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The orientation behavior of fiber is of great significance in improving the performance of fiber-reinforced polymer products. Generally, the Folgar–Tucker equation can accurately describe the variation of orientation vector of fiber, whereas the stability of numerical algorithms was the major challenge. This paper aims to propose an accurate, stable algorithm to solve the Folgar–Tucker equation for the fiber orientation behavior.

First, the mismatch problem between the strain rate and the pressure field was solved by using the integral transformation method. Then, an accurate, stable algorithm to solve the Folgar–Tucker equation based on the invariant-based optimal fitting method was proposed. The equation was discretized by finite element/finite difference method, and the Lagrange multiplier method was applied to ensure stability.

The proposed algorithm is proven to accurately and steadily coincide with the experimental results for different cases, including the fiber orientation behaviors under combined flow field, rectangular sheet, three-dimensional computed tomography imaging of tensile specimen and box cases.

The fiber orientation behavior during the injection molding can be accurately predicted, which plays a significant role in determining the mechanical properties of products.

Lattice Boltzmann method (LBM) has made great success in computational fluid dynamics, and this paper aims to establish an efficient simulation model for the polymer injection molding process using the LBM. The study aims to validate the capacity of the model for accurately predicting the injection molding process, to demonstrate the superior numerical efficiency in comparison with the current model based on the finite volume method (FVM).

The study adopts the stable multi-relaxation-time scheme of LBM to model the non-Newtonian polymer flow during the filling process. The volume of fluid method is naturally integrated to track the movement of the melt front. Additionally, a novel fractional-step thermal LBM is used to solve the convection-diffusion equation of the temperature field evolution, which is of high Peclet number. Through various simulation cases, the accuracy and stability of the present model are validated, and the higher numerical efficiency verified in comparison with the current FVM-based model.

The paper provides an efficient alternative to the current models in the simulation of polymer injection molding. Through the test cases, the model presented in this paper accurately predicts the filling process and successfully reproduces several characteristic phenomena of injection molding. Moreover, compared with the popular FVM-based models, the present model shows superior numerical efficiency, more fit for the future trend of parallel computing.

Limited by the authors’ hardware resources, the programs of the present model and the FVM-based model are run on parallel up to 12 threads, which is adequate for most simulations of polymer injection molding. Through the tests, the present model has demonstrated the better numerical efficiency, and it is recommended for the researcher to investigate the parallel performance on even larger-scale parallel computing, with more threads.

To the authors’ knowledge, it is for the first time that the lattice Boltzmann method is applied in the simulation of injection molding, and the proposed model does obviously better in numerical efficiency than the current popular FVM-based models.

The purpose of this paper is to develop a finite volume approach for the simulation of three-dimensional two-phase (polymer melt and air) flow in plastic injection molding which is capable of robustly handling the mesh non-orthogonality and the discontinuities in fluid properties.

The presented numerical method is based on a cell-centered unstructured finite volume discretization with a volume-of-fluid technique for interface capturing. The over-relaxed approach is adopted to handle the non-orthogonality involved in the discretization of the face normal derivatives to enhance the robustness of the solutions on non-orthogonal meshes. A novel interpolation method for the face pressure is derived to address the numerical stability issues resulting from the density and viscosity discontinuities at the melt–air interface. Various test cases are conducted to evaluate the proposed method.

The presented method was shown to be satisfactorily accurate by comparing simulations with analytical and experimental results. Besides, the effectiveness of the proposed face pressure interpolation method was verified by numerical examples of a two-phase flow problem with various density and viscosity ratios. The proposed method was also successfully applied to the simulation of a practical filling case.

The proposed finite volume approach is more tolerant of non-orthogonal meshes and the discontinuities in fluid properties for two-phase flow simulation; therefore, it is valuable for engineers in engineering computations.

The purpose of this paper is to develop a coupled approach to solve the pressure–velocity-coupled problem efficiently in the three-dimensional injection molding simulation.

A fully coupled pressure–velocity algorithm is developed to solve the coupled problem, by treating the pressure gradient term implicitly. And, the Schur complement preconditioned FGMRES is applied to decompose the resulting coupled pressure–velocity equation into pressure and velocity subsystems. Then, BoomerAMG is adopted to solve the pressure subsystem, and block Jacobi preconditioned FGMRES is applied to the velocity subsystem.

According to the several experiments, the fully coupled pressure–velocity algorithm was demonstrated to have faster convergence than the traditional SIMPLE algorithm, and the calculating time was reduced by up to 70 per cent. And, the Schur complement preconditioned FGMRES worked more efficiently than block Gauss–Seidel preconditioned FGMRES, block-selective AMG and AMG with block ILU(0) smoother and could take at least 47.4 per cent less time. The proposed solver had good scalability for different-size problems, including various cases with different numbers of elements. It also kept good speedup and efficiency in parallel performance.

A coupled solver has been proposed to effectively solve the coupled problem in the three-dimensional injection molding simulation, which is more robust and efficient than existing methods.

This study aims to investigate the effects of different surface-to-jet velocity ratios (Rsj) on the flow structure and the heat transfer of the floatation nozzle under different ratios (h/w) of the separation distance (h) to the slot width (w) and the differences of the flow structure and the heat transfer between the floatation nozzle and the slot nozzle.

The Nusselt number (Nu) and the pressure distribution of the floatation nozzle with a stationary wall are measured. Then the experimental results are used to validate the numerical model. Finally, a series of numerical simulations is carried out to achieve the purpose of this study.

The flow structure and heat transfer differences between the floatation nozzle and the slot nozzle are clarified. The floatation nozzle has more than 18 times the floatation ability of the unconfined slot nozzle. The Nu and pressure distributions of the floatation nozzle are experimentally measured. The effects of wall motion on the Nu and pressure distributions are identified.

The effects of the wall motion on the flow structure and the heat transfer of the floatation nozzle, and the differences between the floatation nozzle and the slot nozzle are first obtained. Therefore, it is valuable for engineers in engineering design of the floatation nozzle.

The numerical simulation of dispersed-phase evolution in injection molding process of polymer blends is of great significance in both adjusting material microstructure and improving performances of the final products. This paper aims to present a numerical strategy for the simulation of dispersed-phase evolution for immiscible polymer blends in injection molding.

First, the dispersed-phase modeling is discussed in detail. Then the Maffettone–Minale model, affine deformation model, breakup model and coalescence statistical model are chosen for the dispersed-phase evolution. A general coupled model of microscopic morphological evolution and macroscopic flow field is constructed. Besides, a stable finite element simulation strategy based on pressure-stabilizing/Petrov–Galerkin/streamline-upwind/Petrov–Galerkin method is adopted for both scales.

Finally, the simulation results are compared and evaluated with the experimental data, suggesting the reliability of the presented numerical strategy.

The coupled modeling of dispersed-phase and complex flow field during injection molding and the tracing and simulation of droplet evolution during the whole process can be achieved.

The purpose of this paper is to propose a new surface model combining the eccentric shell with multi-point constraint (MPC) for warpage prediction of injection molded plastics.

In this paper, three benchmark tests and a practical example are implemented to evaluate the performance of the new surface model and existing models.

The results demonstrate that the proposed model could give satisfactory solutions and has advantages over the existing models.

More precisely predicted warpage field for injection molded plastics can be achieved with the purposed model, such as that in the practical case.

The surface models are efficient and still popular for practical injection molding analysis. However, the existing models for warpage prediction cannot properly represent the true strain energy and obey material continuity assumption, and also they have not been assessed rigorously by benchmark tests. To overcome above-mentioned difficulty, a new surface model is proposed, which employs the eccentric shell without shear factor and MPC equation that ensuring material continuity. The results from experiment illustrate that the new model is superior to existing models.

The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD), to improve a preconditioned general minimal residual method for solving equations using Lagrange multiplier method, and facilitates the choice of the reordering for the iterative method.

To reordering the coefficient matrix before a preconditioned iterative method will greatly impact its convergence behavior, but the effect is very problem-dependent, even performs very differently when different preconditionings applied for an identical problem or the scale of the problem varies. The proposed reordering scheme is designed based on the features of two popular ordering schemes, RCM and AMD, and benefits from each of them.

Via numerical experiments for the cases of various scales and difficulties, the effects of RCM-AMD on the preconditioner and the convergence are investigated and the comparisons of RCM, AMD and RCM-AMD are presented. The results show that the proposed reordering scheme RCM-AMD is appropriate for large-scale and difficult problems and can be used more generally and conveniently. The reason of the reordering effects is further analyzed as well.

The proposed RCM-AMD reordering scheme preferable for solving equations using Lagrange multiplier method, especially considering that the large-scale and difficult problems are very common in practical application. This combined reordering scheme is more wide-ranging and facilitates the choice of the reordering for the iterative method, and the proposed iterative method has good performance for practical cases in in-house and commercial codes on PC.

This paper aims to develop an integrated cooling simulation for the temperature history of the panel during the forming process.

A local one‐dimensional transient analysis in the thickness direction is adopted for the panel part, which employs finite‐difference method. And a three‐dimensional, boundary element method is used for the numerical implementation of the heat transfer analysis in the mold region, which is considered as three‐dimensional conduction. The Renormalization‐Group turbulence model is applied for the jet impinging cooling. The part and mold analyses are coupled so as to match the temperature and heat flux on the glass‐mold interface.

The paper provides mathematical model and numerical strategy adapted to the problem, with experimental verification that shows a good agreement.

Cooling design in the forming operation of picture tube panel is of great importance because it significantly affects the part quality associated with residual stresses and productivity. The developed simulation package is a tool in the optimization of processing parameters and in‐mold cooling system structure design.

This paper presents a realistic, integrated, and coupled numerical model for analyzing the panel cooling process that retains important aspects of the problem. The paper could be very valuable to the researchers in this field as a benchmark for their analyses.

The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with multi-point constraint using Lagrange multiplier method.

In this paper, taking warpage analysis of polymer injection molding based on surface model as an example, the performance of several popular Krylov subspace methods, including conjugate gradient, BiCGSTAB and generalized minimal residual (GMRES), with diffident Incomplete LU (ILU)-type preconditions is investigated and compared. For controlling memory usage, GMRES(m) is also considered. And the ordering technique, commonly used in the direct method, is introduced into the presented iterative method to improve the preconditioner.

It is found that the proposed preconditioned GMRES method is robust and effective for solving problems considered in this paper, and approximate minimum degree (AMD) ordering is most beneficial for the reduction of fill-ins in the ILU preconditioner and acceleration of the convergence, especially for relatively accurate ILU-type preconditioning. And because of concerns about memory usage, GMRES(m) is a good choice if necessary.

In this paper, for overcoming difficulties of bad numerical stability resulting from Lagrange multiplier method, together with increasing scale of problems in engineering applications and limited hardware conditions of computer, a stable and efficient preconditioned iterative method is proposed for practical purpose. Before the preconditioning, AMD reordering, commonly used in the direct method, is introduced to improve the preconditioner. The numerical experiments show the good performance of the proposed iterative method for practical cases, which is implemented in in-house and commercial codes on PC.