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This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes.

The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement.

The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions.

Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

Computational fluid dynamics (CFD) simulation of the flow field around marine propellers is challenging because of geometric complexity and rotational effects. To capture the flow structure, grid quality and distribution around the blades is primordial. This paper aims to demonstrate that solution-based automatic mesh optimization is the most logical and practical way to achieve optimal CFD solutions.

In the current paper, open water propeller performance coefficients such as thrust and torque coefficients are numerically investigated. An anisotropic mesh adaptation technique is applied, believed for the first time, to marine propellers and to two computational domains.

The current study’s performance coefficients are compared with other previously published CFD results and improvements in terms of accuracy and computational cost are vividly demonstrated for different advance coefficients, as well as a much sharper capture of the complex flow features.

It will be clearly demonstrated that these two improvements can be achieved, surprisingly, at a much lower meshing and computational cost.

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity.

The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level.

Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure.

This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder metallurgy and composite material processing are briefly discussed. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.

Structural performance of additively manufactured parts is deposition path-dependent because of the induced material anisotropy. Hence, this paper aims to contribute a novel idea of concurrently performing the deposition path planning and the structural topology optimization for additively manufactured parts.

The concurrent process is performed under a unified level set framework that: the deposition paths are calculated by extracting the iso-value level set contours, and the induced anisotropic material properties are accounted for by the level set topology optimization algorithm. In addition, the fixed-geometry deposition path optimization problem is studied. It is challenging because updating the zero-value level set contour cannot effectively achieve the global orientation control. To fix this problem, a level set-based multi-step method is proposed, and it is proved to be effective.

The proposed concurrent design method has been successfully applied to designing additively manufactured parts. The majority of the planned deposition paths well match the principle stress direction, which, to the largest extent, enhances the structural performance. For the fixed geometry problems, fast and smooth convergences have been observed.

The concurrent deposition path planning and structural topology optimization method is, for the first time, developed and effectively implemented. The fixed-geometry deposition path optimization problem is solved through a novel level set-based multi-step method.

The purpose of this paper is to find a more performing and automated procedure for linking an identification algorithm implemented in a general‐purpose environment with a commercial finite‐element code for magnetic field analysis. In particular, the use of a multiprocessor computer makes it possible to perform parallel computations keeping the calculation time reasonably low.

The method is applied to identify the B‐H curve of anisotropic magnetic laminations in the direction normal to the sheet surface. In total, three different optimization methods have been applied. First an evolution strategy algorithm for solving the identification problem was used; then genetic algorithm (GA) was applied. The results obtained using different methods were compared and discussed. The computation time is reduced by adjusting the refinement of the FEM mesh.

The key point has been the use of a derivative‐free and global‐search oriented algorithm. Even if a starting point far from the solution is chosen, a suitably large initial value of the search radius makes the convergence possible. The effect of the historical parameter of the minimization algorithm on convergence has also been investigated.

The main new idea presented in this paper is equipping a GA‐based identification procedure with an additional objective function describing the sensitivity of the flux density against a small perturbation in parameters. This approach gives a multiple objective problem which introduces possibility of choosing a compromise solution among many optimal solutions instead of only one, as in classical GA optimization algorithm. The paper is mainly addressed to readers interested in the efficient use of GA‐based identification.

The primary objective of this study is to tackle the enduring challenge of preserving feature integrity during the manipulation of geometric data in computer graphics. Our work aims to introduce and validate a variational sparse diffusion model that enhances the capability to maintain the definition of sharp features within meshes throughout complex processing tasks such as segmentation and repair.

We developed a variational sparse diffusion model that integrates a high-order L₁ regularization framework with Dirichlet boundary constraints, specifically designed to preserve edge definition. This model employs an innovative vertex updating strategy that optimizes the quality of mesh repairs. We leverage the augmented Lagrangian method to address the computational challenges inherent in this approach, enabling effective management of the trade-off between diffusion strength and feature preservation. Our methodology involves a detailed analysis of segmentation and repair processes, focusing on maintaining the acuity of features on triangulated surfaces.

Our findings indicate that the proposed variational sparse diffusion model significantly outperforms traditional smooth diffusion methods in preserving sharp features during mesh processing. The model ensures the delineation of clear boundaries in mesh segmentation and achieves high-fidelity restoration of deteriorated meshes in repair tasks. The innovative vertex updating strategy within the model contributes to enhanced mesh quality post-repair. Empirical evaluations demonstrate that our approach maintains the integrity of original, sharp features more effectively, especially in complex geometries with intricate detail.

The originality of this research lies in the novel application of a high-order L₁ regularization framework to the field of mesh processing, a method not conventionally applied in this context. The value of our work is in providing a robust solution to the problem of feature degradation during the mesh manipulation process. Our model’s unique vertex updating strategy and the use of the augmented Lagrangian method for optimization are distinctive contributions that enhance the state-of-the-art in geometry processing. The empirical success of our model in preserving features during mesh segmentation and repair presents an advancement in computer graphics, offering practical benefits to both academic research and industry applications.