Adaptive Mesh Algorithm Research Articles

Development of multilevel mesh adaptivity for global variance reduction in Monte Carlo code cosRMC

The mesh-based weight window method is a widely used global variance reduction technique for Monte Carlo particle transport calculation. In order to meet the fine voxel division required for high-quality weight window distribution, the uniform structured mesh division will lead to large memory footprint pressure. This work focused on the research of the multilevel adaptive mesh algorithm, using a recursive algorithm to adjust the voxel resolution adaptively according to the material of geometry. Then the adaptive mesh algorithm was applied to the weight window generator based on the response matrix method by establishing the neighbor relationship of adaptive mesh. And an optimization method for memory allocation of the response matrix solver was proposed, effectively reducing the memory footprint of the response matrix solver in parallel computing. In the calculation of the CFETR model, the calculation efficiency under the weight window based on adaptive mesh was increased by 53.3 % compared with the weight window based on uniform mesh, and the proportion of voxels with a statistical error less than 10 % reached 93.33 %, which verified the effectiveness of the multilevel adaptive mesh algorithm.

An R-adaptive algorithm based on self-organizing maps for solving incompressible flows with high-order discontinuous Galerkin methods

Mesh quality is critical for the numerical accuracy of CFD (Computational Fluid Dynamics). Although various techniques have been developed to improve mesh applicability to complex flows, r-adaptive methods have received far too little attention. This paper introduces an r-adaptive algorithm based on the self-organizing maps (SOM) of Kohonen and applies it to unsteady CFD applications using the Discontinuous Galerkin (DG) method. Inspired by the properties of the DG method, the numerical discontinuity over the element interface is quantified as an adaptation indicator. The method requires only one adaptation, followed by solution projection onto the new mesh to save computational costs in unsteady cases. A significant advantage of this method is its higher efficiency without solving complex equations during the adaptation. The performance of the developed mesh adaptation algorithm is tested on the steady laminar viscous flow past a circular cylinder at Re=40 and the unsteady laminar viscous flow past a circular cylinder at Re=100 and two circular cylinders in a side-by-side arrangement at Re=200. Significant improvements in flow contours and coefficients are obtained after adaptation.

Metric-based anisotropic mesh adaptation for viscoelastic flows

The computation of flows of viscoelastic fluids is expensive compared to standard fluids. Besides degrees-of-freedom for velocity and pressure, the viscoelastic stresses introduce an additional unknown to the system. While adaptive meshing techniques are commonly used for simulations of standard fluids, their application is seldom explored in the context of viscoelastic fluids. In this work, we apply an anisotropic mesh adaptation algorithm to solve the viscoelastic flow problem. Our flow solver is based on a logarithmic reformulation of the viscoelastic constitutive laws, which greatly reduces the stringent stability requirements on the mesh size and allows adaptive meshing in this context. For discretization, we use a stabilized finite element method. We present numerical results for a flow past a cylinder. The adaptive method produces near mesh-independent results up to Weissenberg number Wi=0.7. Our results indicate that with an anisotropic refinement strategy, fewer mesh elements are needed to maintain the same error level as with an isotropic refinement strategy. In a stick-slip transition flow, we demonstrate the capability of the adaptive method to produce optimal meshes even in the presence of a singularity in the solution.

A parameter-free LES model for anisotropic mesh adaptivity

Balancing accuracy and computational cost is a challenge in the modelling of turbulent flows. A widely used method for turbulence modelling is large–eddy simulation (LES). LES allows one to describe large scale flow features at a reasonable computational cost compared to the more accurate direct numerical simulation (DNS), making it a popular choice for engineering applications. One strategy to balance accuracy and cost with LES is through the use of mesh adaptivity, which allows the degrees of freedom in a problem to be reduced by changing spatial discretisation. However, mesh adaptivity can affect accuracy when using the standard Smagorinsky LES model with an implicit filter, considering that the parameter Cs is highly dependent on the filter width, which depends on mesh resolution. This work is aimed to develop an LES model that does not require any user–defined parameters and is suitable for mesh adaptivity with implicit filter. In this study we introduce a parameter–free LES model incorporating an anisotropic eddy–viscosity formulation combined with anisotropic mesh adaptivity. In our model, the parameter Cs in the eddy–viscosity formulation of the Smagorinsky model, is replaced by a function that evaluates the relative location of turbulence fluctuations in each element with respect to the turbulence spectrum inertial range. The anisotropic formulation of the eddy–viscosity allows for the application of an appropriate filter width in different directions, improving accuracy. Additionally, the mesh adaptivity algorithm assesses the local turbulence fluctuations via local Reynolds number and vortex identification criteria. This assessment leads to the refinement of regions with higher turbulence fluctuations down to the smallest scale limit in the inertial range in the corresponding direction, and also leads to the coarsening of regions without turbulence fluctuation up to largest scale limit in the inertial range. This method is tested using a flow past a sphere test case. The results are compared both qualitatively and quantitatively to results obtained with the standard Smagorinsky model, and demonstrate the better performance of our method with lower computational cost. This allows us to simulate large Reynolds number cases and compare our quantitative results to experimental results found in the literature, emphasising that our method produces good results at reasonable computational cost.

In-Timestep Remeshing for Contacting Elastodynamics

We propose In-Timestep Remeshing, a fully coupled, adaptive meshing algorithm for contacting elastodynamics where remeshing steps are tightly integrated, implicitly, within the timestep solve. Our algorithm refines and coarsens the domain automatically by measuring physical energy changes within each ongoing timestep solve. This provides consistent, degree-of-freedom-efficient, productive remeshing that, by construction, is physics-aware and so avoids the errors, over-refinements, artifacts, per-example hand-tuning, and instabilities commonly encountered when remeshing with timestepping methods. Our in-timestep computation then ensures that each simulation step's output is both a converged stable solution on the updated mesh and a temporally consistent trajectory with respect to the model and solution of the last timestep. At the same time, the output is guaranteed safe (intersection- and inversion-free) across all operations. We demonstrate applications across a wide range of extreme stress tests with challenging contacts, sharp geometries, extreme compressions, large timesteps, and wide material stiffness ranges - all scenarios well-appreciated to challenge existing remeshing methods.

Goal-Oriented Mesh Adaptivity of Three-Dimensional Neutron Transport Calculation Using Weighted Difference Scheme and Dual-Weighted Residual Error Indicators

Maintaining a reasonable balance between computational accuracy and overhead is important for neutron transport simulations of engineering problems. This paper presents a goal-oriented mesh adaptive algorithm applied to the multigroup discrete ordinates equation for fixed source and criticality problems. The dual-weighted residual (DWR) approach estimates numerical solution errors and drives local mesh refinement for specific targets, such as detector response, integral flux, and multiplication factor. We employ a reconstruction method to evaluate the spatial residuals of the fluxes obtained by the weighted difference scheme. To improve the performance of adaptive algorithms, new estimation models are proposed for adjoint fluxes needed by the DWR theory, including a regional goal model for fixed source problems and an inconsistent fission source model for k-eigenvalue problems. Additionally, we analyze the impact of the truncation of flux reconstruction and isotropic approximation of adjoint fluxes on grid error indicators and adaptive calculations. Numerical results demonstrate that for the quantities of interest, our adaptive approach saves more than 70% of computational effort and run time when obtaining a level of high accuracy comparable to that of uniform fine grids.

A fast dynamic smooth adaptive meshing scheme with applications to compressible flow

We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on a fast solution strategy of the time-dependent Monge-Ampère (MA) equation, det⁡∇ψ(x,t)=G∘ψ(x,t). The novelty of our approach is a new so-called perturbation formulation of MA, which constructs the solution map ψ via composition of a sequence of near-identity deformations of a reference mesh. Then, we formulate a new version of the deformation method [21] that results in a simple, fast, and high-order accurate numerical scheme and a dynamic SAM algorithm that is of optimal complexity when applied to time-dependent mesh generation for solutions to hyperbolic systems such as the Euler equations of gas dynamics. We perform a series of challenging 2D and 3D mesh generation experiments for grids with large deformations, and demonstrate that SAM is able to produce smooth meshes comparable to state-of-the-art solvers [22,18], while running approximately 200 times faster. The SAM algorithm is then coupled to a simple Arbitrary Lagrangian Eulerian (ALE) scheme for 2D gas dynamics. Specifically, we implement the C-method [64,65] and develop a new ALE interface tracking algorithm for contact discontinuities. We perform numerical experiments for both the Noh implosion problem as well as a classical Rayleigh-Taylor instability problem. Results confirm that low-resolution simulations using our SAM-ALE algorithm compare favorably with high-resolution uniform mesh runs.

An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control

We propose an efficient mesh adaptive method for the numerical solution of time-dependent partial differential equations considered in the fixed space-time cylinder varOmega times (0,T). We employ the space-time discontinuous Galerkin method which enables us to use different meshes at different time levels in a natural way. The mesh adaptive algorithm is based on control of the interpolation error in the L^infty (0,T; L^q(varOmega ))-norm. The goal is to construct a sequence of conforming triangular meshes in such a way that the interpolation error bound is under a given tolerance and the number of degrees of freedom is minimal. The resulting grids consist of anisotropic mesh elements with varying polynomial approximation degrees with respect to space. We present a theoretical framework of this approach as well as several numerical examples demonstrating the accuracy, efficiency, and applicability of the method.

Pressure-induced damage monitoring in prestressed concrete of nuclear containment wall segments using acoustic emission technique – Application to VeRCoRs containment building

This paper reports benchmark findings of an experimental study of pressure-induced damage monitoring in a nuclear containment building (NCB) reproducing realistic conditions of internal pressure increase accidents. The leak-tightness of NCBs is assessed every 10 years during integrated leak-rate tests (IRLT). For double-wall containments, which have no metallic liners, the leak-tightness is strongly influenced by the degree of cracking of concrete and opening of the cracks. This paper is focused on assessing the effectiveness of the Acoustic Emission (AE) technique to evaluate the damage evolution of a reinforced concrete containment wall under pressure loading test. Piezoelectric accelerometers were mounted on the internal containment wall of the VeRCoRs mockup, which constitutes the containment building of a Nuclear Power Plant in a 1:3 scale. The Akaike criterion (AIC) as an AE hit picking method and the adaptive meshing algorithm (AMA) as an AE events localization algorithm have been applied for damage and cracking monitoring. A benchmark analysis based on the distribution of AE events and energy is presented for the detection of damages and the monitoring of crack propagation in correlation with the known locations of main cracks. The potential and limitations of the AE technique for in situ damage sources estimation are discussed upon two experimental campaigns (2017 and 2019), and the main conclusions of the benchmark survey are given. The results show that the AE technique is adequate for damage evaluation in large-scale concrete structures. It provides important information about the integrity of the structure and the assessment of damage evolution with time.

Declarative Specification for Unstructured Mesh Editing Algorithms

We introduce a novel approach to describe mesh generation, mesh adaptation, and geometric modeling algorithms relying on changing mesh connectivity using a high-level abstraction. The main motivation is to enable easy customization and development of these algorithms via a declarative specification consisting of a set of per-element invariants, operation scheduling, and attribute transfer for each editing operation. We demonstrate that widely used algorithms editing surfaces and volumes can be compactly expressed with our abstraction, and their implementation within our framework is simple, automatically parallelizable on shared-memory architectures, and with guaranteed satisfaction of the prescribed invariants. These algorithms are readable and easy to customize for specific use cases. We introduce a software library implementing this abstraction and providing automatic shared-memory parallelization.

Multilevel mesh adaptivity for discrete ordinates transport calculation with spatial-moment-ratio indicators

It is difficult to control discretization errors and reduce computational cost at the same time for multi-scale neutron transport problems, and the adaptive mesh refinement technique is one of the powerful and effective methods for high-resolution transport calculation. We propose a multilevel mesh adaptivity algorithm and develop a discrete ordinates calculation framework on 3-D Cartesian meshes. Data management and transport sweep are optimized based on the multilevel pyramid data structure containing pointer-type and array-type variables. A new spatial-moment-ratio error indicator is derived to measure the leading term of distribution functions and to drive the local mesh refinement. The numerical properties of spatial moment factors are better than the normalized gradient of angular flux. Compared with uniform refinement, our adaptivity algorithm reaches the same accuracy level with a computational cost saving of 60%-80% for heterogeneous problems.

A novel dynamic adaptive unstructured mesh algorithm for simulating multi‐object relative motion in incompressible fluid

AbstractA novel dynamic adaptive unstructured mesh (DAUM) algorithm is proposed to solve incompressible multi‐object relative motion (MORM). The DAUM algorithm, consisting of exponential function deformation, adaptive edge swapping, and area Laplace smoothing, can greatly improve dynamic mesh robustness and perfectly overcome mesh skewness. The core of DAUM is the adaptive edge swapping inspired by Delaunay triangulation, which is distinguished from traditional edge swapping. The adaptive edge swapping can fully consider the relationship of neighbor elements only using Delaunay triangulation. Meanwhile, the implementation and reliability of adaptive edge swapping are better than the traditional edge swapping method due to eliminating the interference of the non‐convex polygon, so more code remedies can be avoided. Using the DAUM, none of the vertices is inserted or deleted so that the manipulation of the dynamic mesh is easily implemented and maintains computational efficiency in the process of mesh motion. Three representative geometries are used to assess the performance of the DAUM in MORM. To systematically analyze the advantages of DAUM, two relatively moving cylinders have been numerically investigated in incompressible flow. The inline force and lift force profiles on two cylinders are obtained and analyzed by using the flow field information. Three interaction stages are divided based on the parameter G and the interactional intensity of two inner anticlockwise vortices is considered as the division criteria. At the running process of the DAUM algorithm, the dynamic mesh quality is well controlled and remains in the high‐quality range based on the aspect ratio (AR) criterion. The results indicate that the proposed DAUM algorithm can properly solve the difficulties caused by MORM, especially for period oscillation motion.

Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations

In this paper, we present a mesh adaptation algorithm for the unsteady compressible Navier-Stokes equations under the framework of local discontinuous Galerkin methods coupled with implicit-explicit Runge-Kutta or spectral deferred correction time discretization methods. In both of the two high order semi-implicit time integration methods, the convective flux is treated explicitly and the viscous and heat fluxes are treated implicitly. The remarkable benefits of such semi-implicit temporal discretizations are that they can not only overcome the stringent time step restriction compared with time explicit methods, but also avoid the construction of the large Jacobian matrix as is done for fully implicit methods, thus are relatively easy to implement. To save computing time as well as capture the flow structures of interest accurately, a local mesh refinement (h-adaptive) technique, in which we present detailed criteria for selecting candidate elements and complete strategies to refine and coarsen them, is also applied for the Navier-Stokes equations. Numerical experiments are provided to illustrate the high order accuracy, efficiency and capabilities of the semi-implicit schemes in combination with adaptive local discontinuous Galerkin methods for the Navier-Stokes equations.

Formulating delamination-fretting wear failure predictive equation in HAp coated hip arthroplasty using multiple linear regression model

Present paper addresses the formulation of delamination-fretting wear failure predictive equation in HAp-Ti-6Al-4V interface of hip arthroplasty femoral stem component using multiple linear regression model. A finite element computational model utilising adaptive meshing algorithm via ABAQUS/Standard user subroutine UMESHMOTION is developed. The developed FE model is employed to examine effect of different HAp-Ti-6Al-4V interface mechanical and tribological properties on delamination-fretting wear behaviour. The FE result is utilised to formulate predictive equations for different stress ratio conditions using multiple linear regression analysis. Delamination-fretting wear predictive equations are successfully formulated with significant goodness of fit and reliability as a fast failure prediction tool in HAp coated hip arthroplasty. The robustness of predictive equations is validated as good agreement is noted with actual delamination-fretting wear results. The influence of different mechanical and tribological properties such as delamination length, normal loading, fatigue loading, bone elastic modulus and cycle number under different stress ratio on delamination-fretting wear failure is analysed to formulate failure predictive equations. The formulated predictive equation can serve as a fast delamination-fretting wear failure prediction tool in hip arthroplasty femoral stem component. Limited attempt is done to explore the potential of utilizing multiple linear regression model to predict failures in hip arthroplasty. Thus, present study attempt to formulate delamination-fretting wear failure predictive equation in HAp -Ti-6Al-4V interface of hip arthroplasty femoral stem component using multiple linear regression model.

Design of cellular materials for multiscale topology optimization: application to patient-specific orthopedic devices

A flexible problem-specific multiscale topology optimization is introduced to associate different areas of the design domain with diverse microstructures extracted from a dictionary of optimized unit cells. The generation of the dictionary is carried out by exploiting micro-SIMP with AnisoTropic mesh adaptivitY (microSIMPATY) algorithm, which promotes the design of free-form layouts. The proposed methodology is particularized in a proof-of-concept setting for the design of orthotic devices for the treatment of foot diseases. Different patient-specific settings drive the prototyping of customized insoles, which are numerically verified and successively validated in terms of mechanical performances and manufacturability.

An adaptive finite element method for high-frequency scattering problems with smoothly varying coefficients

We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency ω, but is especially efficient for high-frequency problems. It is based on a time-domain approach and consists of three steps: i) computation of a suitable incoming plane wavelet with compact support in the propagation direction; ii) solving a scattering problem in the time domain for the incoming plane wavelet; iii) reconstruction of the time-harmonic solution from the time-domain solution via a Fourier transform in time. An essential ingredient of the new method is a front-tracking mesh adaptation algorithm for solving the problem in ii). By exploiting the limited support of the wave front, this allows us to make the number of the required degrees of freedom to reach a given accuracy significantly less dependent on the frequency ω. We also present a new algorithm for computing the Fourier transform in iii) that exploits the reduced number of degrees of freedom corresponding to the adapted meshes. Numerical examples demonstrate the advantages of the proposed method and the fact that the method can also be applied with external source terms such as point sources and sound-soft scatterers. The gained efficiency, however, is limited in the presence of trapping modes.

A mesh adaptation algorithm using new monitor and estimator function for discontinuous and layered solution

<p style='text-indent:20px;'>In this work a novel mesh adaptation technique is proposed to approximate discontinuous or boundary layer solution of partial differential equations. We introduce new estimator and monitor function to detect solution region containing discontinuity and layered region. Subsequently, this information is utilized along with equi-distribution principle to adapt the mesh locally. Numerical tests for numerous scalar problems are presented. These results clearly demonstrate the robustness of this method and non-oscillatory nature of the computed solutions.</p>

Modified equation based mesh adaptation algorithm for evolutionary scalar partial differential equations

AbstractIt is well known that on uniform mesh classical higher order schemes for evolutionary problems yield an oscillatory approximation of the solution containing discontinuity or boundary layers. In this article, an entirely new approach for constructing locally adaptive mesh is given to compute nonoscillatory solution by representative “second” order schemes. This is done using modified equation analysis and a notion of data dependent stability of schemes to identify the solution regions for local mesh adaptation. The proposed algorithm is applied on scalar problems to compute the solution with discontinuity or boundary layer. Presented numerical results show underlying second order schemes approximate discontinuities and boundary layers without spurious oscillations.

A tracking strategy for multi‐branched crack tips in phase‐field modeling of dynamic fractures

AbstractThe well‐received phase‐field method smears the discrete cracks in the damaged bands, blurring the explicit crack tip. However, identifying the location of the crack tip is sometimes vital. The widely used scheme at present considers the forefront of a phase‐field contour as the crack tip. Such a method, to our best knowledge, is inapplicable for branched cracks, which motivates us to develop a novel stepwise identification strategy for multi‐branched crack tips termed si‐MCT. Instead of searching for crack tips globally, the proposed si‐MCT realizes this in the chosen deliberately local regions (searching regions), and then automatically updates these regions as the cracks propagate. For the robust implementation of si‐MCT, a novel concept of active crack tip zone is also proposed to cope with the extreme circumstances where adjacent crack paths are too close to interfere with identifying the crack tip. Furthermore, the core algorithms and specific procedures of the proposed strategy are also elaborated. Moreover, several representative tests are studied, showing the bright prospect of si‐MCT in dynamic multi‐branch crack tracking and adaptive mesh algorithm.

SPEARS: A Database-Invariant Spectral modeling API

The Spectral Physics Environment for Advanced Remote Sensing (SPEARS) application programming interface (API) is a Python-based, line-by-line, local thermal equilibrium (LTE) spectral modeling code which is optimized for simultaneously synthesizing optical spectra from any combination of fundamental spectroscopic databases. In this article, we contribute two novel spectral modeling techniques to the scientific literature. First we describe how SPEARS integrates a physics-based collisional model for calculating pressure broadening in the absence of available broadening coefficients. With this collisional model implementation, a generalized approach to fundamental spectroscopic databases can be achieved across multiple databases. We also detail our adaptive grid mesh algorithm developed to make the code scalable for simulating large spectral bandwidths at high spectral fidelity using intuitive grid parameters. We present comparisons to other modeling tools, experiments, and provide a discussion on the SPEARS user interface.