The present paper addresses the development and implementation of the first r-adaptive mesh refinement (r-AMR) algorithm for a high-order Flux Reconstruction solver. The r-refinement consists on ...nodal re-positioning while keeping the number of mesh nodes and their connectivity frozen. The developed algorithm is based on physics-driven spring-analogies, where the mesh can be seen as a network of fictitious springs. While AMR increases the local mesh density, the high-order Flux Reconstruction method potentially provides a more accurate detection of complex flow features over relatively coarser mesh, when compared to low-order methods. In this work, a concise overview of the Flux Reconstruction method and spring-based AMR techniques will be given, followed by some promising results of r-AMR applied to benchmark high-order steady-state supersonic flow simulations.
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This study aims to develop an adaptive mesh refinement (AMR) algorithm combined with Cut-Cell IBM using two-stage pressure-velocity corrections for thin-object FSI problems. To achieve the objective ...of this study, the AMR-immersed boundary method (AMR-IBM) algorithm discretizes and solves the equations of motion for the flow that involves rigid thin structures boundary layer at the interface between the structure and the fluid. The body forces are computed in proportion to the fraction of the solid volume in the IBM fluid cells to incorporate fluid and solid motions into the boundary. The corrections of the velocity and pressure is determined by using a novel simplified marker and cell scheme. The new developed AMR-IBM algorithm is validated using a benchmark data of fluid past a cylinder and the results show that there is good agreement under laminar flow. Simulations are conducted for three test cases with the purpose of demonstration the accuracy of the AMR-IBM algorithm. The validation confirms the robustness of the new algorithms in simulating flow characteristics in the boundary layers of thin structures. The algorithm is performed on a staggered grid to simulate the fluid flow around thin object and determine the computational cost.
•Very high order accurate adaptive mesh refinement (AMR) with local time stepping.•A posteriori subcell limiter for arbitrary high order accurate DG schemes.•Simple troubled zones indicator based on ...positivity and discrete maximum principle.•Troubled zones are recomputed with ADER-WENO finite volume scheme on the subgrid.•Unprecedented resolution of shocks due to the combination of AMR with subgrid limiters.
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space–time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order a posteriori sub-cell ADER-WENO finite volume limiter. Notoriously, the original DG method produces strong oscillations in the presence of discontinuous solutions and several types of limiters have been introduced over the years to cope with this problem. Following the innovative idea recently proposed in 53, the discrete solution within the troubled cells is recomputed by scattering the DG polynomial at the previous time step onto a suitable number of sub-cells along each direction. Relying on the robustness of classical finite volume WENO schemes, the sub-cell averages are recomputed and then gathered back into the DG polynomials over the main grid. In this paper this approach is implemented for the first time within a space–time adaptive AMR framework in two and three space dimensions, after assuring the proper averaging and projection between sub-cells that belong to different levels of refinement. The combination of the sub-cell resolution with the advantages of AMR allows for an unprecedented ability in resolving even the finest details in the dynamics of the fluid. The spectacular resolution properties of the new scheme have been shown through a wide number of test cases performed in two and in three space dimensions, both for the Euler equations of compressible gas dynamics and for the magnetohydrodynamics (MHD) equations.
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We present an open-source plasma fluid code for 2D, cylindrical and 3D simulations of streamer discharges. The code is based on the Afivo framework, which features adaptive mesh refinement on ...quadtree/octree grids, geometric multigrid methods for Poisson's equation, and OpenMP parallelism. We describe the numerical implementation of a fluid model of the drift-diffusion-reaction type, combined with the local field approximation. Then we demonstrate its functionality with 3D simulations of long positive streamers in nitrogen in undervolted gaps. Three examples are presented. The first one shows how a stochastic background density affects streamer propagation and branching. The second one focuses on the interaction of a streamer with preionized regions, and the third one investigates the interaction between two streamers. The simulations use up to 108 grid cells and run in less than a day; without mesh refinement they would require more than 1012 grid cells.
This study proposes a novel computationally efficient methodology to perform topology optimization (TO) of fourth-order plate structures within the framework of multi-patch isogeometric analysis. ...This is realized by taking the multifold benefits of isogeometric PHT-Splines to (1) discretize the C1 continuous weak form of plate structures, (2) develop a C0 continuous density field for the material distribution in TO and inherently remove the need for filters, and (3) provide a hierarchical tree structure for the structural mesh to effortlessly implement an adaptive mesh refinement (AMR) strategy. Moreover, to ensure continuity between isogeometric patches, we adopt a strong C1 coupling between the boundaries. This is established by constructing new basis functions, defined as a linear combination of existing C0 functions at the patch interfaces. The density field in TO is further enhanced with a first-neighbourhood smoothening algorithm based on the Shepard function to generate printable topologies and alleviate the post-processing stages after optimization. An element-centre density, based on the control point densities of the isogeometric mesh, is used as the marking scheme for the AMR to determine the subdomains to be refined. Utilizing the Geometry Independent Field approximaTion, the design and adaptive analysis-optimization stages were independently discretized respectively through NURBS and PHT-Splines, allowing easy transfer of multi-patch geometries from industry-standard packages. Multiple numerical examples illustrate the stability of the multi-patch algorithm in optimizing the geometries effectively. The results also show considerable advantages in terms of solution accuracy such as precise field, smooth topology and computational efficiency.
•Isogeometric topology optimization (ITO) for fourth-order plate structures.•Continuous material distribution to ensure smooth topology.•Boundary-tracking AMR strategy for computational efficiency.•Robust C1 coupling for seamless solution continuity across patches.•Integrating AMR into C1 coupling for ITO of multi-patch plate structures.
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We review some of the recent advances in level-set methods and their applications. In particular, we discuss how to impose boundary conditions at irregular domains and free boundaries, as well as the ...extension of level-set methods to adaptive Cartesian grids and parallel architectures. Illustrative applications are taken from the physical and life sciences. Fast sweeping methods are briefly discussed.
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In this work, an adaptive phase-field method is proposed for modeling fracture of hyperelastic materials at large deformations. The adaptive mesh refinement is facilitated by the variable-node ...elements, which are flexible to act as transition elements in the employed quadtree mesh. To control the adaptive process, we propose a combined phase-field and energetic mesh refinement criterion, where the energetic part exploits the strain energy threshold of the AT1 phase-field model which is used in this work. Both the compressible and incompressible neo-Hookean models are taken into account, and the latter is enforced by the plane stress condition to simplify the implementation. Several representative examples are studied to verify the accuracy and efficiency of the proposed adaptive phase-field method, in comparison to the available numerical and experimental reference data as well as the fixed locally pre-refined mesh. The simulated results show that the energetic part of the mesh refinement criterion can effectively prevent the delayed damage evolution when the phase-field initiates. Finally, the fracture process of a hyperelastic composite with inclusions is simulated to demonstrate the capacity of the proposed method for reproducing complex failure phenomena at large deformations.
•An adaptive phase-field model for hyperelastic fracture is proposed.•Variable-node element is employed as transition element in quadtree mesh refinement scheme.•A combined phase-field and energetic mesh refinement criterion is developed.•Several examples including a hyperelastic composite show accuracy and efficiency of the method.
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Data compression can efficiently reduce the memory and persistence storage cost, which is highly desirable in modern computing systems, such as enterprise, cloud, and High-Performance Computing (HPC) ...environments. However, the main challenges of existing data compressors are the insufficient compression ratio and low throughput. This paper focuses on improving the compression ratio of state-of-the-art lossy compression algorithms from the view of applications. Besides, we also use the characteristics of the applications to reduce the runtime overhead. To this end, we explore the idea with Adaptive Mesh Refinement (AMR), which is widely adopted as a computational technique to reduce the amount of computation and memory required in scientific simulations. We propose Level Associated Mapping-based Preconditioning (LAMP) to improve the storage efficiency of AMR applications. The main idea is twofold. First, we utilize the high similarities among the adjacent AMR levels to precondition the data prior to compression. Second, AMR has a unique characteristic of grid structures. We utilize grid structures to rebuild a level associated mapping table, which significantly reduces the runtime overhead of LAMP. Thanks to the optimization techniques of General Matrix Multiplication (GEMM), we further accelerate the process of rebuilding AMR hierarchy for LAMP. Besides, we also block multiple adjacent coordinates within a box and further improve cache locality. The experimental results show that the compression ratios of LAMP are improved up to 63.8% compared to directly compressing the data.
This paper presents an adaptive phase field model for simulating fracture due to coupled interactions (such as thermal quenching and hot cracking in additive manufacturing). The proposed model is ...implemented in an open-source finite element framework, FEniCS. The model considers spatial variations of the fracture toughness and differential coefficients of thermal shrinkage. Several paradigmatic case studies are addressed to demonstrate the potential of the proposed modeling framework. Specifically, we (a) benchmark our crack predictions for mechanical and thermal boundary condition interactions with the results from alternative numerical methods, (b) accurately reproduce experimentally observed complex crack trajectories due to thermal quenching and hot cracking in additive manufacturing, and (c) demonstrate the ease of extending of the proposed framework to thermal cracking problems in three dimensions. The current implementation provides the basic for an efficient framework for fracture problems due to multi-physical interactions for practical engineers with less programming expertise.
•An adaptive phase-field method for multi-physical interactions is implemented in FEniCS.•Error indicator is based on phase-field and energy density.•The model accounted for temperature-dependent fracture toughness and thermal shrinkage.•Thermal quenching and hot cracking in additive manufacturing are accurately predicted.•Adaptive mesh refinement strategy significantly reduces the computational cost.
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The damage mechanics challenge (DMC) represents a critical step in predicting the damage evolution and failure in rock-like materials displaying brittle/quasi-brittle characteristics. The phase-field ...fracture (PFF) model is a type of damage mechanics model that is thermodynamically consistent and is well suited for capturing complex crack patterns and interactions in 3D. However, there are two main shortcomings: (1) the definition of the crack driving force function and calibration of model parameters give rise to uncertainty in predictions of load–displacement curves; and (2) the finite element implementation of the PFF model generally necessitates the use of fine meshes, leading to higher computational costs. This study presents a novel numerical methodology that employs h-adaptive algorithms in combination with the stress-based PFF model, and demonstrates its validity against experimental data, as required by the DMC. The core strength of our methodology lies in its computational efficiency derived from dynamically-adaptive local mesh refinement. The potential of our methodology is further demonstrated through calibration, verification, and validation studies. Our 2D and 3D simulation results show good agreement with the benchmark laboratory data from three-point bending experiments, within the bounds of data uncertainty. Our blind prediction of the 3D crack geometry for the final challenge shows good agreement with the corresponding experimental data. We find that the stress-based PFF model simplifies the parameter calibration process to a single critical stress parameter, which reduces uncertainty.
•An adaptive phase-field fracture algorithm to solve the damage mechanics challenge.•Simplified model calibration with a single critical stress parameter reduces uncertainty.•The calibrated model predicts peak load in 3D printed rock with less than 10 % error.•Simulated crack morphology in 2D and 3D matches well with experimental crack surfaces.•Adaptive mesh refinement significantly reduces the cost of fracture simulations.
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