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

2021 ◽  
Vol 11 (21) ◽  
pp. 9879
Author(s):  
Wanjun Xu ◽  
Kang Li ◽  
Zhengyang Geng ◽  
Mingjie Zhang ◽  
Jiangang Yang
Keyword(s):  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Posteriori Error ◽  
Uniform Mesh ◽  
Nonuniform Mesh ◽  
A Cell ◽  
The Difference ◽  
Richardson Extrapolation Method

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.

scholarly journals AMReX: Block-structured adaptive mesh refinement for multiphysics applications

2021 ◽  
pp. 109434202110228
Author(s):  
Weiqun Zhang ◽  
Andrew Myers ◽  
Kevin Gott ◽  
Ann Almgren ◽  
John Bell
Keyword(s):  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Uniform Mesh ◽  
Physical Processes ◽  
Structured Adaptive Mesh Refinement ◽  
Core Elements ◽  
Accelerator Design ◽  
Block Structured

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.

scholarly journals Implementation and performance of adaptive mesh refinement in the Ice Sheet System Model (ISSM v4.14)

2019 ◽  
Vol 12 (1) ◽  
pp. 215-232 ◽  
Author(s):  
Thiago Dias dos Santos ◽  
Mathieu Morlighem ◽  
Hélène Seroussi ◽  
Philippe Remy Bernard Devloo ◽  
Jefferson Cardia Simões
Keyword(s):  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Ice Sheet ◽  
Adaptive Mesh ◽  
System Model ◽  
Computational Time ◽  
Error Estimator ◽  
Fine Mesh ◽  
Grounding Line

Abstract. Accurate projections of the evolution of ice sheets in a changing climate require a fine mesh/grid resolution in ice sheet models to correctly capture fundamental physical processes, such as the evolution of the grounding line, the region where grounded ice starts to float. The evolution of the grounding line indeed plays a major role in ice sheet dynamics, as it is a fundamental control on marine ice sheet stability. Numerical modeling of a grounding line requires significant computational resources since the accuracy of its position depends on grid or mesh resolution. A technique that improves accuracy with reduced computational cost is the adaptive mesh refinement (AMR) approach. We present here the implementation of the AMR technique in the finite element Ice Sheet System Model (ISSM) to simulate grounding line dynamics under two different benchmarks: MISMIP3d and MISMIP+. We test different refinement criteria: (a) distance around the grounding line, (b) a posteriori error estimator, the Zienkiewicz–Zhu (ZZ) error estimator, and (c) different combinations of (a) and (b). In both benchmarks, the ZZ error estimator presents high values around the grounding line. In the MISMIP+ setup, this estimator also presents high values in the grounded part of the ice sheet, following the complex shape of the bedrock geometry. The ZZ estimator helps guide the refinement procedure such that AMR performance is improved. Our results show that computational time with AMR depends on the required accuracy, but in all cases, it is significantly shorter than for uniformly refined meshes. We conclude that AMR without an associated error estimator should be avoided, especially for real glaciers that have a complex bed geometry.

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

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Daniel J. Dunning ◽  
Robert W. Robey ◽  
Jeffery A. Kuehn ◽  
Jeanine Cook
Keyword(s):  
Adaptive Mesh Refinement ◽  
Graphics Processing Unit ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Processing Unit ◽  
Regular Grid ◽  
A Cell ◽  
Grid Applications ◽  
Graphics Processing ◽  
Phantom Cell

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.

scholarly journals Implementation and Performance of Adaptive Mesh Refinement in the Ice Sheet System Model (ISSM v4.14)

2018 ◽  
Author(s):  
Thiago Dias dos Santos ◽  
Mathieu Morlighem ◽  
Hélène Seroussi ◽  
Philippe Remy Bernard Devloo ◽  
Jefferson Cardia Simões
Keyword(s):  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Ice Sheet ◽  
Adaptive Mesh ◽  
System Model ◽  
Computational Time ◽  
Error Estimator ◽  
Grounding Line ◽  
Refined Meshes

Abstract. Accurate projections of the evolution of ice sheets in a changing climate require a fine mesh/grid resolution to correctly capture fundamental physical processes, such as the evolution of the grounding line, the region where grounded ice starts to float. The evolution of the grounding line indeed plays a major role in ice sheet dynamics, as it is a fundamental control on marine ice sheet stability. Numerical modeling of grounding line requires significant computational resources since the accuracy of its position depends on grid or mesh resolution. A technique that improves accuracy with reduced computational cost is the adaptive mesh refinement approach, AMR. We present here the implementation of the AMR technique in the finite element Ice Sheet System Model (ISSM) to simulate grounding line dynamics under two different benchmarks, MISMIP3d and MISMIP+. We test different refinement criteria: (a) distance around grounding line, (b) a posteriori error estimator, the Zienkiewicz-Zhu (ZZ) error estimator, and (c) different combinations of (a) and (b). We find that for MISMIP3d setup, refining 5 km around the grounding line, both on grounded and floating ice, is sufficient to produce AMR results similar to the ones obtained with uniformly refined meshes. However, for the MISMIP+ setup, we note that there is a minimum distance of 30 km around the grounding line required to produce accurate results. We find this AMR mesh-dependency is linked to the complex bedrock topography of MISMIP+. In both benchmarks, the ZZ error estimator presents high values around the grounding line. Particularly for MISMIP+ setup, the estimator also presents high values in the grounded part of the ice sheet, following the complex shape of the bedrock geometry. This estimator helps guide the refinement procedure such that AMR performance is improved. Our results show that computational time with AMR depends on the required accuracy, but in all cases, it is significantly shorter than for uniformly refined meshes. We conclude that AMR without an associated error estimator should be avoided, especially for real glaciers that have a complex bed geometry.

scholarly journals Efficient Simulations of Propagating Flames and Fire Suppression Optimization Using Adaptive Mesh Refinement

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 323
Author(s):  
Caelan Lapointe ◽  
Nicholas T. Wimer ◽  
Sam Simons-Wellin ◽  
Jeffrey F. Glusman ◽  
Gregory B. Rieker ◽  
...  
Keyword(s):  
Adaptive Mesh Refinement ◽  
Optimization Problems ◽  
Solid Phase ◽  
Fire Suppression ◽  
Spatial Scales ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Fire Spread ◽  
Wide Range

Fires are complex multi-physics problems that span wide spatial scale ranges. Capturing this complexity in computationally affordable numerical simulations for process studies and “outer-loop” techniques (e.g., optimization and uncertainty quantification) is a fundamental challenge in reacting flow research. Further complications arise for propagating fires where a priori knowledge of the fire spread rate and direction is typically not available. In such cases, static mesh refinement at all possible fire locations is a computationally inefficient approach to bridging the wide range of spatial scales relevant to fire behavior. In the present study, we address this challenge by incorporating adaptive mesh refinement (AMR) in fireFoam, an OpenFOAM solver for simulations of complex fire phenomena involving pyrolyzing solid surfaces. The AMR functionality in the extended solver, called fireDyMFoam, is load balanced, models gas, solid, and liquid phases, and allows us to dynamically track regions of interest, thus avoiding inefficient over-resolution of areas far from a propagating flame. We demonstrate the AMR capability and computational efficiency for fire spread on vertical panels, showing that the AMR solver reproduces results obtained using much larger statically refined meshes, but at a substantially reduced computational cost. We then leverage AMR in an optimization framework for fire suppression based on the open-source Dakota toolkit, which is made more computationally tractable through the use of fireDyMFoam, minimizing a cost function that balances water use and solid-phase mass loss. The extension of fireFoam developed here thus enables the use of higher fidelity simulations in optimization problems for the suppression of fire spread in both built and natural environments.

scholarly journals Analysis of marking criteria for mesh adaptation in Cosserat elasticity

2018 ◽  
Vol 245 ◽  
pp. 08004 ◽  
Author(s):  
Maria Churilova
Keyword(s):  
Adaptive Mesh Refinement ◽  
Error Control ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Posteriori Error ◽  
Mesh Adaptation ◽  
Adaptive Meshes ◽  
A Posteriori Error ◽  
Cosserat Elasticity ◽  
Elasticity Problems

The article is devoted to comparison of finite element marking criteria for adaptive mesh refinement while solving plane Cosserat elasticity problems. The goal is to compare the resulting adaptive meshes obtained with different marking strategies. Mesh refinement and error control is done using the functional type a posteriori error majorant. Implemented algorithms use the zero-order Raviart-Thomas approximation on triangular meshes. Four widely used marking criteria are utilized for mesh adaptation. The comparative analysis is presented for two plane-strain problems.

Accuracy Verification of a 2D Adaptive Mesh Refinement Method Using Backward-Facing Step Flow of Low Reynolds Numbers

2020 ◽  
pp. 2041012
Author(s):  
Zhenquan Li ◽  
Miao Li
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Navier Stokes ◽  
Vortex Center ◽  
Backward Facing Step ◽  
Step Flow

Identifying centers of vortices of fluid flow accurately is one of the accuracy measures for computational methods. After verifying the accuracy of the 2D adaptive mesh refinement (AMR) method in the benchmarks of 2D lid-driven cavity flow, this paper shows the accuracy verification by the benchmarks of 2D backward-facing step flow. The AMR method refines a mesh using the numerical solution of the Navier–Stokes equations computed on the mesh by an open source software Navier2D which implemented a vertex centered finite volume method (FVM) using the median dual mesh to form control volumes about each vertex. The accuracy is shown by the comparison between vortex center locations calculated from the linearly interpolated numerical solutions and those obtained in the benchmark. The AMR method is proposed based on the qualitative theory of differential equations, and it can be applied to refine a mesh as many times as required and used to seek accurate numerical solutions of the mathematical models including the continuity equation for incompressible fluid or steady-state compressible flow with low computational cost.

The Initial Condition of Cosmological High-Resolution Simulations

2005 ◽  
Vol 201 ◽  
pp. 499-500
Author(s):  
Tomoya. Ogawa ◽  
Shuuichi. Ebi ◽  
Kazuyuki. Yamashita ◽  
Mitsue. Den
Keyword(s):  
High Resolution ◽  
High Frequency ◽  
Adaptive Mesh Refinement ◽  
Initial Conditions ◽  
Mesh Refinement ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Initial Condition ◽  
Cosmological Simulations ◽  
Frequency Components

Recently, High-resolution algorithms such as the adaptive mesh refinement (AMR) method have been applied to cosmological simulations by several authors. However, the resolution of their INITIAL conditions is not high. We argue the need for cosmological high-resolution simulations to use a high-resolution initial condition or an initial condition including high-frequency components. Then we present the method of creating such initial condition, and estimate its computational cost.

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