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.

An Embedded Ghost-Fluid Method for Compressible Flow in Complex Geometry

2016 ◽  
Vol 366 ◽  
pp. 31-39
Author(s):  
M. Al-Marouf ◽  
R. Samtaney
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Solutions ◽  
Complex Geometry ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Navier Stokes ◽  
Ghost Fluid Method ◽  
Structured Adaptive Mesh Refinement ◽  
Number Flow ◽  
High Mach

We present an embedded ghost-fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. The PDE multidimensional extrapolation approach of Aslam [1] is used to reconstruct the solution in the ghost-fluid regions and impose boundary conditions at the fluid-solid interface. The CNS equations are numerically solved by the second order multidimensional upwind method of Colella [2] and Saltzman [3]. Block-structured adaptive mesh refinement implemented under the Chombo framework is utilized to reduce the computational cost while keeping high-resolution mesh around the embedded boundary and regions of high gradient solutions. Numerical examples with different Reynolds numbers for low and high Mach number flow will be presented. We compare our simulation results with other reported experimental and computational results. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

scholarly journals A Material Interface Transition Algorithm for Multiphase Flow

2008 ◽  
Author(s):  
Marianne M. Francois ◽  
Robert B. Lowrie ◽  
Edward D. Dendy
Keyword(s):  
Adaptive Mesh Refinement ◽  
Stokes Equations ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Navier Stokes ◽  
Material Interface ◽  
Navier Stokes Equations ◽  
Interface Reconstruction ◽  
Rayleigh Taylor Instability ◽  
Interface Treatment

Volume tracking method, also referred to as the volume-of-fluid (VOF) method introduces “numerical surface tension” that breaks a filament into a series of droplets whenever the filament is under-resolved. Adaptive mesh refinement can help avoid under-resolution, but a fully-developed flow will still generate filaments that cannot be resolved without enormous computational cost. We propose a complementary new approach that consists of transitioning to a continuous interface representation (i.e. without interface reconstruction) in regions of under-resolved interfacial curvature where volume tracking has become erroneous. The price of the continuous interface treatment is a small amount of numerical mass diffusion, even if the physical interface is immiscible. However, we have found that for certain measures, the overall accuracy is greatly improved by using our transitioning algorithm. The algorithm is developed in the context of the single fluid formulation of the incompressible Navier-Stokes equations. Numerical standard vortices advection test cases and Rayleigh-Taylor instability computations are presented to illustrate the transition algorithm potential.

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.

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.

Optimal Location of a Synthetic Jet on an Airfoil for Stall Control

2007 ◽  
Vol 129 (7) ◽  
pp. 825-833 ◽  
Author(s):  
R. Duvigneau ◽  
A. Hay ◽  
M. Visonneau
Keyword(s):  
Reynolds Number ◽  
Optimization Algorithm ◽  
Adaptive Mesh Refinement ◽  
Stokes Equations ◽  
Adaptive Mesh ◽  
Suction Side ◽  
Optimal Location ◽  
Synthetic Jet ◽  
Navier Stokes ◽  
Physical Analysis

This study deals with the optimization of the location of a synthetic jet on the suction side of an airfoil to control stall. The optimal location is found by coupling a time-accurate flow solver with adaptive mesh refinement/coarsening techniques and an automatic optimization algorithm. The flow and jet are modeled by the unsteady Reynolds-averaged Navier-Stokes equations (URANSE) with a near-wall low-Reynolds number turbulence closure. An unstructured grid refinement/coarsening method is used to automatically generate meshes adapted to the presence of the synthetic jet at a prescribed location. An optimization algorithm modifies the location of the synthetic jet to determine the best actuator location to increase the time-averaged lift for high angles of attack. The proposed methodology is applied to optimize the location of a synthetic jet on the suction side of the NACA 0012 airfoil at a Reynolds number Re=2×106 and incidences of 18deg and 20deg. Finally, a physical analysis of the influence of the synthetic jet location on the control efficiency is proposed to provide some guidelines for practical jet positioning.

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