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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.

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.

The purpose of this paper is to present an immersed volume method that accounts for solid conductive bodies (hat‐shaped disk) in calculation of time‐dependent, three‐dimensional, conjugate heat transfer and fluid flow.

The incompressible Navier‐Stokes equations and the heat transfer equations are discretized using a stabilized finite element method. The interface of the immersed disk is defined and rendered by the zero isovalues of a level set function. This signed distance function allows turning different thermal properties of each component into homogeneous parameters and it is coupled to a direct anisotropic mesh adaptation process enhancing the interface representation. A monolithic approach is used to solve a single set of equations for both fluid and solid with different thermal properties.

In the proposed immersion technique, only a single grid for both air and solid is considered, thus, only one equation with different thermal properties is solved. The sharp discontinuity of the material properties was captured by an anisotropic refined solid‐fluid interface. The robustness of the method to compute the flow and heat transfer with large materials properties differences is demonstrated using stabilized finite element formulations. Results are assessed by comparing the predictions with the experimental data.

The proposed method demonstrates the capability of the model to simulate an unsteady three‐dimensional heat transfer flow of natural convection, conduction and radiation in a cubic enclosure with the presence of a conduction body. A previous knowledge of the heat transfer coefficients between the disk and the fluid is no longer required. The heat exchange at the interface is solved and dealt with naturally.

This paper aims to develop a robust set of advanced numerical tools to simulate multiphase flows under the superimposition of external uniform magnetic fields.

The flow has been simulated in a fully Eulerian framework by a {\it variational multi-scale} method, which allows to take into account the small-scale turbulence without explicitly model it. The multi-fluid problem has been solved through the convectively re-initialized level-set method to robustly deal with high density and viscosity ratio between the phases and the surface tension has been modelled implicitly in the level-set framework. The interaction with the magnetic field has been modelled through the classic induction equation for 2D problems and the time step computation is based on the electromagnetic interaction to guarantee convergence of the method. Anisotropic mesh adaptation is then used to adapt the mesh to the main problem’s variables and to reach good accuracy with a small number of degrees of freedom. Finally, the variational multiscale method leads to a natural stabilization of the finite elements algorithm, preventing numerical spurious oscillations in the solution of Navier–Stokes equations (fluid mechanics) and the transport equation (level-set convection).

The methodology has been validated, and it is shown to produce accurate results also with a low number of degrees of freedom. The physical effect of the external magnetic field on the multiphase flow has been analysed.

The dam-break benchmark case has been extended to include magnetically constrained flows.

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.

The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows.

Unsteady Euler equations are discretized on meshes of linear and quadratic triangular and quadrilateral elements using LSFEM. Backward Euler scheme is used for time discretization. For the refinement of linear triangular elements, a modified version of the simple bisection algorithm is used. Mesh coarsening is performed with the edge collapsing technique. Pressure gradient-based error estimation is used for refinement and coarsening decision. The developed solver is tested with flow over a circular bump, flow over a ramp and flow through a scramjet inlet problems.

Pressure difference based error estimator, modified simple bisection method for mesh refinement and edge collapsing method for mesh coarsening are shown to work properly with the LSFEM formulation. With the proper use of mesh adaptation, time and effort necessary to prepare a good initial mesh reduces and mesh independency control of the final solution is automatically taken care of.

LSFEM is used for the first time for the solution of inviscid compressible flows with h-type mesh refinement and coarsening on triangular elements. It is shown that, when coupled with mesh adaptation, inherent viscous dissipation of LSFEM technique is no longer an issue for accurate shock capturing without unphysical oscillations.

This paper aims to describe the physical and numerical modeling of a new computational fluid dynamics solver for hypersonic flows in thermo-chemical non-equilibrium. The code uses a blend of numerical techniques to ensure accuracy and robustness and to provide scalability for advanced hypersonic physics and complex three-dimensional (3D) flows.

The solver is based on an edge-based stabilized finite element method (FEM). The chemical and thermal non-equilibrium systems are loosely-coupled to provide flexibility and ease of implementation. Chemical non-equilibrium is modeled using a laminar finite-rate chemical kinetics model while a two-temperature model is used to account for thermodynamic non-equilibrium. The systems are solved implicitly in time to relax numerical stiffness. Investigations are performed on various canonical hypersonic geometries in two-dimensional and 3D.

The comparisons with numerical and experimental results demonstrate the suitability of the code for hypersonic non-equilibrium flows. Although convergence is shown to suffer to some extent from the loosely-coupled implementation, trading a fully-coupled system for a number of smaller ones improves computational time. Furthermore, the specialized numerical discretization offers a great deal of flexibility in the implementation of numerical flux functions and boundary conditions.

The FEM is often disregarded in hypersonics. This paper demonstrates that this method can be used successfully for these types of flows. The present findings will be built upon in a later paper to demonstrate the powerful numerical ability of this type of solver, particularly with respect to robustness on highly stretched unstructured anisotropic grids.

The purpose of this paper is to develop parallel algorithms for moving boundary simulations by local remeshing and compose them to a fully parallel simulation cycle for the solution of problems with engineering interests.

The moving boundary problems are solved by unsteady flow computations coupled with six-degrees-of-freedom equations of rigid body motion. Parallel algorithms are developed for both computational fluid dynamics (CFD) solution and grid deformation steps. Meanwhile, a novel approach is developed for the parallelization of the local remeshing step. It inputs a distributed mesh after deformation, then marks low-quality elements to be deleted on the respective processors. After that, a parallel domain decomposition approach is used to repartition the hole mesh and then to redistribute the resulting sub-meshes onto all available processors. Then remesh individual sub-holes in parallel. Finally, the element redistribution is rebalanced.

If the CFD solver is parallelized while the remaining steps are executed in sequential, the performance bottleneck of such a simulation cycle is observed when the simulation of large-scale problem is executed. The developed parallel simulation cycle, in which all of time-consuming steps have been efficiently parallelized, could overcome these bottlenecks, in terms of both memory consumption and computing efficiency.

A fully parallel approach for moving boundary simulations by local remeshing is developed to solve large-scale problems. In the algorithm level, a novel parallel local remeshing algorithm is present. It repartitions distributed hole elements evenly onto all available processors and ensures the generation of a well-shaped inter-hole boundary always. Therefore, the subsequent remeshing step can fix the inter-hole boundary involves no communications.

To provide an efficient numerical eigenvalue solution for open waveguides with lossy anisotropic materials.

Vector edge elements are used to represent the core of the problem, and an adaptive perfectly matched layer (PML) is used to truncate the surrounding region. The parameters of the PML are allowed to change at each frequency to obtain accurate results using small number of unknowns.

The method is able to solve many configurations, and considerable reduction in mesh size has been reported. In addition, by adapting the solution according to some error criterion, it will be possible to minimize the dependence on human experience and rely more on automated algorithms.

There is a need to improve the performance of the adaptive algorithm by building an automatic adaptive procedure that can work without human intervention.

A systematic full‐wave algorithm for solving practical electromagnetic engineering problems associated with open waveguides, such as planar transmission lines and optical waveguides, using relatively small computer resources.

Proposed a new “dimension” of adaptation for PML, besides the classical h‐/p‐/hp adaptation methods available in literature. Thus, the requirement for smaller computer resources makes this method cost‐effective for industry in the design of practical open waveguides.