Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement
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Mathematics and Computing, Computer science↗
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Results for “Mesh Refinement”
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Developing Performance Portable Adaptive Mesh Refinement for Astrophysics
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Computer Science↗
Parthenon: Adaptive Mesh Refinement for Exascale Astrophysics
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Astronomy and Astrophysics↗
Smoothed boundary method for simulating incompressible flow in complex geometries
Simulating flow through porous media with explicit considerations of complex microstructures is very challenging using conventional sharp-interface methods because of the difficulties in generating meshes conformal to complex geometries. In this work, a diffuse interface embedded boundary method known as the Smoothed Boundary Method (SBM) is utilized to facilitate simulations of fluid dynamics involving complex geometries. In diffuse-interface methods, the geometry is described by a domain parameter. The SBM allows the straightforward reformulation of the time-dependent Navier-Stokes equations in terms of this domain parameter, using only algebraic identities. Thus, enforcing the appropriate boundary conditions at the irregular embedded boundary is greatly simplified. Adaptive mesh refinement is used to increase the accuracy of the diffuse interface method by allowing thinner interfacial thickness to be used in the domain parameter. Here, the SBM-formulated Navier-Stokes equations are solved with the Finite Difference Method on refined mesh systems. Sharp-interface Finite Element Method simulations using the commercial software COMSOL on body-conforming meshes are also provided for comparison. Favorable agreement between the two methods is observed. Since it is no longer necessary for the mesh to conform to the complex geometry, the grid system for the SBM simulations can be generated rapidly and without additional manual interventions, making the entire simulation process more expedient.
36 MATERIALS SCIENCE↗
Numerical Differentiation for Adaptively Refined Finite Element Meshes
Postprocessing of point-wise data is a fundamental process in many fields of research. Numerical differentiation is a key operation in computational electromagnetics. In the case of data obtained from a finite element method with automatic mesh refinement much work needs still to be done. This paper addresses some issues in differentiating data obtained from a finite element electromagnetic code with adaptive mesh refinement, and it proposes a methodology for deriving the electric field given the magnetic field on a mesh of linear triangular elements. The procedure itself is nevertheless more general and might be extended for numerically differentiating any point-wise solution based on triangular meshes.
Borgioli, Andrea↗
A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes
The design and implementation of Pyramid (http://www-hpc.jpl.nasa.gov/APPS/AMR/), a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described.
parallel↗
Coupling Noah-Multiparameterization land-surface Model with Energy Research and Forecasting Model
The Energy Research and Forecasting (ERF) model is a high-performance atmospheric model built on the AMReX adaptive mesh refinement (AMR) framework, enabling efficient simulations on heterogeneous computing platforms that combine multicore processors with hardware accelerators. To support land–atmosphere interactions within ERF’s AMR-based environment, a land-surface model must be capable of operating directly on hierarchically refined meshes. In this work, we present a methodology for coupling the Fortran-based Noah-Multiparameterization (Noah-MP) land-surface model with ERF’s C++ codebase. Rather than rewriting Noah-MP, we construct a Fortran–C interoperability layer using CodeScribe, a tool that leverages large language models (LLMs) to automate the generation of interface code. CodeScribe applies structured prompting techniques to generate bindings that support efficient data exchange and function calls between ERF and Noah-MP. The coupling framework also incorporates AMR-aware data handling strategies, allowing NoahMP to operate seamlessly within ERF’s hierarchical mesh structure. This work provides a structured approach for integrating legacy Fortran models into modern C++-based modeling systems using LLM-assisted code generation.
54 ENVIRONMENTAL SCIENCES↗
Dynamic mesh adaption for triangular and tetrahedral grids
The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.
Rupak Biswas↗
A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes
The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.
Lou, John Z.↗
Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries
This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.
Aftosmis, M. J.↗
Correlation of Structural Analysis and Test Results for the McDonnell Douglas Stitched/RFI All-Composite Wing Stub Box
The analytical and experimental results of an all-composite wing stub box are presented in this report. The wing stub box, which is representative of an inboard portion of a commercial transport high-aspect-ratio wing, was fabricated from stitched graphite-epoxy material with a Resin Film Infusion manufacturing process. The wing stub box was designed and constructed by the McDonnell Douglas Aerospace Company as part of the NASA Advanced Composites Technology program. The test article contained metallic load-introduction structures on the inboard and outboard ends of the graphite-epoxy wing stub box. The root end of the inboard load introduction structure was attached to a vertical reaction structure, and an upward load was applied to the outermost tip of the outboard load introduction structure to induce bending of the wing stub box. A finite element model was created in which the center portion of the wing-stub-box upper cover panel was modeled with a refined mesh. The refined mesh was required to represent properly the geometrically nonlinear structural behavior of the upper cover panel and to predict accurately the strains in the stringer webs of the stiffened upper cover panel. The analytical and experimental results for deflections and strains are in good agreement.
Wang, John T.↗
Model problem
Our purpose in examining this test problem is to measure directly the effect of mesh refinement and the resulting mesh interfaces on a known wave that is sensitive to phase errors, while concurrently being able to visually display a meaningful picture of the effects of the refinement induced error on the solution. The refined mesh must be able to adequately capture the diffraction behavior, so that the plane wave front bends as it passes through the slit. Given that the coarse and refined meshes are sufficiently accurate, the phase errors introduced during the problem solution will be a function of th sound speed on the two grids plus the coarse/refined grid interaction errors.
Perkins, A. Louise↗
Fully Threaded Tree for Adaptive Refinement Fluid Dynamics Simulations
A fully threaded tree (FTT) for adaptive refinement of regular meshes is described. By using a tree threaded at all levels, tree traversals for finding nearest neighbors are avoided. All operations on a tree including tree modifications are O(N), where N is a number of cells, and are performed in parallel. An efficient implementation of the tree is described that requires 2N words of memory. A filtering algorithm for removing high frequency noise during mesh refinement is described. A FTT can be used in various numerical applications. In this paper, it is applied to the integration of the Euler equations of fluid dynamics. An adaptive mesh time stepping algorithm is described in which different time steps are used at different l evels of the tree. Time stepping and mesh refinement are interleaved to avoid extensive buffer layers of fine mesh which were otherwise required ahead of moving shocks. Test examples are presented, and the FTT performance is evaluated. The three dimensional simulation of the interaction of a shock wave and a spherical bubble is carried out that shows the development of azimuthal perturbations on the bubble surface.
FINITE ELEMENT ANALYSIS↗
The Pele Simulation Suite for Reacting Flows at Exascale
In this work, we present the Pele suite of software tools for compressible and incompressible reacting flows. The Pele suite leverages several different libraries, notably AMReX and SUNDIALS, to achieve performance portability on heterogeneous computing architectures across the supercomputing landscape. The Pele suite is comprised of PeleC, a compressible reacting flow block-structured adaptive mesh refinement solver, PeleLMeX, a low-Mach number reacting flow block-structured adaptive mesh refinement solver, Pele-Physics, a library for transport, thermodynamics, finite rate chemistry, soot, spray and radiation physics. The objective of this paper is (i) to present the code development efforts necessary to achieve highly effective and scalable applications for exascale machines and (ii) to detail the performance results of the Combustion-Pele project applications on Oak Ridge National Laboratory's Frontier. We show good weak and strong scaling results for both PeleC and PeleLMeX up to more than 50 billion cells on more than 4096 Frontier graphics processing unit nodes. We also present a capability demonstration simulation of a dual-fuel pulse compression ignition engine (six adaptive mesh refinement levels, and 60 billion cells or 2.1 trillion degrees of freedom) on Frontier, to date one of the largest simulations performed on the first exascale-class supercomputer.
adaptive mesh refinement↗
Diffusion Limit–Preserving Lumped DFEMs on AMR Meshes
Here, we present sweep-compatible, novel upwinding recipes for the bilinear discontinuous (BLD) finite element method (FEM) that allows lumped BLD to be used on adaptive mesh refinement (AMR) meshes for thick transport applications without adding additional degrees of freedom at hanging nodes that exist on refinement boundaries. We analyze the properties of the upwinding and lumping that are needed for BLD to get the thick diffusion limit on such meshes, present results demonstrating locking with the wrong recipe, and present results showing error convergence and robustness properties for two diffusive problems on a variety of AMR meshes.
42 ENGINEERING↗
An adaptively-refined Cartesian mesh solver for the Euler equations
A method for adaptive refinement of a Cartesian mesh for the solution of the steady Euler equations is presented. The algorithm creates an initial uniform mesh and cuts the body out of that mesh. The mesh is then refined based on body curvature. Next, the solution is converged to a steady state using a linear reconstruction and Roe's approximate Riemann solver. Solution-adaptive refinement of the mesh is then applied to resolve high-gradient regions of the flow. The numerical results presented show the flexibility of this approach and the accuracy attainable by solution-based refinement.
De Zeeuw, Darren↗
High Fidelity Adaptively Refined CFD and Reduced Order Models of a High Aspect Ratio Aeroelastic Wing Wind Tunnel Model
Robust adaptive mesh refinement for transonic conditions is one of the most difficult challenges to advancing CFD usage for certification by analysis. Transonic fluid-structure interaction cases represent an even more difficult challenge for adaptive mesh refinement. Production aircraft furthermore have structural models that have gaps and discontinuities that make the interdomain transfer of loads and deflections difficult. This adds to the challenge of adaptive mesh refinement. An initial attempt to create an adaptive mesh refinement process that refines regions of high flow gradient based around the HeldenMesh software is presented. The method is applied to the Integrated Adaptive Wing Technology Maturation (IAWTM) configuration. That has developed an aspect ratio 13.5 wing aeroelastic wind-tunnel model for testing in the Transonic Dynamics Tunnel (TDT). The high levels of deformation of this wing make the adaptation of meshes for the static shape difficult and has necessitated some creativity in how to efficiently adapt meshes. A time-domain identification of the unsteady system based on flexible modes using the adapted meshes is performed.
Robert E. Bartels↗
An efficient second-order adaptive procedure for inserting CAD geometries into hexahedral meshes using volume fractions
Here, this paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The procedure consists of two steps. The first step performs spatial acceleration using a k-d tree. The second step involves subdividing individual hexahedra in an adaptive mesh refinement (AMR)-like fashion and approximating the CAD geometry linearly (as a plane) at the finest subdivision. The procedure requires only two geometric queries from a CAD kernel: determining whether or not a queried spatial coordinate is inside or outside the CAD geometry and determining the closest point on the CAD geometry’s surface from a given spatial coordinate. We prove that the procedure is second-order accurate for sufficiently smooth geometries and sufficiently refined background meshes. We demonstrate the expected order of accuracy is achieved with several verification tests and illustrate the procedure’s effectiveness for several exemplar CAD geometries.
Adaptive↗