Hexahedral Mesh Research Articles

Plastic hexahedral FEM for surgical simulation.

Soft-tissue manipulations, such as collecting, stretching or tearing tissue, are a common component of surgery. When too much force is applied, these manipulations result in a residual plastic deformation that surgeons should be aware of and that should be modeled by surgical simulation. Many tissues, vessels and organs can be modeled as offsets of curved simple shapes with primary directions, e.g., radial and axial for cylinders yield a rectangular mesh whose normal offset naturally yields a hexahedral mesh that can serve as a thick shell. Other organs are easy to embed into and deform following a hex mesh. We extend existing code for the volumetric finite element method (FEM) to model tissue plasticity as hexahedral thick shells or embedded organs. Specifically, the work extends the open source Simulation Open Framework Architecture and its newest hyperelastic deformation addition, Caribou, with focus on surgical simulation. The extension factors deformation gradients into (corotational or hyperelastic) elastic factors and plastic factors and enforces volume preservation. Limits on per-element twist, twist torque, material hardening and bounds on plasticity where elements invert avoid the need for re-meshing. Our hexahedral FEM avoids the biased outcomes of asymmetric coarsely-partitioned tetrahedral FEM. Caribou's hyperelastic FEM is extended to hex-FEM stretching plasticity. Our high-order accurate blended-vertex deformation enables coarse hex meshes to model large plastic rotational and stretch deformations without re-meshing. We compare a vertex-blended to a cell-centered piecewise constant approach; contrast plasticity based on corotational FEM and hyperelastic FEM; and test the computation under mesh refinement. The volume is preserved also for large deformations. On-the-fly generated hexahedral meshes can directly be used as finite element domains for plastic deformation based on corotational or hyperelastic elasticity. The outcome is suitable for surgical simulation.

Spectral element method for 3-D controlled-source electromagnetic forward modelling using unstructured hexahedral meshes

SUMMARYFor forward modelling of realistic 3-D land-based controlled-source electromagnetic (EM) problems, we develop a parallel spectral element approach, blending the flexibility and versatility of the finite element method in using unstructured grids with the accuracy of the spectral method. Complex-shaped structures and topography are accommodated by using unstructured hexahedral meshes, in which the elements can have curved edges and non-planar faces. Our code is the first spectral element algorithm in EM geophysics that uses the total field formulation (here that of the electric field). Combining unstructured grids and a total field formulation provides advantages in dealing with topography, in particular, when the transmitter is located on rough surface topography. As a further improvement over existing spectral element methods, our approach does not only allow for arbitrary distributions of conductivity, but also of magnetic permeability and dielectric permittivity. The total electric field on the elements is expanded in terms of high-order Lagrangian interpolants, and element-wise integration in the weak form of the boundary value problem is accomplished by Gauss–Legendre–Lobatto quadrature. The resulting complex-valued linear system of equations is solved using the direct solver MUMPS, and, subsequently, the magnetic field is computed at the points of interest by Faraday’s law. Five numerical examples comprehensively study the benefits of this algorithm. Comparisons to semi-analytical and finite element results confirm accurate representation of the EM responses and indicate low dependency on mesh discretization for the spectral element method. A convergence study illuminates the relation between high order polynomial approximation and mesh size and their effects on accuracy and computational cost revealing that high-order approximation yields accurate modelling results for very coarse meshes but is accompanied by high computational cost. The presented numerical experiments give evidence that 2nd and 3rd degree polynomials in combination with moderately discretized meshes provide better trade-offs in terms of computational resources and accuracy than lowest and higher order spectral element methods. To our knowledge, our final example that includes pronounced surface topography and two geometrically complicated conductive anomalies represents the first successful attempt at using 2nd order hexahedral elements supporting curved edges and non-planar faces in controlled-source EM geophysics.

Performance Assessment of Tesla Expander Using 3D Numerical Simulation

Abstract Bladeless or Tesla turbines consist of several flat parallel disks mounted on a shaft with a narrow gap between them. The analytical solution of Navier-Stokes equations for the flow between disks has been extensively studied in the past. However, there is a significant impact of the stator exit-flow conditions on the performance and flow behavior inside the rotor of the Tesla turbine. There has been limited research on flow characterization and performance evaluation of stator-rotor interaction of the Tesla expander using 3D numerical simulation. The challenge arises due to a very high aspect ratio of the Tesla rotor (diameter to gap ratio > 1000). 3D numerical modeling with a hexahedral mesh of the nozzle/stator with the commercial software is presented. The simulation is performed for a wide range of inlet pressures and rotational speeds. This work focuses on the stator performance, the stator-rotor interaction, the rotor entry losses due to disk tip, the rotor tip velocity ratio and the degree of reaction on the performance of the Tesla expander.The peak efficiency of 58% is predicted for 3 bar inlet pressure and a rotational speed of 30000 rpm for a 3 kW machine with air as a working fluid. The 3D numerical analysis provides insights on flow characterization, mainly stator-rotor interaction and flow between disks at different mass flows. Numerical results are also compared with experimented test results performed on a 100-W and a 3-kW air expander.

Robust Quantization for Polycube Maps

An important part of recent advances in hexahedral meshing focuses on the deformation of a domain into a polycube; the polycube deformed by the inverse map fills the domain with a hexahedral mesh. These methods are appreciated because they generate highly regular meshes. In this paper we address a robustness issue that systematically occurs when a coarse mesh is desired: algorithms produce deformations that are not one-to-one, leading to collapse of large portions of the model when trying to apply the (undefined) inverse map. The origin of the problem is that the deformation requires to perform a mixed integer optimization, where the difficulty to enforce the integer constraints is directly tied to the expected coarseness. Our solution is to introduce sanity constraints preventing the loss of bijectivity due to the integer constraints.

An optimally convergent smooth blended B-spline construction for semi-structured quadrilateral and hexahedral meshes

Easy to construct and optimally convergent generalisations of B-splines to unstructured meshes are essential for the application of isogeometric analysis to domains with non-trivial topologies. Nonetheless, especially for hexahedral meshes, the construction of smooth and optimally convergent isogeometric analysis basis functions is still an open question. We introduce a simple partition of unity construction that yields smooth blended B-splines, referred to as SB-splines, on semi-structured quadrilateral and hexahedral meshes, i.e. on mostly structured meshes with sufficiently separated unstructured regions. To this end, we first define the mixed smoothness B-splines that are C0 continuous in the unstructured regions of the mesh but have higher smoothness everywhere else. Subsequently, the SB-splines are obtained by smoothly blending in the physical space the mixed smoothness B-splines with Bernstein bases of equal degree. One of the key novelties of our approach is that the required smooth weight functions are assembled from the available smooth B-splines on the unstructured mesh. The SB-splines are globally smooth, non-negative, have no breakpoints within the elements and reduce to conventional B-splines away from the unstructured regions of the mesh. Although we consider only quadratic mixed smoothness B-splines in this paper, the construction generalises to arbitrary degrees. We demonstrate the excellent performance of SB-splines studying Poisson and biharmonic problems on semi-structured quadrilateral and hexahedral meshes, and numerically establishing their optimal convergence in one and two dimensions.

Two-stage fourth-order subcell finite volume method on hexahedral meshes for compressible flows

As an extension of the two-stage fourth-order subcell finite volume (SCFV) method that we developed for two-dimensional compressible flows [C. Zhang et al., “Two-stage fourth-order gas kinetic solver based compact subcell finite volume method for compressible flows on triangular meshes,” Phys. Fluids 33, 126108 (2021)], this study continues our efforts toward three-dimensional (3D) simulations on hexahedral meshes. The two components of subcell divisions and two-stage fourth-order time stepping are utilized to improve efficiency and enhance compactness, which are crucial for 3D simulations. In particular, the current method subdivides each cell into a set of subcells or control volumes (CVs) to increase the degrees of freedom for high-order reconstruction, which involves only face-neighboring cells. For traditional finite volume (FV) methods, high-order reconstruction is performed on each CV individually. In contrast, the reconstruction of SCFV is shared by a set of CVs belonging to the same cell, which can be much more efficient and compact. Moreover, the SCFV framework is combined with the high-order flux evolution by adopting a robust and time-dependent gas-kinetic flux solver and an efficient two-stage fourth-order temporal discretization. The multi-stage Runge–Kutta (RK) method is thus avoided. The coupling of inviscid and viscous terms in the gas-kinetic flux enables us to directly simulate viscous flows. To capture shocks, a limiting procedure by hierarchical reconstruction is developed for effectively preserving the accuracy in smooth flow regions and suppressing numerical oscillations near flow discontinuities. Several benchmark cases are tested. The high-order accuracy and efficiency of this scheme are validated and compared to the k-exact FV method and the traditional Riemann solver combined with a multi-stage RK method. In particular, the simulation of the supersonic Taylor–Green vortex problem demonstrates the good performance of this scheme in compressible turbulence with the presence of shock waves.

Hex Me If You Can.

HexMe consists of 189 tetrahedral meshes with tagged features and a workflow to generate them. The primary purpose of HexMe meshes is to enable consistent and practically meaningful evaluation of hexahedral meshing algorithms and related techniques, specifically regarding the correct meshing of specified feature points, curves, and surfaces. The tetrahedral meshes have been generated with Gmsh, starting from 63 computer-aided design (CAD) models from various databases. To highlight and label the diverse and challenging aspects of hexahedral mesh generation, the CAD models are classified into three categories: simple, nasty, and industrial. For each CAD model, we provide three kinds of tetrahedral meshes (uniform, curvature-adapted, and box-embedded). The mesh generation pipeline is defined with the help of Snakemake, a modern workflow management system, which allows us to specify a fully automated, extensible, and sustainable workflow. It is possible to download the whole dataset or select individual meshes by browsing the online catalog. The HexMe dataset is built with evolution in mind and prepared for future developments. A public GitHub repository hosts the HexMe workflow, where external contributions and future releases are possible and encouraged. We demonstrate the value of HexMe by exploring the robustness limitations of state-of-the-art frame-field-based hexahedral meshing algorithm. Only for 19 of 189 tagged tetrahedral inputs all feature entities are meshed correctly, while the average success rates are 70.9% / 48.5% / 34.6% for feature points/curves/surfaces.

Turbulence dissipation of leakage flow in supercritical CO2 labyrinth seals

Supercritical CO2 (S-CO2) leakage through seals significantly reduces the efficiency of turbomachinery. Improving the labyrinth seal structure is potentially the key to the reduction of the leakage flow rate, but its application is greatly limited by the uncertainties of supercritical CO2 turbulent flow inside the turbomachines with irregular chambers. In this work, we numerically investigated the S-CO2 flow field and dissipation rate of turbulence kinetic energy in stepped labyrinth seals. The RANS method and hexahedral structural mesh were employed. The look-up table containing the real gas properties of carbon dioxide was created and imported into the flow solver. The developed numerical method was validated by experiment results and proved its applicability. We have discovered that the fully developed rotating vortices inside each chamber of the turbomachine significantly increase the turbulent dissipation rate and decrease the fluid carried energy, thus reducing the leakage flow rate. With the seal clearance increasing form 0.5 mm–1.3 mm at pressure ratio π = 0.7, the vortices development is gradually limited, causing the decrease of turbulent dissipation rate. The leakage rate is found to be heavily dependent on the distance between the seal tip and step. The increase in this distance from 2 mm to 6 mm results in greater space for the continued development of the vortices within the first chamber, thus the enhancement of the turbulent dissipation rate of fluid. Therefore, we defined a geometry coefficient, (δ-b)/s, and analyzed its effects on turbulent dissipation rate and leakage flow rate. With this geometry coefficient increases from 2.8 to 11.2 at π = 0.7, the maximum turbulent dissipation rate increases from 7.09 × 107 to 1.23 × 108 and the leakage flow rate decreases from 3.98 × 10−2 kg/s to 1.62 × 10−2 kg/s. An improved leakage model characterizing seal geometry, gas properties and compressibility effects was proposed.

Volume parametrization quantization for hexahedral meshing

Developments in the field of parametrization-based quad mesh generation on surfaces have been impactful over the past decade. In this context, an important advance has been the replacement of error-prone rounding in the generation of integer-grid maps, by robust quantization methods. In parallel, parametrization-based hex mesh generation for volumes has been advanced. In this volumetric context, however, the state-of-the-art still relies on fragile rounding, not rarely producing defective meshes, especially when targeting a coarse mesh resolution. We present a method to robustly quantize volume parametrizations, i.e., to determine guaranteed valid choices of integers for 3D integer-grid maps. Inspired by the 2D case, we base our construction on a non-conforming cell decomposition of the volume, a 3D analogue of a T-mesh. In particular, we leverage the motorcycle complex, a recent generalization of the motorcycle graph, for this purpose. Integer values are expressed in a differential manner on the edges of this complex, enabling the efficient formulation of the conditions required to strictly prevent forcing the map into degeneration. Applying our method in the context of hexahedral meshing, we demonstrate that hexahedral meshes can be generated with significantly improved flexibility.

Distortion analysis of generatively designed hinge bracket using meso-scaled thermomechanical simulation with experimental validation

ABSTRACT The accuracy of meso-scaled thermomechanical method (TMM) in analysing distortion of hinge bracket additively manufactured using selective laser melting (SLM) is investigated with SS316L as material and optimised design using Generative Design (GD) approach in which loads, boundaries, and constraints are considered as parametric inputs and stress goal as output. Prior to 3D printing, process simulation for predicting distortion was conducted including a geometrical model with hexahedral mesh type, temperature dependent material and flow curve referred from specialised software. To reduce computational time, a lumping approach with volume fraction was implemented considering heat flux parameters. For validation purposes, a series of experiments was accomplished using SLM, manual support structure removal, and surface finishing process by sandblasting. Furthermore, the finished bracket was measured using an optical scanner and compared with the simulation result. In conclusion, TMM can predict the distortion accurately with percentage point-by-point and mean error of less than 3% and 1.5%, respectively.

Modeling of Preload Bolted Flange Connection Structure for Loosening Analysis and Detection

The specified finite element model is proposed for preload bolted flange connection structure widely used in aerospace and rocket design. A fine hexahedral mesh model of the bolt is used to predict the dynamic response of the structure accurately. The tightening process, which is ignored in the traditional I-shaped simplified model of bolted flange connection structure, can be simulated well based on the proposed model. After the vibration analysis and stress analysis of the bolted flange connection structure under impact load, it is found that the change of contact state of the flange surface results in a larger sticking contact area. And the reduction of the contact area at the thread causes slippage when the bolt is loose. As bolt loosening leads to changes in the time and frequency domain of response, a new loosening detection method for the preload bolted flange connection is provided. The index for identifying the loosening is designed using empirical mode decomposition and discrete integral in the high-frequency domain. The experiment of the preload bolted flange connection structure under impact load shows the efficiency of the proposed method which can identify loosening based on acceleration signal quickly and nondestructively.

Numerical Investigation of 3D Flow Properties around Finite Emergent Vegetation by Using the Two-Phase Volume of Fluid (VOF) Modeling Technique

This study predicts how the Free Surface Level (FSL) variations around finite length vegetation affect flow structure by using a numerical simulation. The volume of fluid (VOF) technique with the Reynolds stress model (RSM) was used for the simulation. Multizone Hexahedral meshing was adopted to accurately track the free surface level with minimum numerical diffusion at the water–air interface. After the validation, finite length emergent vegetation patches were selected based on the aspect ratio (AR = vegetation width-length ratio) under constant subcritical flow conditions for an inland tsunami flow. The results showed that the generation of large vortices was predominated in wider vegetation patches (AR > 1) due to the increase and decrease in the FSL at the front and back of the vegetation compared to longer vegetation patches (AR ≤ 1), as this offered more resistance against the approaching flow. The wider vegetation patches (AR > 1) are favorable in terms of generating a large area of low velocity compared to the longer vegetation patch (AR < 1) directly downstream of the vegetation patch. On the other hand, it has a negative impact on the adjacent downstream gap region, where a 14.3–34.9% increase in velocity was observed. The longer vegetation patches (AR < 1) generate optimal conditions within the vegetation region due to great velocity reduction. Moreover, in all the AR vegetation cases, the water turbulent intensity was maximum in the vegetation region compared to the adjacent gap region and air turbulent intensity above the FSL, suggesting strong air entrainment over this region. The results of this study are important in constructing vegetation layouts based on the AR of the vegetation for tsunami mitigation.

The 3D Motorcycle Complex for Structured Volume Decomposition

AbstractThe so‐called motorcycle graph has been employed in recent years for various purposes in the context of structured and aligned block decomposition of 2D shapes and 2‐manifold surfaces. Applications are in the fields of surface parametrization, spline space construction, semi‐structured quad mesh generation, or geometry data compression. We describe a generalization of this motorcycle graph concept to the three‐dimensional volumetric setting. Through careful extensions aware of topological intricacies of this higher‐dimensional setting, we are able to guarantee important block decomposition properties also in this case. We describe algorithms for the construction of this 3D motorcycle complex on the basis of either hexahedral meshes or seamless volumetric parametrizations. Its utility is illustrated on examples in hexahedral mesh generation and volumetric T‐spline construction.

CFD simulation of shockwave-boundary layer interaction induced oscillation in NACA SC2-0714 transonic airfoil

Abstract To develop an advanced way of designing transonic airfoils for industry, a reliable and user-friendly mesh generator and a robust CFD solver are necessary. Especially, the prediction of unsteady shock buffet phenomenon is always a focus for the CFD simulation of transonic airfoils. In this study, BOXERmesh (an automatic mesh generator) and NEWT (a robust CFD solver), which are developed by CFS (Cambridge Flow Solutions) in collaboration with MHI (Mitsubishi Heavy Industries), are used to perform the CFD simulation of NACA SC2-0714 transonic airfoil. CFD simulation is conducted at two different attack angles with Mach number as 0.74 and Reynold number as 1.5×107 (non-buffet: α=2°; shock buffet: α=3°). A hexahedral dominant mesh is generated by BOXERmesh with the cell number as 5.52 million. Both unsteady RANS (URANS) and LES are performed using the CFD solver NEWT. Specifically, the governing equation is discretized by central differencing scheme with 2nd order accuracy in space by applying Swanson and Turkel type artificial viscosity, and the Adams-Bashford time integration with the dual-time stepping method is applied for temporal discretization in the density-based solver. Results show CFD simulation could reproduce the time averaged chordwise distribution of pressure coefficient at the two conditions. Both URANS and LES successfully capture the unsteady shock buffet phenomenon when increasing attack angle from 2° to 3°. However, the calculated peak oscillation location and the shock buffet frequency are different between URANS and LES. Applying the same mesh resolution, URANS performances better than LES, with the deviation of the shock buffet frequency less than 6% (Exp.: 69 Hz; URANS: 73 Hz). The reason is considered as the wall-normal mesh refinement near the airfoil surface (y+∼66) being not enough for LES to accurately resolve the turbulence scale and capture the boundary layer separation behavior. On the other hand, URANS is thought to be enough to reproduce the periodic moving of the onset of boundary separation and to predict the main characteristics of the shock buffet phenomenon.

Simulation of primary current distribution in Tesla-type pulse generators.

In a Tesla-type pulse generator, self-inductance of the primary coil is a crucial parameter to determine the final oscillating condition. However, the accurate value of this inductance might be changed due to the uneven primary current distribution caused by practical configuration of the primary side. Consequently, in order to precisely design the transformer, it is helpful to evaluate the primary inductance based on electromagnetic simulation instead of conventional approximate calculation. In this paper, a simulation model based on the finite integration technique is established to solve the uneven primary current problem. A primary coil with multiple contacting points is designed, and hexahedral mesh generation of the coil is also discussed. Hence, a series of verification tests using different primary structures are performed to support the results of simulation. Both results of the simulation model and the verification test presented that the variation of the primary inductance will affect the performance of the generator, and the number of contacting points is the main cause to determine the maximum current density of the coil.

Geometric 3-D inversion of airborne time-domain electromagnetic data with applications to kimberlite pipes prospecting in a complex medium

We consider an approach to solving 3-D inverse problems of airborne time-domain electromagnetic (TD-EM) survey in complex geoelectrical conditions, when the responses of target objects in the measured signal are relatively small and mixed with responses of rugged topography, 3-D inhomogeneities in overburden layers, and other interfering 3-D objects. For parameterization of the geoelectrical model of the geological medium, global and local structures are used. A block structure is a grid with large cells whose boundaries can move during the inversion process. Block structures are characterized by two types of parameters: geometric and physical. Geometric parameters include the coordinates of the boundaries of blocks in block structures, which are used for recovering local bodies or 3-D inhomogeneities within the layers, and physical parameters are the conductivities inside the blocks. In addition, the geometric parameters include displacements of control points, which are used for describing curved surfaces. The functional employed for inversion includes regularizing terms that allow controlling the self-crossing of geometric boundaries and extension of physical parameters beyond the boundaries of the allowed values range. Regularization coefficients are calculated adaptively at each iteration of the nonlinear 3-D inversion. In order to separate the responses of 3-D inhomogeneities located under the overburdens from those of 3-D inhomogeneities inside the overburdens, we propose to carry out 3-D inversion in two stages. At the first stage, over a shortened time range, we recover the conductivity distribution using global block structures and the shape of the boundaries of the overburden layers using control points. At the second stage, the entire time range is used. In those places where the significant residuals remained at late times, local block structures are employed to recover local objects (including target ones) under the overburden layers. This enables us to define quite accurately the position in plan, top border depth, and type of 3-D inhomogeneities, which are located under the overburdens, at the second stage of geometric inversion. To calculate 3-D time-domain electromagnetic fields, we use the vector finite element method implemented on optimized non-conforming hexahedral meshes with the possibility of adjoining the faces of several finite elements to the face of one finite element. The workability of the proposed approaches is demonstrated on synthetic airborne TD-EM data as well as on experimental airborne data, which are obtained as a result of methodical work over the kimberlite pipe deposit. The proposed geoelectrical model parameterization and the approach to 3-D inversion allow the discovery of relatively small 3-D target objects, when many non-target objects, including 3-D inhomogeneities in the overburdens, give several times greater responses in the measured signals.

L0-Regularization based Material Design for Hexahedral Mesh Models

Computer-Aided Design and Applications is an international journal on the applications of CAD and CAM. It publishes papers in the general domain of CAD plus in emerging fields like bio-CAD, nano-CAD, soft-CAD, garment-CAD, PLM, PDM, CAD data mining, CAD and the internet, CAD education, genetic algorithms and CAD engines. The journal is aimed at all developers and users of CAD technology to ptovide CAD solutions for various stages of design and manufacturing. The journal publishes all about Computer-Aided Design and Computer-Aided technologies.

A Large-Scale Comparison of Tetrahedral and Hexahedral Elements for Solving Elliptic PDEs with the Finite Element Method

The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs. The goal of this benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance. As a specific application of our geometry and benchmark dataset, we explore the question of relative advantages of unstructured (triangular/ tetrahedral) and structured (quadrilateral/hexahedral) discretizations. We observe that for Lagrange-type elements, while linear tetrahedral elements perform poorly, quadratic tetrahedral elements perform equally well or outperform hexahedral elements for our set of problems and currently available mesh generation algorithms. This observation suggests that for common problems in structural analysis, thermal analysis, and low Reynolds number flows, high-quality results can be obtained with unstructured tetrahedral meshes, which can be created robustly and automatically. We release the description of the benchmark problems, meshes, and reference implementation of our testing infrastructure to enable statistically significant comparisons between different FE methods, which we hope will be helpful in the development of new meshing and FEA techniques.

Enhanced anisotropic block-based adaptive mesh refinement for three-dimensional inviscid and viscous compressible flows

A parallel anisotropic block-based adaptive mesh refinement (AMR) algorithm is proposed for the prediction of physically complex flow problems having disparate spatial and temporal scales and exhibiting highly anisotropic features on three-dimensional multi-block body-fitted hexahedral meshes with non-uniform grid blocks. The proposed AMR scheme makes use of a binary tree hierarchical data structure to permit anisotropic refinement of grid blocks in a preferred coordinate direction as dictated by appropriately selected physics-based refinement criteria. The anisotropic coarsening of the grid blocks in a manner that is independent of the refinement history allows the mesh to rapidly re-adapt for evolving unsteady flow applications. Moreover, the proposed anisotropic AMR scheme adopts a non-uniform representation of the cells within each block by directly using the neighboring cells as the ghost cells, even at a grid resolution change. This affords a number of computational advantages especially related to evaluating the solution in the ghost cells as well as to ensuring flux conservation at block interfaces. A modified upwind-based finite-volume spatial discretization scheme is applied in conjunction with the AMR scheme to the solution of Euler and Navier-Stokes equations for inviscid and viscous compressible gaseous flows. Steady-state and time-varying flow problems are considered on anisotropic adapted meshes. The potential flexibility and efficiency of the proposed enhanced anisotropic AMR scheme are demonstrated for the simulation of a number of representative flows of varying complexity.

Intrinsic mixed-integer polycubes for hexahedral meshing

Polycube mapping is an attractive approach for the generation of all-hexahedral meshes with a fully regular interior, i.e. free of internal singular edges or vertices. It is based on determining a low distortion map between the input model and a polycube domain, which then pulls back the regular voxel grid to form a hexahedral mesh for the model. Automatically finding an appropriate polycube domain for a given model, however, is a challenging problem. Existing algorithms are either very sensitive to the embedding and orientation of the input model, restricted to only subclasses of possible domains, or depend crucially on some initialization because they rely on a non-convex optimization formulation. This can easily lead to unsatisfactory and unnecessary corners and edges in the polycube structure. We present a novel approach to the problem of finding high-quality polycube domains. It is based on an entirely intrinsic formulation as a mixed integer optimization problem, which can be tackled by solving a series of simple convex problems, each of which can be solved to the global optimum. Experiments demonstrate that our method avoids many of the undesired corners and surface irregularities common to many previous methods.