Structured Adaptive Mesh Refinement Research Articles

Automated Reconstruction and Conforming Mesh Generation for Polycrystalline Microstructures from Imaging Data

A new algorithm named PolyCISAMR is introduced to automatically generate high-fidelity conforming finite element (FE) meshes for two-dimensional polycrystalline microstructures. PolyCISAMR extends the capabilities of the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) algorithm, which transforms a structured grid overlaid on the domain geometry into a high-quality conforming mesh. The PolyCISAMR approach uses a segregated meshing strategy, where CISAMR is used to discretize each grain independently and the resulting matching meshes are merged to form the final FE model. In addition, this article presents a set of integrated algorithms for processing low-resolution images of a polycrystal, reconstructed using DREAM.3D software (Version 6.5.121), to generate NURBS characterizations for each grain prior to mesh generation. Example problems demonstrate the effectiveness of PolyCISAMR in creating high-quality meshes for various polycrystalline metallic microstructures along with corresponding crystal plasticity finite element (CPFE) simulations.

A thermal equilibrium approach to modelling multiple solid–fluid interactions with phase transitions, with application to cavitation

This paper presents a new approach to model phase transitions in multi-material problems based on the assumption of thermal equilibrium. The method is used to construct an equation of state for water which captures the liquid–vapour phase transition and is suitable for simulating cavitating flows. A key advantage of this approach is that the physics of the phase transition is entirely encoded within the equation of state. Complex multi-physics models can therefore be augmented to include the physics of phase transitions without further complicating the partial evolution equations. This is substantiated by integrating the model within a diffuse interface scheme for coupled solid–fluid dynamics, and implemented using a structured adaptive mesh refinement (SAMR) strategy. The combined model facilitates the fully-coupled simulation of complex multi-material, multi-physics problems featuring elastoplastic solids, gases, cavitating liquids and reactive materials. Evaluation of the model is shown to add little overhead – for parts of the domain without cavitation the equations reduce to those of the underpinning model with simple stiffened gas equation of state for liquid components; for parts of the domain where cavitation does occur, it requires a non-linear relaxation with only one degree of freedom. The method is applied to several strenuous test cases for cavitating flows and shown to be in good agreement with previously published works.

A two-dimensional geometric multigrid model for Poisson equation with interface on structured adaptive mesh refinement grid

In this study, a two-dimensional Geometric Multigrid (GMG) model for Poisson equation with interface on Structured Adaptive Mesh Refinement (SAMR) grid is developed. The model is designed to be combined with Navier-Stokes solvers with staggered arrangements of variables, although solvers with collocated arrangement are also applicable. Based on a general GMG method, special attention for flux conservation is taken on the coarse-fine interface. As large density ratios commonly exist in interface flows such as free surface flows, Galerkin Coarse grid Approximation (GCA) method is adopted to generate coefficients on coarse grids to enhance the robustness and efficiency of the model. Benchmark case is carried out for the validation of the model, and it is demonstrated to obtain 2nd-order accuracy and acceptable efficiency for even the density ratio reaches 104. Point iteration and line relaxation iteration of Gauss-Seidel methods are compared to obtain a better performance. Furthermore, the model is implemented in a developed Navier-Stokes solver to validate its performance in simulating interface problems. The numerical results are compared with theoretical solution or experimental data from reliable sources.

A structured adaptive mesh refinement strategy with a sharp interface direct-forcing immersed boundary method for moving boundary problems

We develop a versatile and accurate structured adaptive mesh refinement (S-AMR) strategy with a moving least square sharp-direct forcing immersed boundary method (IBM) for incompressible fluid-structure interaction (FSI) simulations. The computational grid consists of several nested blocks in different refinement levels. While blocks with the coarsest grid cover the entire computational domain, the computational domain is locally refined at the location of solid boundary (moving or fixed) by bisecting selected blocks in every coordinate direction. The grid topology and data structure is managed by an extended version of Afivo toolkit (Teunissen and Ebert, 2018), where a novel technique is introduced for conservative data transfer between the coarser and the finer blocks, particularly in velocity transformation for which the mass conservation plays a crucial role. In the present study, the continuity and Navier-Stokes equations for incompressible flows are spatially discretized with a second order central finite difference method using a collocated arrangement and are time-integrated using a semi-implicit second order fractional step method, although the proposed S-AMR strategy can be used with different discretization schemes. An IBM using a moving least square approach is utilized to impose boundary conditions. To handle FSI problems, all the governing equations for the dynamics of fluid and structure are simultaneously advanced in time by a predictor-corrector strategy. Several test cases of increasing complexity are solved in order to demonstrate the robustness and accuracy of the proposed method as well as its capability in simulation-driven mesh adaptivity.

Higher-order mesh generation using CISAMR: A case study on bias in presentation and interpretation of results

A modified version of the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) algorithm is presented for the construction of higher-order Lagrangian and NURBS-enhanced (NE) finite element meshes. CISAMR non-iteratively transforms a structured grid into a conforming mesh with an upper bound of three on elements aspect ratio. In this work, we introduce new algorithmic aspects for generating higher-order Lagrangian and NE meshes using CISAMR. For each type of element, a comprehensive study is then provided on the performance of first, second, and third-order meshes for solving linear elastic problems with smooth and oscillatory curvilinear edges. Local gradient recovery error and computational cost are used as performance metrics in these examples. Outcomes are then used as a case study to elucidate common sources of bias in presenting and interpreting results. In particular, we show how bias, whether purposeful or not, could lead to misleading conclusions regarding the performance of a method.

Multiresolution analysis as a criterion for effective dynamic mesh adaptation – A case study for Euler equations in the SAMR framework AMROC

Dynamic mesh adaptation methods require suitable refinement indicators. In the absence of a comprehensive error estimation theory, adaptive mesh refinement (AMR) for nonlinear hyperbolic conservation laws, e.g. compressible Euler equations, in practice utilizes mainly heuristic smoothness indicators like combinations of scaled gradient criteria. As an alternative, we describe in detail an easy to implement and computationally inexpensive criterion built on a two-level wavelet transform that applies projection and prediction operators from multiresolution analysis. The core idea is the use of the amplitude of the wavelet coefficients as smoothness indicator, as it can be related to the local regularity of the solution. Implemented within the fully parallelized and structured adaptive mesh refinement (SAMR) software system AMROC (Adaptive Mesh Refinement in Object-oriented C++), the proposed criterion is tested and comprehensively compared to results obtained by applying the scaled gradient approach. A rigorous quantification technique in terms of numerical adaptation error versus used finite volume cells is developed and applied to study typical two- and three-dimensional problems from compressible gas dynamics. It is found that the proposed multiresolution approach is considerably more efficient and also identifies – besides discontinuous shock and contact waves – in particular smooth rarefaction waves and their interaction as well as small-scale disturbances much more reliably. Aside from pathological cases consisting solely of planar shock waves, the majority of realistic cases show reductions in the number of used finite volume cells between 20 to 40%, while the numerical error remains basically unaltered.

Automated homogenization-based fracture analysis: Effects of SVE size and boundary condition

To model the sample-to-sample variations and the effect of microscale inhomogeneities on fracture response, statistical volume elements (SVEs) are employed to homogenize the elastic and fracture properties of ZrB2-SiC, a two-phase particulate composite often used as a thermal coating. In the mesoscale analysis, 2D finite element models are generated using a non-iterative, automated mesh generation algorithm named Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR). The analysis of SVEs under mixed, traction, and minimal kinematic boundary conditions yields their angle-dependent tensile and shear fracture strengths and elastic stiffnesses. This study shows that homogenized fracture strengths are highly dependent on the SVE size and the particular geometric distribution of inclusions (even for similar volume ratios), whereas elastic properties are mainly a function of the volume fraction. Moreover, mean values of strength and bulk modulus, respectively, decrease and remain almost constant as the SVE size increases. For the macroscale analysis, an isotropic, inhomogeneous field of fracture strength is generated from the homogenization of SVEs. The asynchronous Spacetime Discontinuous Galerkin (aSDG) method is subsequently employed for fracture analysis under uniaxial tensile and thermal strain loadings.

An ideal compressible magnetohydrodynamic solver with parallel block-structured adaptive mesh refinement

We present an adaptive parallel solver for the numerical simulation of ideal magnetohydrodynamics in two and three space dimensions. The discretisation uses a finite volume scheme based on a Cartesian mesh and an explicit compact Runge–Kutta scheme for time integration. Numerically, a generalized Lagrangian multiplier approach with a mixed hyperbolic-parabolic correction is used to guarantee a control on the incompressibility of the magnetic field. We implement the solver in the AMROC (Adaptive Mesh Refinement in Object-oriented C++) framework that uses a structured adaptive mesh refinement (SAMR) method discretisation-independent and is fully parallelised for distributed memory systems. Moreover, AMROC is a modular framework providing manageability, extensibility and efficiency. In this paper, we give an overview of the ideal magnetohydrodynamics solver developed in this framework and its capabilities. We also include an example of this solver’s verification with other codes and its numerical and computational performance.

A non-iterative local remeshing approach for simulating moving boundary transient diffusion problems

A computational framework relying on a non-iterative mesh generation algorithm is introduced for modeling moving boundary transient diffusion problems, with a special focus on its application for simulating corrosion phenomena. In this approach, the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique is employed to adapt the finite element mesh to the evolving morphology of the problem. CISAMR combines customized h-adaptivity, r-adaptivity, and sub-triangulation algorithms to transform a simple structured mesh into a high quality hybrid conforming mesh composed of rectangular and triangular elements. A key advantage of this method for modeling moving boundary problems is that only the elements located along the moving boundary must be modified to regenerate a conforming mesh at each step. This feature not only facilitates the remeshing process but also reduces the error associated with projecting nodal values of the solution to the new mesh. After a convergence study, we verify the accuracy of CISAMR for modeling pitting corrosion problems by comparing results with analytical solutions and phase field simulations. Additional examples are also provided to show the application of CISAMR for simulating corrosion problems with intricate morphologies.

Adaptive THINC-GFM for compressible multi-medium flows

In this paper, a THINC (tangent of hyperbola for interface capturing) (Xiao F. et al., 2005) [26] coupled with GFM (Ghost Fluid Method) is proposed for numerical simulation of compressible multi-medium flows. The THINC scheme, which was first developed for incompressible flows, is applied for capturing the distorted material interface of compressible flows. The hybrid WENO (weighted essentially non-oscillatory) scheme with the blocked structured adaptive mesh refinement (AMR) method is implemented. Load balancing is considered in the parallel computing. Several well documented numerical tests are performed and the results show that the THINC scheme behaviors better in mass conservation. It is the first endeavor to implement THINC scheme with adaptive mesh for computing the compressible multiphase problems. The shock wave–helium bubble interaction test reveals that the present method is efficient in prediction of the deformed interface. The solver is further validated by shock wave impact SF6 interface with square, rectangle, forward and backward triangle shapes in which the wave positions and intersecting angles are compared quantitatively. Finally, the collapse of an air bubble under shock in water is simulated, global agreement with experimental and other numerical results are obtained.

Numerical quantification of the impact of microstructure on the mechanical behavior of particulate Al/SiC composites in 2D

The objectives of the current manuscript are twofold: (i) Introducing an automated computational framework for creating realistic finite element models of metal matrix composites (MMCs) microstructures; (ii) Implementing this technique to investigate the effect of microstructure on the mechanical behavior of an Al/SiC particulate MMC. A microstructure reconstruction algorithm is proposed, which relies on the Centroidal Voronoi tessellation, together with the erosion, random movement, and iterative elimination of the resulting Voronoi cells to create an initial periodic virtual microstructure. Non-Uniform Rational B-Splines are also employed to capture the realistic shapes of embedded particles. High fidelity finite element models of the composite microstructure are then created using a non-iterative Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique. This integrated numerical framework is employed to analyze the effect of an Al/SiC MMC microstructure on its mechanical behavior, considering the plastic deformation of the Al matrix and damage in the SiC particles.

A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems

A Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique is introduced for the automated transformation of a structured grid into a conforming mesh with appropriate element aspect ratios. The CISAMR algorithm is composed of three main phases: (i) Structured Adaptive Mesh Refinement (SAMR) of the background grid; (ii) r-adaptivity of the nodes of elements cut by the crack; (iii) sub-triangulation of the elements deformed during the r-adaptivity process and those with hanging nodes generated during the SAMR process. The required considerations for the treatment of crack tips and branching cracks are also discussed in this manuscript. Regardless of the complexity of the problem geometry and without using iterative smoothing or optimization techniques, CISAMR ensures that aspect ratios of conforming elements are lower than three. Multiple numerical examples are presented to demonstrate the application of CISAMR for modeling linear elastic fracture problems with intricate morphologies.

Conforming to interface structured adaptive mesh refinement: New technique for the automated modeling of materials with complex microstructures

This manuscript introduces a new method named Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) for the automated finite element modeling of problems with complex morphologies. The CISAMR transforms a simple structured mesh of quadrilateral elements into a conforming hybrid mesh composed of quadrilateral and triangular elements with low aspect ratios using a non-iterative algorithm. The automated construction of the mesh begins with implementing a customized Structured Adaptive Mesh Refinement (SAMR) algorithm to achieve the desired element size along materials interfaces. A new r-adaptivity algorithm is then employed to move selected nodes of nonconforming elements to intersection points of their edges with the interface, followed by the diagonal sub-triangulation of all elements deformed during this process into conforming sub-triangles. CISAMR does not require relocating the nodes of the background mesh or creating any new node away from materials interfaces after the completion of the SAMR phase. Further, this method can easily handle special cases such as intersecting boundaries/interfaces, while ensuring that aspect ratios of resulting sub-elements are lower than three. A comprehensive discussion is provided on different aspects of the implementation of CISAMR, followed by several example problems to show its application for modeling materials with complex microstructures.

A new parallelization scheme for adaptive mesh refinement

We present a new method for parallelization of adaptive mesh refinement called Concurrent Structured Adaptive Mesh Refinement (CSAMR). This new method offers the lower computational cost (i.e. wall time×processor count) of subcycling in time, but with the runtime performance (i.e. smaller wall time) of evolving all levels at once using the time step of the finest level (which does more work than subcycling but has less parallelism). We demonstrate our algorithm's effectiveness using an adaptive mesh refinement code, AMSS-NCKU, and show performance on Blue Waters and other high performance clusters. For the class of problem considered in this paper, our algorithm achieves a speedup of 1.7–1.9 when the processor count for a given AMR run is doubled, consistent with our theoretical predictions.

Advances in patch-based adaptive mesh refinement scalability

Patch-based structured adaptive mesh refinement (SAMR) is widely used for high-resolution simulations. Combined with modern supercomputers, it could provide simulations of unprecedented size and resolution. A persistent challenge for this combination has been managing dynamically adaptive meshes on more and more MPI tasks. The distributed mesh management scheme in SAMRAI has made some progress SAMR scalability, but early algorithms still had trouble scaling past the regime of 105 MPI tasks. This work provides two critical SAMR regridding algorithms, which are integrated into that scheme to ensure efficiency of the whole. The clustering algorithm is an extension of the tile-clustering approach, making it more flexible and efficient in both clustering and parallelism. The partitioner is a new algorithm designed to prevent the network congestion experienced by its predecessor. We evaluated performance using weak- and strong-scaling benchmarks designed to be difficult for dynamic adaptivity. Results show good scaling on up to 1.5M cores and 2M MPI tasks. Detailed timing diagnostics suggest scaling would continue well past that.

Experiences from Software Engineering of Large Scale AMR Multiphysics Code Frameworks

Among the present generation of multiphysics HPC simulation codes there are many that are built upon general infrastructural frameworks. This is especially true of the codes that make use of structured adaptive mesh refinement (SAMR) because of unique demands placed on the housekeeping aspects of the code. They have varying degrees of abstractions between the infrastructure such as mesh management and IO and the numerics of the physics solvers. In this experience report we summarize the experiences and lessons learned from two of such major software efforts, FLASH and Chombo.

Block-structured Adaptive Mesh Refinement - Theory, Implementation and Application

Structured adaptive mesh refinement (SAMR) techniques can enable cutting-edge simulations of problems governed by conservation laws. Focusing on the strictly hyperbolic case, these notes explain all algorithmic and mathematical details of a technically relevant implementation tailored for distributed memory computers. An overview of the background of commonly used finite volume discretizations for gas dynamics is included and typical benchmarks to quantify accuracy and performance of the dynamically adaptive code are discussed. Large-scale simulations of shock-induced realistic combustion in non-Cartesian geometry and shock-driven fluid-structure interaction with fully coupled dynamic boundary motion demonstrate the applicability of the discussed techniques for complex scenarios.

An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry

A hybrid weighted essentially non-oscillatory (WENO)/centered-difference numerical method, with low numerical dissipation, high-order shock-capturing, and structured adaptive mesh refinement (SAMR), has been developed for the direct numerical simulation of the multicomponent, compressible, reactive Navier–Stokes equations. The method enables accurate resolution of diffusive processes within reaction zones. The approach combines time-split reactive source terms with a high-order, shock-capturing scheme specifically designed for diffusive flows. A description of the order-optimized, symmetric, finite difference, flux-based, hybrid WENO/centered-difference scheme is given, along with its implementation in a high-order SAMR framework. The implementation of new techniques for discontinuity flagging, scheme-switching, and high-order prolongation and restriction is described. In particular, the refined methodology does not require upwinded WENO at grid refinement interfaces for stability, allowing high-order prolongation and thereby eliminating a significant source of numerical diffusion within the overall code performance. A series of one-and two-dimensional test problems is used to verify the implementation, specifically the high-order accuracy of the diffusion terms. One-dimensional benchmarks include a viscous shock wave and a laminar flame. In two-space dimensions, a Lamb–Oseen vortex and an unstable diffusive detonation are considered, for which quantitative convergence is demonstrated. Further, a two-dimensional high-resolution simulation of a reactive Mach reflection phenomenon with diffusive multi-species mixing is presented.

Quasi-interpolation operators based on a cubic spline and applications in SAMR simulations

In this paper, we consider the properties of monotonicity-preserving and global conservation-preserving for interpolation operators. These two properties play important role when interpolation operators used in many real numerical simulations. In order to attain these two aspects, we propose a one-dimensional (1D) new cubic spline, and extend it to two-dimensional (2D) using tensor-product operation. Based on discrete convolution, 1D and 2D quasi-interpolation operators are presented using these functions. Both analysis and numerical results show that the interpolation operators constructed in this paper are monotonic and conservative. In particular, we consider the numerical simulations of 2D Euler equations based on the technique of structured adaptive mesh refinement (SAMR). In SAMR simulations, effective interpolators are needed for information transportation between the coarser/finer meshes. We applied the 2D quasi-interpolation operator to this environment, and the simulation result show the efficiency and correctness of our interpolator.

A direct-forcing embedded-boundary method with adaptive mesh refinement for fluid–structure interaction problems

In the present work we developed a structured adaptive mesh refinement (S-AMR) strategy for fluid–structure interaction problems in laminar and turbulent incompressible flows. The computational grid consists of a number of nested grid blocks at different refinement levels. The coarsest grid blocks always cover the entire computational domain, and local refinement is achieved by the bisection of selected blocks in every coordinate direction. The grid topology and data-structure is managed using the Paramesh toolkit. The filtered Navier–Stokes equations for incompressible flow are advanced in time using an explicit second-order projection scheme, where all spatial derivatives are approximated using second-order central differences on a staggered grid. For transitional and turbulent flow regimes the large-eddy simulation (LES) approach is used, where special attention is paid on the discontinuities introduced by the local refinement. For all the fluid–structure interaction problems reported in this study the complete set of equations governing the dynamics of the flow and the structure are simultaneously advanced in time using a predictor–corrector strategy. An embedded-boundary method is utilized to enforce the boundary conditions on a complex moving body which is not aligned with the grid lines. Several examples of increasing complexity are given to demonstrate the robustness and accuracy of the proposed formulation.