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Numerical simulation of polymer injection processes has become increasingly common in mould design. In industry, such a task is accomplished mainly by using commercial packages. Owing to the complexities inherent of this class of problems, most commercial codes attempt to combine realistic rheological descriptions with simplified numerical models. In spite of the apparent success, such approaches are not able to capture important aspects of the flow topology. The present work aims to describe a more elaborate mathematical model based on finite volumes which is able to provide both accurate solutions and further insights on the physics of the polymer flow.

The mathematical model comprises the momentum and energy equations and a Poisson equation for pressure to impose the incompressibility constraint. The governing equations are discretized using the finite volume method based on central, second‐order accurate formulas for both convection and diffusion terms. Artificial dissipation terms are added externally in order to control the odd‐even decoupling problem.

The numerical model was conceived within the framework of a generalized Newtonian formulation. The capability of the numerical scheme is illustrated by simulations using three distinct constitutive relations to approach the non‐Newtonian behaviour of the polymer melt: isothermal power‐law, modified Arrhenius power‐law and cross models.

This paper extends the computational strategies previously developed to Newtonian fluids to account for more complex constitutive relations. The velocity and temperature coupled solution for polymer melts using only second‐order accurate formulas constitute also a relevant contribution.

The purpose of this paper is to develop Triple Finite Volume Method (tFVM), the author discretizes incompressible Navier-Stokes equation by tFVM, which leads to a special linear system of saddle point problem, and most computational efforts for solving the linear system are invested on the linear solver GMRES.

In this paper, by recently developed preconditioner Hermitian/Skew-Hermitian Separation (HSS) and the parallel implementation of GMRES, the author develops a quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation.

Computational results show that, the quick solver HSS-pGMRES-tFVM significantly increases the solution speed for saddle point problem from incompressible Navier-Stokes equation than the conventional solvers.

Altogether, the contribution of this paper is that the author developed the quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation.

The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele‐Shaw model.

The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi‐static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non‐Newtonian.

Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power‐law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries.

With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so‐called “meshless” scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill‐time errors that might be addressed by introducing suitable projections. The general question of “rate of convergence” of these schemes requires analysis. Numerical results here suggest first‐order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods.

This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed “on‐the‐fly” for each “active point” to form a dynamic virtual mesh of active elements that evolves with the moving interface.

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.

This paper aims to investigate the convergence and error properties of a finite volume-based heat conduction code that uses automatic differentiation to evaluate derivatives of solutions outputs with respect to arbitrary solution input(s). A problem involving conduction in a plane wall with convection at its surfaces is used as a test problem, as it has an analytical solution, and the error can be evaluated directly.

The finite volume method is used to discretize the transient heat diffusion equation with constant thermophysical properties. The discretized problem is then linearized, which results in two linear systems; one for the primary solution field and one for the secondary field, representing the derivative of the primary field with respect to the selected input(s). Derivatives required in the formation of the secondary linear system are obtained by automatic differentiation using an operator overloading and templating approach in C++.

The temporal and spatial discretization error for the derivative solution follows the same order of accuracy as the primary solution. Second-order accuracy of the spatial and temporal discretization schemes is confirmed for both primary and secondary problems using both orthogonal and non-orthogonal grids. However, it has been found that for non-orthogonal cases, there is a limit to the error reduction, which is concluded to be a result of errors in the Gauss-based gradient reconstruction method.

The convergence and error properties of derivative solutions obtained by forward mode automatic differentiation of finite volume-based codes have not been previously investigated.

In the present study, a finite volume approach for solving two‐dimensional, two‐fluids flows with heat and mass transfer was developed for predicting the flow of particulate materials through pneumatic dryer. The model was solved for a two‐dimensional steady‐state condition and considering axial and radial profiles for the flow variables. A two‐stage drying process was implemented. The numerical procedure includes discretization of calculation domain into torus‐shaped final volumes, solving the gas phase conservation equations by a modified semi‐implicit method for pressure‐linked equations algorithm, and the conservation equations of particulate phase were solved by the explicit forward difference algorithm. The mass momentum and energy coupling between the phases were considered by principles of the Interphase slip algorithm. In order to validate the theoretical and the numerical models, the developed models were applied to simulate the drying process of wet PVC particles in a large‐scale pneumatic dryer and to the drying process of wet sand in a laboratory‐scale pneumatic dryer. The predictions of the numerical simulations were compared successfully with the results of independent numerical and experimental investigations. Following the models validation, the two‐dimensional distributions of the flow characteristics were examined.

This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks.

The work presents a detailed comparison with reference solutions published in the literature –when available– and numerical results computed using a commercial cell-centred finite volume software.

The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%.

The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.

A general methodology for deriving thin plate bending elements with a single degree of freedom per node is presented. The formulation is based on the combination of a standard C0 finite element interpolation for the deflection field with an independent approximation of the curvatures which are expressed in terms of the deflection gradient along the sides using a finite volume‐like approach. The formulation is particularized for the simplest element of the family, i.e. the three node triangle with three degrees of freedom. The potential of the new element is shown through different examples of application.

A pseudo steady‐state model is developed to study heat transfer, fluid flow, and the interface shape in the liquid encapsulated vertical Bridgman crystal growth. The model, which is governed by momentum, heat, and overall mass balances in the system, is solved by a finite‐volume/Newton method. Flow and temperature fields, as well as unknown melt/crystal and melt/encapsulant interfaces, are calculated simultaneously. Sample calculations are mainly conducted for the GaAs/B₂O₃/PBN system. Calculated results for the Germanium/graphite system are compared with finite element calculations by Adornato and Brown, and they are in good agreement. The effects of some process parameters, including the growth speed, ambient temperature profile and heat transfer conditions, on flow patterns, temperature fields and the interface shape are illustrated through calculated results. Interface inversion from concave to convex, by modifying the ambient temperature profile, is also demonstrated through computer simulation. Particularly, through an inverse problem approach, a flat interface can be easily obtained for various operation conditions.

This paper aims to propose an adaptive unstructured finite volume procedure for efficient prediction of propellant feedline dynamics in fluid network.

The adaptive strategy is based on feedback control of errors defined by changes in key variables in two subsequent time steps.

As an evaluation of the proposed approach, two feedline dynamics problems are formulated and solved. First problem involves prediction of pressure surges in a pipeline that has entrapped air and the second is a conjugate heat transfer problem involving prediction of chill down of cryogenic transfer line. Numerical predictions with the adaptive strategy are compared with available experimental data and are found to be in good agreement. The adaptive strategy is found to be efficient and robust for predicting feedline dynamics in flow network at reduced CPU time.

This study uses an adaptive reduced-order network modeling approach for fluid network.