Cell-based Adaptive Mesh Refinement Research Articles

Polymeric droplet formation and flow pattern evolution in capillary microchannels: Effect of fluid elasticity

Polymeric droplets are widely employed in fields such as chemical, biomedical, and materials engineering. However, the study of polymeric droplet formation is still insufficient due to the complex elasticity. In this work, the effect of fluid elasticity on the flow patterns for polymeric droplet formation in cross-junction microchannels is investigated by means of finite-volume direct numerical simulations. The volume of fluid method with cell-based adaptive mesh refinement technique is used to capture the interface. Additionally, the rheological behavior of polymeric fluids is described using the exponential Phan-Thien–Tanner constitutive model. The simulated flow behaviors are highly consistent with the experimental observations. The results indicate that three typical flow patterns of dripping, jetting, and threading flows are obtained at different fluid elasticities (denoted by the Weissenberg number Wi) and viscosities (denoted by the Capillary number Ca). Meanwhile, the elastic effect is found to be greater in the dripping flow, significantly reducing the axial tensile stress. It is demonstrated that changes in the stretched state of polymer macromolecules with the same Wi at different Ca lead to variations in the strength of elastic action, which, in turn, affects the extension length and the pinch-off time of droplets. Finally, a relationship equation between the extension length and time of the polymer fluid is established. This present study aims to provide important insight into the preparation of polymeric droplets in microchannels.

An Immersed Boundary Method Based on Parallel Adaptive Cartesian Grids for High Reynolds Number Turbulent Flow

In this paper, a set of parallelised adaptive hierarchical Cartesian-based immersed boundary methodology is developed for high Reynolds number compressible flow. First, a robust and efficient grid generation method based on the separation axis theorem for arbitrary geometry is presented for automatic Cartesian grid generation. Second, an immersed boundary method (IBM) is presented coupling with wall model for high Reynolds number flow. Third, a parallel strategy is implemented and special treatment is proposed to guarantee large-scale computing. Finally, cell-based adaptive mesh refinement (AMR) technology is used to capture fluid phenomena under different regimes including but not limited to shock waves and vortices. The overall performance of the methodology is tested through a wide range of regimes including transonic and supersonic flow with high Reynolds number in both two and three dimensions. Results are in good agreement with reference data and indicate the capability and robustness of the present methodology.

A Local Adaptive Mesh Refinement for JFO Cavitation Model on Cartesian Meshes

Nonuniform mesh is beneficial to reduce computational cost and improve the resolution of the interest area. In the paper, a cell-based adaptive mesh refinement (AMR) method was developed for bearing cavitation simulation. The bearing mesh can be optimized by local refinement and coarsening, allowing for a reasonable solution with special purpose. The AMR algorithm was constructed based on a quadtree data structure with a Z-order filling curve managing cells. The hybrids of interpolation schemes on hanging nodes were applied. A cell matching method was used to handle periodic boundary conditions. The difference schemes at the nonuniform mesh for the universal Reynolds equation were derived. Ausas’ cavitation algorithm was integrated into the AMR algorithm. The Richardson extrapolation method was employed as an a posteriori error estimation to guide the areas where they need to be refined. The cases of a journal bearing and a thrust bearing were studied. The results showed that the AMR method provided nearly the same accuracy results compared with the uniform mesh, while the number of mesh was reduced to 50–60% of the number of the uniform mesh. The computational efficiency was effectively improved. The AMR method is suggested to be a potential tool for bearing cavitation simulation.

A Performance Analysis of Phantom-Cell Adaptive Mesh Refinement on CPUs and GPUs

Abstract This paper presents an implementation of phantom-cell adaptive mesh refinement (AMR) on a graphics processing unit (GPU) using CLAMR, a cell-based mini-app that runs on a variety of next-generation platforms. Phantom-cell AMR is a hybrid method of cell-based AMR and patch-based AMR that provides a separation of physics and mesh codes. By designing a structure that allows each level of the mesh to be independent, there are minimal development requirements that are needed to convert regular grid applications to AMR. The decoupling of physics and mesh codes through these phantom cells improves composability and creates an easy pathway toward implementing AMR codes on Exascale systems, specifically targeting GPUs. Physics and mesh codes can be accelerated individually, allowing for fewer dependencies and more opportunities for optimization. A complete implementation of phantom-cell AMR on a GPU with opencl is presented for the purpose of showing the simplicity of porting the algorithms to accelerator-based architectures and the performance and optimization improvements that are made as a result.

Adaptive mesh refinement in the fast lane

This paper presents an approach for constructing an adaptive mesh refinement (AMR) scheme, targeting next-generation computing hardware. The key to the design is the particular combination of aspects of cell-based AMR and patch-based AMR. We examine the feasibility of this new method with respect to correctness, preservation of circular symmetry, ease of programming and performance impacts on runtime and memory usage. This method exploration is done in CLAMR, a cell-based AMR mini-app that already runs on GPUs and other next-generation hardware platforms. The composability of the application is improved by decoupling the physics code and mesh code. Each level of the mesh is made independent through the use of phantom cells. The net result is a clear pathway to getting the full application on the GPU while also minimizing development requirements to convert a regular grid application to AMR.

Adaptive mesh refinement on graphics processing units for applications in gas dynamics

We present novel algorithms for cell-based adaptive mesh refinement on unstructured meshes of triangles on graphics processing units. Our implementation makes use of improved memory management techniques and a coloring algorithm for avoiding race conditions. Both the solver and AMR algorithms are entirely implemented on the GPU, with negligible communication between device and host. We show that the overhead of the AMR subroutines is small compared to the high order solver and that the proportion of total runtime spent adaptively refining the mesh decreases with the order of approximation. We apply our code to a number of benchmark problems as well as more recently proposed problems for the Euler equations that require extremely high resolution. We present the solution to a shock reflection problem that addresses the von Neumann triple point paradox with an accurately computed triple point location. Finally, we present the first solution on the full Euler equations to the problem of shock disappearance and self-similar diffraction of weak shocks around thin films.

GPU accelerated cell-based adaptive mesh refinement on unstructured quadrilateral grid

A GPU accelerated inviscid flow solver is developed on an unstructured quadrilateral grid in the present work. For the first time, the cell-based adaptive mesh refinement (AMR) is fully implemented on GPU for the unstructured quadrilateral grid, which greatly reduces the frequency of data exchange between GPU and CPU. Specifically, the AMR is processed with atomic operations to parallelize list operations, and null memory recycling is realized to improve the efficiency of memory utilization. It is found that results obtained by GPUs agree very well with the exact or experimental results in literature. An acceleration ratio of 4 is obtained between the parallel code running on the old GPU GT9800 and the serial code running on E3-1230 V2. With the optimization of configuring a larger L1 cache and adopting Shared Memory based atomic operations on the newer GPU C2050, an acceleration ratio of 20 is achieved. The parallelized cell-based AMR processes have achieved 2x speedup on GT9800 and 18x on Tesla C2050, which demonstrates that parallel running of the cell-based AMR method on GPU is feasible and efficient. Our results also indicate that the new development of GPU architecture benefits the fluid dynamics computing significantly.

Electrostatic PIC with adaptive Cartesian mesh

We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are related to a decrease of the particle-per-cell number in the refined cells with a corresponding increase of the numerical noise. The developed ES-PIC solver is validated for capacitively coupled plasma, its AMR capabilities are demonstrated for simulations of streamer development during high-pressure gas breakdown. It is shown that cell-based AMR provides a convenient particle management algorithm for exponential multiplications of electrons and ions in the ionization events.

A GPU-accelerated adaptive mesh refinement for immersed boundary methods

A new patch-based adaptive mesh refinement (AMR) code is developed. The fully threaded tree (FTT) data structure (Khokhlov, 1998) originally developed for cell-based AMR is extended to organize the patch-based adaptive meshes. We demonstrate the accuracy of the AMR code by performing the simulations of the two and three-dimensional Sedov blast wave problems. We measure the performance of the code by solving the same problems in different grid resolutions on a single CPU, where detailed timing analyses provide comparison between the current AMR code and a conventional oct-tree-based AMR code (FLASH 4.0.1) (Fryxell et al., 2000). For the two-dimensional cases, maximum speed-up ratio of 58.23 is obtained versus FLASH 4.0.1 with 5122 effective grid resolution. For the three-dimensional cases, maximum speed-up ratios of 32.16 is achieved over FLASH 4.0.1 with 1283 effective grid resolution. We present the implementation and performance of a patch-based AMR algorithm with the immersed boundary method (IBM) on Graphic Processing Units (GPU). We also applied several optimizations in GPU computation, including the asynchronous memory copy, the concurrent execution between CPU and GPU and hybrid MPI/OpenMP/GPU parallelization. Performance benchmarks are conducted on the GPU cluster on SHARCNET (https://www.sharcnet.ca/) using 1–8 Tesla M2070 GPUs. Maximum speed-up factors of 22.3 and 20.5 are demonstrated using one GPU and 8 GPUs with 20483 effective resolution, respectively.

Parallel Compact Hash Algorithms for Computational Meshes

We employ compact hashing and the discrete properties of computational meshes to optimize spatial operations in scientific computing applications. Our target is to develop highly parallel compact hashing methods suitable for the fine-grained parallelism of GPU and MIC architectures that will scale to the next generation of computing systems. As a model, we apply spatial hashing methods to the problem of determining neighbor elements in adaptive mesh refinement (AMR) schemes. By applying memory savings techniques, we extend the perfect spatial hash algorithm to a compact hash by compressing the resulting sparse data structures. Using compact hashing and specific memory optimizations, we increase the range of problems that can benefit from our ideal $O(n)$ algorithms. The spatial hash methods are tested and compared across a variety of architectures on both a randomly generated sample mesh and an existing cell-based AMR shallow-water hydrodynamics scheme. We demonstrate consistent speed-up and increased performance across every device tested and explore the ubiquitous application of spatial hashing in scientific computing.