on Explicit Dynamics." Advanced Materials Research 919-921 (April 2014): 226–38. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.226.

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According to the theory of collapse numerical simulation, the explicit finite element algorithm based on explicit dynamics was chose as the numerical calculation method. And combined with the plane RC frame collapse test and the example of ten layers frame structure, the wire frame model, integrated model and separate model were established and the alternate path method was adopted to study the simulate method of structural collapse. With the comparison of several aspects to the results, the rationality of the numerical simulation method and the applicability of the numerical models were verified respectively. At the same time, according to the complex pre-treatment process to the numerical simulation of structural collapse, an MFC program with the function of exporting APDL file which can generate wireframe models for structural collapse simulation in ANSYS/LS-DYNA was developed using VC++ language with the purpose of offering convenience to the numerical simulation process of structure collapse.

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Chronopoulos, Anthony Theodore, and Gang Wang. "Traffic Flow Simulation through Parallel Processing." Transportation Research Record: Journal of the Transportation Research Board 1566, no. 1 (1996): 31–38. http://dx.doi.org/10.1177/0361198196156600104.

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Numerical methods for solving traffic flow continuum models have been studied and efficiently implemented in traffic simulation codes in the past. Explicit and implicit methods have been used in traffic simulation codes in the past. Implicit methods allow a much larger time step size than explicit methods to achieve the same accuracy. However, at each time step a nonlinear system must be solved. The Newton method, coupled with a linear iterative method (Orthomin), is used. The efficient implementation of explicit and implicit numerical methods for solving the high-order flow conservation traffic model on parallel computers was studied. Simulation tests were run with traffic data from an 18-mile freeway section in Minnesota on the nCUBE2 parallel computer. These tests gave the same accuracy as past tests, which were performed on one-processor computers, and the overall execution time was significantly reduced.

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Liu, Ming Qin, Yu Ling Liu, and Wen Li Wei. "Numerical Simulation of 2D Flow in a Curved Channel." Advanced Materials Research 374-377 (October 2011): 378–81. http://dx.doi.org/10.4028/www.scientific.net/amr.374-377.378.

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This paper is concerned with a new numerical method of two-dimensional flow. The governing system of differential equations is transformed into an equivalent system applied over a square-grid network in order to overcome the difficulties and inaccuracies associated with the determination of characteristics near the flow boundaries. The MacCormack two-step explicit scheme with second-order accuracy is used for the solution of the transformed system of equations. The present numerical model has been used to numerically compute flow in sharply curved channel.

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Wang, Zhen Ye, Jiang Fei Li, Lian Yuan, et al. "Numerical Simulation of Transient Flow in Products Pipeline." Advanced Materials Research 732-733 (August 2013): 487–90. http://dx.doi.org/10.4028/www.scientific.net/amr.732-733.487.

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In this paper, explicit difference scheme, implicit difference scheme and characteristics method are separately used to simulate the transient flow in products pipeline. The simulation result can be used to prevent water hammer in the pipeline of unsteady situation and to improve the efficiency and safety in oil transmission systems. And then, the stability and accuracy of the three methods are compared by adopting different time steps. For explicit difference method, large fluctuation may occur in case of large time step. For implicit method, the result is weakly affected by time step, only if the relaxation factor selected is reasonable. For characteristics method, the results have a high convergence speed and precision. The results show that, in the situation of valve shut down in terminal, it takes about 1.1×104 seconds to return to a new steady state.

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Zhang, Xiang Rong, Xu Dan, and Lin Zhou. "Numerical Simulation of Thermal Sensitivity for Explosives." Advanced Materials Research 734-737 (August 2013): 2116–19. http://dx.doi.org/10.4028/www.scientific.net/amr.734-737.2116.

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In order to compare the thermal sensitivity of several typical explosives, this article solved numerically one-dimensional transient heat conduction equation including thermal decomposition for explosives with finite difference method. The explicit difference equations under different boundary conditions were established, and the corresponding stability criterion was derived. The ignition times for typical explosives were calculated, which was used to evaluate thermal sensitivity of explosives.

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Chetverushkin, B. N., and A. V. Gulin. "Explicit schemes and numerical simulation using ultrahigh-performance computer systems." Doklady Mathematics 86, no. 2 (2012): 681–83. http://dx.doi.org/10.1134/s1064562412050213.

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Hu, Yijing, Qiangqiang Shi, Valmor F. De Almeida, and Xiaolin Li. "Numerical simulation of phase transition problems with explicit interface tracking." Chemical Engineering Science 128 (May 2015): 92–108. http://dx.doi.org/10.1016/j.ces.2014.11.053.

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Chung, D., L. Chan, M. MacDonald, N. Hutchins, and A. Ooi. "A fast direct numerical simulation method for characterising hydraulic roughness." Journal of Fluid Mechanics 773 (May 26, 2015): 418–31. http://dx.doi.org/10.1017/jfm.2015.230.

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We describe a fast direct numerical simulation (DNS) method that promises to directly characterise the hydraulic roughness of any given rough surface, from the hydraulically smooth to the fully rough regime. The method circumvents the unfavourable computational cost associated with simulating high-Reynolds-number flows by employing minimal-span channels (Jiménez & Moin, J. Fluid Mech., vol. 225, 1991, pp. 213–240). Proof-of-concept simulations demonstrate that flows in minimal-span channels are sufficient for capturing the downward velocity shift, that is, the Hama roughness function, predicted by flows in full-span channels. We consider two sets of simulations, first with modelled roughness imposed by body forces, and second with explicit roughness described by roughness-conforming grids. Owing to the minimal cost, we are able to conduct direct numerical simulations with increasing roughness Reynolds numbers while maintaining a fixed blockage ratio, as is typical in full-scale applications. The present method promises a practical, fast and accurate tool for characterising hydraulic resistance directly from profilometry data of rough surfaces.

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Abbassi, Adil, and Gawtum Namah. "Characterization of the speed of a two-phase interface in a porous medium." Mathematical Problems in Engineering 2005, no. 6 (2005): 641–61. http://dx.doi.org/10.1155/mpe.2005.641.

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A typical situation of oil reservoir simulation is considered in a porous medium where the resident oil is displaced by water injection. An explicit expression of the speed of the oil-water interface is given in a pseudo-2D case via the resolution of an auxiliary Riemann problem. The explicit 2D solution is then corroborated with numerical simulations by solving the transport equation with a generalized scheme of Harten type.

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CHO, HYUN-JIK, and JEONG-SEO KOO. "ORBITAL FORMING SIMULATION OF AUTOMOTIVE HUB BEARING USING THE EXPLICIT FINITE ELEMENT METHOD." International Journal of Modern Physics B 22, no. 09n11 (2008): 1626–33. http://dx.doi.org/10.1142/s0217979208047171.

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In this paper, the orbital forming simulation of an automotive hub bearing was studied to predict forming conditions and performances using the explicit finite element method. To set up an efficient solution technique for the orbital forming, axisymmetric finite element models and 3D solid element models were numerically solved and compared to each other. The time scaling and mass scaling techniques were introduced to reduce the excessive computational time caused by small element size in case of the explicit finite element method. It was found from the numerical results on the orbital forming that the axisymmetric element models showed the similar results to the 3D solid element models in forming loads whereas the deformations at the bearing inner race were quite different. Finally the strains at the bearing inner race and the forming forces of the peen were measured by test for the same product used in the numerical analysis, and were compared with the 3D solid element results. It was shown that the test results were in good agreements with the numerical ones.

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von Hoyningen-Huene, Martin, and Alexander R. Jung. "Comparison of Different Acceleration Techniques and Methods for Periodic Boundary Treatment in Unsteady Turbine Stage Flow Simulations." Journal of Turbomachinery 122, no. 2 (1999): 234–46. http://dx.doi.org/10.1115/1.555440.

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This paper studies different acceleration techniques for unsteady flow calculations. The results are compared with a nonaccelerated, fully explicit solution in terms of time-averaged pressure distributions, the unsteady pressure and entropy in the frequency domain, and the skin friction factor. The numerical method solves the unsteady three-dimensional Navier–Stokes equations via an explicit time-stepping procedure. The flow in the first stage of a modern industrial gas turbine is chosen as a test case. After a description of the numerical method used for the simulation, the test case is introduced. The purpose of the comparison of the different numerical algorithms for explicit schemes is to facilitate the decision as to which acceleration technique should be used for calculations with regard to accuracy and computational time. The convergence acceleration methods under consideration are explicit time-stepping with implicit residual averaging, explicit time-consistent multigrid, and implicit dual time stepping. The investigation and comparison of the different acceleration techniques apply to all explicit unsteady flow solvers. This paper also examines the influence of the stage blade count ratio on the flowfield. For this purpose, a simulation with a stage pitch ratio of unity is compared with a calculation using the real ratio of 78:80, which requires a more sophisticated method for periodic boundary condition treatment. This paper should help to decide whether it is crucial from the turbine designer’s point of view to model the real pitch ratio in unsteady flow simulations in turbine stages. [S0889-504X(00)00702-9]

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Mijajlovic, Miroslav, Dragan Milcic, and Miodrag Milcic. "Numerical simulation of friction stir welding." Thermal Science 18, no. 3 (2014): 967–78. http://dx.doi.org/10.2298/tsci1403967m.

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Friction stir welding is a solid-state welding technique that utilizes thermo-mechanical influence of the rotating welding tool on parent material resulting with monolith joint-weld. On the contact of welding tool and parent material, significant stirring and deformation of parent material appears, and during this process mechanical energy is partially transformed into heat. The paper describes the software for the numerical simulation of friction stir welding developed at Mechanical Engineering Faculty, University of Nis. Numerical solution for estimation of welding plates temperature is estimated using finite difference method-explicit scheme with adaptive grid, considering influence of temperature on material's conductivity, contact conditions between welding tool and parent material, material flow around welding tool etc. The calculated results are in good agreement with the experimental results.

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Tan, Yang, Yi Lin Chi, Ya Yu Huang, and Ting Qiang Yao. "Numerical Simulation of High Speed Machining of Alloy Cast Iron." Advanced Materials Research 468-471 (February 2012): 2310–14. http://dx.doi.org/10.4028/www.scientific.net/amr.468-471.2310.

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High speed milling of hard alloy steels utilized in dies and molds is a highly demanding operation. The finite element model was developed to investigate the high speed machining of alloy cast iron which is used in auto panel dies. The modified Johnson-cook constitutive model was used to model the complex dynamic material behavior, a damage evaluation law based on Cockroft and Latham model was used to simulate the ductile fracture of alloy cast iron. The crack initiation and propagation was simulated explicitly using an explicit FEM code. Simulation results showed that the chip morphology transited from continuous to saw-tooth chip with increasing cutting speed, cutting force decreased when increasing the cutting speed, which provide a useful understanding of chip formation process in high speed machining of alloy cast iron.

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Haukas, Jarle, Ivar Aavatsmark, Magne Espedal, and Edel Reiso. "A Comparison of Two Different IMPSAT Models in Compositional Simulation." SPE Journal 12, no. 01 (2007): 145–51. http://dx.doi.org/10.2118/101700-pa.

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Summary A new IMPSAT model, with explicit solution of variables that are isochoric (i.e., complementary to volumes), is compared to the conventional IMPSAT model, which determines phase mole fractions explicitly. The compared properties are performance of the nonlinear iteration and numerical stability. The use of complementary variables in the new IMPSAT model makes the nonlinear system better conditioned. Consequently, fewer nonlinear iteration steps are required. The resulting speedup more than compensates for the added costs of introducing and using the isochoric variables. The stability criterion associated with the new IMPSAT model is in many cases significantly less conservative than the conventional criterion. However, for cases in which there is little or no saturation change between the hydrocarbon phases (e.g., for retrograde gas condensate cases or single hydrocarbon phase cases), the difference between the criteria is insignificant. The timestep sizes for which instabilities occur are practically the same for the two models, and no oscillations have been observed unless both the new and the conventional criterion are violated. Consequently, the stability properties are similar, and the new criterion seems to apply to both models. Our conclusions are supported by numerical results. Introduction An isothermal compositional model of Nc components involves the solution of Nc flow equations per gridblock (e.g., the mass balance equations): (Eq. 1) where ?ni is the change in the amount of component i during timestep ?t, while fi and qi are the component interblock flow and source rates. In addition, phase equilibrium between the oil and gas phases (e.g., equalities of fugacities), (Eq. 2) must be taken into account. Because of the large number of equations and the complex thermodynamics, it is too demanding to determine all variables implicitly (i.e., simultaneously in all gridblocks). Instead, we use a partially explicit approach, where some variables are determined implicitly, while others are determined explicitly, gridblock by gridblock. The explicit solution relies on explicit treatment of variables (i.e., evaluating parts of the interblock flow with variables from the previous time level).

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Wang, Di, Fangping Ma, and Hao Chen. "Numerical Simulation for Hydrogen-Assisted Cracking: An Explicit Phase-Field Formulation." Materials 16, no. 4 (2023): 1708. http://dx.doi.org/10.3390/ma16041708.

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Hydrogen-assisted cracking is one of the most dominant failure modes in metal hydrogen-facing materials. Therefore, the hydrogen-assisted cracking mechanism has been a hot topic for a long time. To date, there is very little published research on numerical methods to describe hydrogen-assisted cracking. This paper presents a new method for the description of hydrogen embrittlement crack growth: an explicit phase-field formulation, which is based on the phase-field description of cracks, Fick’s mass diffusion law, and the relationship between hydrogen content and fracture surface energy. A novel computational framework is then developed using the self-developed FEM software DYNA-WD. We numerically calculate several typical conditions in the 3-D coordinates to validate the effectiveness of the proposed computational framework. Specifically, we discuss (i) the failure of a square plate in a hydrogenous environment, (ii) the CT specimen failed with the inner hydrogen, (iii) the plate/failed with the corrosives, and (iv) the failure of the disk test. Finally, the relationship between Mises stress, the concentration of hydrogen, the thickness of the disc, and the loading rate is investigated.

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Cao, Weihao, Guangli Cheng, Bao Liu, and Yangfan Cai. "Research on the Time-Domain Explicit and Implicit Solution Methods of the Shallow Water Seismic Wavefield Equations." Applied Sciences 14, no. 4 (2024): 1598. http://dx.doi.org/10.3390/app14041598.

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The current time-domain solution methods for the wavefield equations of a single medium do not apply to the wavefield equations of shallow water seismic with a fluid–elastomer coupling. To solve this problem, based on the explicit central difference method and implicit Newmark method, the explicit–explicit method, implicit–implicit method, and explicit–implicit method time-domain expressions for the local solution are derived, and the time-domain expressions for the explicit and implicit methods in the global solution are derived.The stability and computational efficiency of different time-domain solving methods for the shallow water seismic wavefield equations are theoretically analyzed. The numerical results are compared with the simulation data from the multiphysics field simulation software COMSOL 6.0, and the numerical stability, computational efficiency and accuracy of the different solving methods are also analyzed theoretically. The results show that the implicit method in the global solution is relatively optimal among the methods proposed in this paper, which ensures numerical stability at the larger step size for improving the computational efficiency and considers the higher computational efficiency and accuracy.

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Fratini, Livan, Marion Merklein, Wolfgang Böhm, and Davide Campanella. "Modelling Aspects in Accumulative Roll Bonding Process by Explicit Finite Element Analysis." Key Engineering Materials 549 (April 2013): 452–59. http://dx.doi.org/10.4028/www.scientific.net/kem.549.452.

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Accumulative Roll-Bonding (ARB) process is a severe plastic deformation (SPD) process, capable of developing grains below 1 μm in diameter and improving mechanical properties of the material. In this study, the authors compared two different FE-codes with respect of its applicability for numerical analysis of the ARB process. Modelling this process was achieved using the explicit code for Abaqus/CAE both in 2D and 3D. The proposed model was used to assess the impact of ARB cycles on the final material properties. The numerical results in 2D and 3D were compared and contrasted. The research work presented in this paper is focused on the simulation optimization based on CPU time minimization. The numerical simulations were also validated through a comparison with the experimental results.

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Kim, Yongho, Gilnam Ryu, and Yongho Choi. "Fast and Accurate Numerical Solution of Allen–Cahn Equation." Mathematical Problems in Engineering 2021 (December 6, 2021): 1–12. http://dx.doi.org/10.1155/2021/5263989.

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Simulation speed depends on code structures. Hence, it is crucial how to build a fast algorithm. We solve the Allen–Cahn equation by an explicit finite difference method, so it requires grid calculations implemented by many for-loops in the simulation code. In terms of programming, many for-loops make the simulation speed slow. We propose a model architecture containing a pad and a convolution operation on the Allen–Cahn equation for fast computation while maintaining accuracy. Also, the GPU operation is used to boost up the speed more. In this way, the simulation of other differential equations can be improved. In this paper, various numerical simulations are conducted to confirm that the Allen–Cahn equation follows motion by mean curvature and phase separation in two-dimensional and three-dimensional spaces. Finally, we demonstrate that our algorithm is much faster than an unoptimized code and the CPU operation.

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Catureba, Rafaela Pedroso, Aldelio Bueno Caldeira, and Rodrigo Otávio de Castro Guedes. "Numerical Simulation of the TNT Solidification Process." Defence Science Journal 69, no. 4 (2019): 336–41. http://dx.doi.org/10.14429/dsj.69.13536.

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The solidification phenomenon is present in the casting process of energetic materials. In defence industry, trinitrotoluene (TNT) is used as main charge for high explosive ammunitions. The present study tackles the numerical simulation of the solidification process of TNT by means of a two-dimensional transient model in cylindrical coordinates. The heat conduction problem is solved by using the enthalpy method that rewrites the governing equation in terms of this variable. The transient diffusive equation is then numerically solved by applying finite volumes in an explicit scheme. The analysis the mold thickness and the convective boundary conditions are analysed to assess how they affect heat transfer during solidification. Results obtained allow for a better comprehension of this type of problem.

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Lee, Chaeyoung, Sungha Yoon, Jintae Park, and Junseok Kim. "An Explicit Hybrid Method for the Nonlocal Allen–Cahn Equation." Symmetry 12, no. 8 (2020): 1218. http://dx.doi.org/10.3390/sym12081218.

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We extend the explicit hybrid numerical method for solving the Allen–Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.

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Zhang, Hong Wei, Yi Du Zhang, and Qiong Wu. "Three-Dimensional Numerical Simulation of Residual Stresses by Shot-Peening." Advanced Materials Research 79-82 (August 2009): 1189–92. http://dx.doi.org/10.4028/www.scientific.net/amr.79-82.1189.

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Shot peening is a complex cold working process used to improve the fatigue life of metallic parts. This investigation is devoted to the modeling and simulation of the residual stress field resulting from the shot peening process, in which the finite element method was employed using a rate sensitive material. The history of energies during explicit dynamic analysis was discussed and the solution time for explicit analysis was analyzed. For the single shot impact model, the effect of shot velocity, shot size, incident angle was studied. In addition, the effect of repeated impacts on the residual stress within the target plate was studied. Furthermore, the multiple shot impacts of shot peening process were accomplished and the effect of peening coverage was investigated based on different shot models.

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Li, Biao, Ya Zhi Li, Xi Li, and Zhen Hua Yao. "Numerical Simulation of Compression-After-Impact Process of Composite Laminates." Key Engineering Materials 525-526 (November 2012): 265–68. http://dx.doi.org/10.4028/www.scientific.net/kem.525-526.265.

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The residual compressive strength of composite laminates subjected to low-velocity impact (CAI) was analyzed using the ABAQUS/Explicit package through a two-step calculation. The finite element model was composed of solid elements and interfacial cohesive elements. The out of plane low-velocity impact process was simulated in the first step and the results of which were taken as the input for the second step of the in-plane compression, until the collapse of the laminate. The usefulness of the explicit solution algorithm in dealing with the quasi-static procedure of the in-plane compression was investigated by examining the effect of different initial velocities of the compression loading on CAI values. The simulation results agree well with the experimental results.

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YAMADA, Yoshinori, Mikio SAKAI, Shin MIZUTANI, Seiichi KOSHIZUKA, Masatoshi OOCHI, and Koji MUROZONO. "Numerical Simulation of Three-Dimensional Free-Surface Flows with Explicit Moving Particle Simulation Method." Transactions of the Atomic Energy Society of Japan 10, no. 3 (2011): 185–93. http://dx.doi.org/10.3327/taesj.j10.033.

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35

Anggono, Agus Dwi, Tri Widodo Besar Riyadi, and Waluyo Adi Siswanto. "Dynamic Explicit Finite Element Code for U-Bending Simulation and Springback Prediction." Applied Mechanics and Materials 660 (October 2014): 337–41. http://dx.doi.org/10.4028/www.scientific.net/amm.660.337.

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In this paper, a dynamic explicit method was used to simulate U-bending processes of aluminium and its springback. The simulation was carried out using a free software of finite element analysis code namely Impact. The model was taken from a benchmark model in Numisheet'93. The numerical results of the dynamic explicit code were compared with the results of the experimental works. After the optimization was done using the simulation process, it was found that the springback results showed a good agreement with that done by the experimental results. The software Impact was capable of simulating the U-bending processes and predicting the occurrence of springback.

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Li, De Bo, Qi Sheng Xu, Yue Liang Shen, Zhi Yong Wen, and Ya Ming Liu. "Parallel Algorithms for Compressible Turbulent Flow Simulation Using Direct Numerical Method." Advanced Materials Research 516-517 (May 2012): 980–91. http://dx.doi.org/10.4028/www.scientific.net/amr.516-517.980.

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In this study, SPMD parallel computation of compressible turbulent jet flow with an explicit finite difference method by direct numerical method is performed on the IBM Linux Cluster. The conservation equations, boundary conditions including NSCBC (charactering boundary conditions), grid generation method, and the solving processing are carefully presented in order to give other researchers a clear understanding of the large scale parallel computing of compressible turbulent flows using explicit finite difference method, which is scarce in the literatures. The speedup factor and parallel computational efficiency are presented with different domain decomposition methods. In order to use our explicit finite method for large scale parallel computing, the grid size imposed on each processor, the speedup factor, and the efficiency factor should be carefully chosen in order to design an efficient parallel code. Our newly developed parallel code is quite efficient from that of implicit finite difference method or spectral method on parallel computational efficiency. This is quite useful for future research for gas and particle two-phase flow, which is still a problem for highly efficient code for two-phase parallel computing.

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Droux, Jean-Jacques. "Three-dimensional numerical simulation of solidification by an improved explicit scheme." Computer Methods in Applied Mechanics and Engineering 85, no. 1 (1991): 57–74. http://dx.doi.org/10.1016/0045-7825(91)90122-m.

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38

Tripoli, G. J. "An explicit three-dimensional nonhydrostatic numerical simulation of a tropical cyclone." Meteorology and Atmospheric Physics 49, no. 1-4 (1992): 229–54. http://dx.doi.org/10.1007/bf01025409.

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39

Hasanah, U., and S. R. Pudjaprasetya. "Numerical simulation of wave phenomena using FreeFEM." Journal of Physics: Conference Series 2072, no. 1 (2021): 012003. http://dx.doi.org/10.1088/1742-6596/2072/1/012003.

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Abstract In this research free surface motion governed by the shallow water equations is considered. A numerical scheme based on the finite element method, which is incorporated in the open source FreeFEM, was used to simulate several wave phenomena. By carefully setting the corresponding initial condition as well as boundary conditions, several numerical computations were conducted. Numerical simulations presented here are standing wave in a closed basin, progressive wave over a flat bottom, as well as wave shoaling over a decreasing depth and wave refraction. In all cases above, the existing analytical formula are used to validate the numerical results. These computations suggest that explicit-implicit scheme is appropriate for varying water wave simulations.

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Dariusz Jakubek. "Numerical Simulation of Temperature Distribution in the Gas Turbine Blade." Communications - Scientific letters of the University of Zilina 23, no. 3 (2021): B227—B236. http://dx.doi.org/10.26552/com.c.2021.3.b227-b236.

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This paper concentrates on temperature distribution in the gas turbine blade equipped by the cooling holes system on transient heat transfer. The present study requires the specification of internal and external boundary conditions. The calculations had been done using both Crank-Nicolson algorithm, explicit and implicit methods, in which different heat transfer coefficients on internal cooling surfaces of the holes were applied. The value of coefficients has a direct and crucial impact on the final result. The heat transfer coefficient of cooling the working surface of the of heat pipes was 1600 W/(m2K). It was found that there were no significant differences of temperature distribution in comparison of results from explicit method in the Ansys analysis, Crank-Nicolson algorithm and implicit method in Matlab. The simulation is based on Finite Element Method, which uses the Crank Nicolson algorithm.

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Liu, Ze Min, Zheng Hua Guo, Gang Yao Zhao, Shu Zhang, and Ji Luan Pan. "3D Numerical Simulation of Linear Friction Welding of 45# Carbon Steel." Advanced Materials Research 476-478 (February 2012): 701–4. http://dx.doi.org/10.4028/www.scientific.net/amr.476-478.701.

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A 3D finite-elements model of 45# carbon steel of linear friction welding is built with the dynamic explicit code ABAQUS/explicit based on the solution of several key techniques, such as contact boundary condition treating, material properties definition, meshing technology, etc. Then the reliability of the model is validated by comparison with experiments in the literature. Furthermore, numerical simulation and analysis of the linear friction welding process of 45# steel have been carried out by using the model. The temperature field of workpiece, the temperature change of center point of welding interface and the metal flow behavior of welding interface are showed in results.

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Handlovičová, A., and Z. Krivá. "PERONA-MALIK EQUATION - ERROR ESTIMATES FOR EXPLICIT FINITE VOLUME SCHEME." Mathematical Modelling and Analysis 10, no. 4 (2005): 353–66. http://dx.doi.org/10.3846/13926292.2005.9637293.

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43

Li, Yong Suo, Ke Neng Zhang, Xian Yang, and Chang Bo Huang. "Numerical Simulation for the Excavation in Tunnel Construction." Applied Mechanics and Materials 90-93 (September 2011): 90–93. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.90.

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Tunnel excavation is often done in underground engineering such as civil tunnel construction and mine excavation. The numerical simulation can output colorful results to interpret the tunnel excavation effect more easier. Among all the numerical simulation methods, fast lagrangian explicit finite difference code of continua (FLAC3D) is widely used to solve practical problems, especially in field of elasto-plastic characteristic and construction procedure. So in the present paper, 3 steps of excavations in a tunnel is modeled by FLAC3D to present the stress and displacement distribution, and give guidance for the real practice.

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Johansson, L. "Numerical Simulation of Contact Pressure Evolution in Fretting." Journal of Tribology 116, no. 2 (1994): 247–54. http://dx.doi.org/10.1115/1.2927205.

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In the present paper an algorithm for frictional contact between two elastic bodies is presented. The algorithm is applied to the calculation of the evolution of contact pressure between two elastic bodies when material is being removed by fretting. To this end Archard’s law of wear is implemented into the algorithm. It is noticed that the calculated pressures after a period of fretting differ considerably from the initial Hertz type pressures. Further, it is noted that numerical instabilities can occur in explicit type wear calculations, and a stability criterion is suggested.

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Čiegis, Raimondas. "NUMERICAL SOLUTION OF HYPERBOLIC HEAT CONDUCTION EQUATION." Mathematical Modelling and Analysis 14, no. 1 (2009): 11–24. http://dx.doi.org/10.3846/1392-6292.2009.14.11-24.

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Hyperbolic heat conduction problem is solved numerically. The explicit and implicit Euler schemes are constructed and investigated. It is shown that the implicit Euler scheme can be used to solve efficiently parabolic and hyperbolic heat conduction problems. This scheme is unconditionally stable for both problems. For many integration methods strong numerical oscillations are present, when the initial and boundary conditions are discontinuous for the hyperbolic problem. In order to regularize the implicit Euler scheme, a simple linear relation between time and space steps is proposed, which automatically introduces sufficient amount of numerical viscosity. Results of numerical experiments are presented.

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Jiao, Yan Hui, and Zhong Gui Ren. "Numerical Simulation and Calculation of Freezing Time of Soil." Applied Mechanics and Materials 246-247 (December 2012): 327–30. http://dx.doi.org/10.4028/www.scientific.net/amm.246-247.327.

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The mathematical model based on temperature formulation for describing freezing course of soil is presented and the explicit finite difference method is used to perform computer simulation of freezing time of soil in this paper. It seems to be satisfactory by comparing the numerical results by the method of TDMA with experimental data. It is significant for freezing process and freezing units, optimum design of practical engineering.

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Gorial, Iman I. "Numerical Simulation for Fractional Percolation Equation." Mathematical Modelling of Engineering Problems 8, no. 3 (2021): 425–30. http://dx.doi.org/10.18280/mmep.080312.

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The aims of this paper are to propose approach of explicit finite difference mathod (EFDM), clarify the problem the mixed fractional derivative in one-dimensional fractional percolation equation (O-DFPE), and the study of consistency, stability, and convergence methods. Use of estimated Grunwald estimation in the analysis of mixed fractional derivatives. However, the given method is successfully applied to the mixed fractional derivative classes with the initial condition (IC) and derivative boundary conditions (DBC). To illustrate the efficiency and validity of the proposed algorithm, examples are given and the results are compared with the exact solution. From the figures shown for the examples in this work, the approximate solution values given by the EFDM for the various grid points are equivalent to the exact solution values with high-precision approximation. To show the effectiveness of the proposed method, where the error between the EFDM and the exact method is zero, the fractional derivative was used with various and random values. Using the package MATLAB and MathCAD 12 Figures were introduced.

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Kaselouris, Evaggelos, Theodoros Papadoulis, Elenh Variantza, Andreas Baroutsos, and Vasilios Dimitriou. "A Study of Explicit Numerical Simulations in Orthogonal Metal Cutting." Solid State Phenomena 261 (August 2017): 339–46. http://dx.doi.org/10.4028/www.scientific.net/ssp.261.339.

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The capability of the explicit numerical methods to simulate accurately the real cutting process is investigated in this research work. Smoothed particle hydrodynamics - SPH, classical Lagrangian finite element method - FEM and Multi-Material Arbitrary Lagrangian Eulerian - ALE methods are chosen for the modeling and simulation of the orthogonal metal cutting process of AISI H13 in LS-DYNA. The cutting tool is modeled as a rigid FEM body that incrementally penetrates into the flexible deformable workpiece. At each numerical model, the dynamic elastoplastic behavior of the workpiece material is investigated by taking into account the Johnson-Cook (J-C) constitutive strength material model. The influence of the J-C parameter values found in literature to the models is explored. The obtained numerical SPH, FEM and ALE results of the estimated cutting and thrust forces, stress, plastic strain and thermal distributions are compared with results found in the literature. This comparison, leads to valuable conclusions for the performance of the three methods, concerning the approximation accuracy, model development complexity and computational time demands. Based on these conclusions the SPH method is chosen to simulate the experimentally performed orthogonal cut of AISI 1045. The obtained SPH numerical results outline its advantages among the other explicit simulation methods.

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Lee, Hyun Geun, Jintae Park, Sungha Yoon, Chaeyoung Lee, and Junseok Kim. "Mathematical Model and Numerical Simulation for Tissue Growth on Bioscaffolds." Applied Sciences 9, no. 19 (2019): 4058. http://dx.doi.org/10.3390/app9194058.

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Tissue growth on bioscaffolds can be controlled using substrate geometry such as substrate curvature. In this study, we present a mathematical model and numerical simulation method for tissue growth on a bioscaffold to investigate the effect of local curvature on tissue growth. The mathematical model is based on the Allen–Cahn (AC) equation, which has been extensively used to model many problems involving motion by mean curvature. By solving the AC equation using the explicit Euler method, the proposed method is simple and fast. Numerical simulations on various geometries are presented to demonstrate the applicability of the proposed framework on tissue growth on a bioscaffold.

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Guo, Xin, Li Hua Zhu, and Tian Li Wang. "Research on Numerical Integration Algorithm for MDOF Pseudo-Dynamic Test." Applied Mechanics and Materials 204-208 (October 2012): 4820–26. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4820.

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This paper focuses on two integration algorithms used for pseudo-dynamic test, explicit Newmark algorithm and implicit alpha-C algorithm. The comparison study between the test and simulation results shows that: the non-uniform distribution of mass, restoring force characteristics and higher frequency vibration modality are simulated more accurately using the alpha-C algorithm than using explicit Newmark algorithm. The alpha-C algorithm also leads to high iterative accuracy and unconditional stability. Replacing the explicit Newmark algorithm in original experimental system by implicit alpha-C algorithm, the MDOF pseudo dynamic test system can be realized successfully.

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