Advances in a 10-node composite tetrahedral framework for shock and mesh adaptivity
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Presenting this work at USNCCM
In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used to project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.
We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.
A flexible framework for the development of block structured volume grids for hypersonic Navier-Stokes flow simulations was developed for analysis of the Shuttle Orbiter Columbia. The development of the flexible framework, resulted in an ability to quickly generate meshes to directly correlate solutions contributed by participating groups on a common surface mesh, providing confidence for the extension of the envelope of solutions and damage scenarios. The framework draws on the experience of NASA Langely and NASA Ames Research Centers in structured grid generation, and consists of a grid generation process that is implemented through a division of responsibilities. The nominal division of labor consisted of NASA Johnson Space Center coordinating the damage scenarios to be analyzed by the Aerothermodynamics Columbia Accident Investigation (CAI) team, Ames developing the surface grids that described the computational volume about the orbiter, and Langely improving grid quality of Ames generated data and constructing the final volume grids. Distributing the work among the participants in the Aerothermodynamic CIA team resulted in significantly less time required to construct complete meshes than possible by any individual participant. The approach demonstrated that the One-NASA grid generation team could sustain the demand for new meshes to explore new damage scenarios within a aggressive timeline.
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
Purpose: To demonstrate the ability to quickly generate an accurate collision avoidance map using multiple stereotactic cameras during simulation. Methods: Three Kinect stereotactic cameras were placed in the CT simulation room and optically calibrated to the DICOM isocenter. Immediately before scanning, the patient was optically imaged to generate a 3D polygon mesh, which was used to calculate the collision avoidance area using our previously developed framework. The mesh was visually compared to the CT scan body contour to ensure accurate coordinate alignment. To test the accuracy of the collision calculation, the patient and machine were physically maneuvered in the treatment room to calculated collision boundaries. Results: The optical scan and collision calculation took 38.0 seconds and 2.5 seconds to complete respectively. The collision prediction accuracy was determined using a receiver operating curve (ROC) analysis, where the true positive, true negative, false positive and false negative values were 837, 821, 43, and 79 points respectively. The ROC accuracy was 93.1% over the sampled collision space. Conclusion: We have demonstrated a framework which is fast and accurate for predicting collision avoidance for treatment which can be determined during the normal simulation process. Because of the speed, the system could be used to add a layer of safety with a negligible impact on the normal patient simulation experience. This information could be used during treatment planning to explore the feasible geometries when optimizing plans. Research supported by Varian Medical Systems.
Boundary conditions appropriate for simulating flow entering or exiting the computational domain to mimic propulsion effects have been implemented in an adaptive Cartesian simulation package. A robust iterative algorithm to control mass flow rate through an outflow boundary surface is presented, along with a formulation to explicitly specify mass flow rate through an inflow boundary surface. The boundary conditions have been applied within a mesh adaptation framework based on the method of adjoint-weighted residuals. This allows for proper adaptive mesh refinement when modeling propulsion systems. The new boundary conditions are demonstrated on several notional propulsion systems operating in flow regimes ranging from low subsonic to hypersonic. The examples show that the prescribed boundary state is more properly imposed as the mesh is refined. The mass-flowrate steering algorithm is shown to be an efficient approach in each example. To demonstrate the boundary conditions on a realistic complex aircraft geometry, two of the new boundary conditions are also applied to a modern low-boom supersonic demonstrator design with multiple flow inlets and outlets.
Here, in this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.
In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes—wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries—and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement. In part two, several applications of the implicit mesh dG framework in two and three dimensions are presented, including examples of single phase flow in nontrivial geometry, surface tension-driven two phase flow with phase-dependent fluid density and viscosity, rigid body fluid–structure interaction, and free surface flow. A class of techniques known as interfacial gauge methods is adopted to solve the corresponding incompressible Navier–Stokes equations, which, compared to archetypical projection methods, have a weaker coupling between fluid velocity, pressure, and interface position, and allow high-order accurate numerical methods to be developed more easily. Convergence analyses conducted throughout the work demonstrate high-order accuracy in the maximum norm for all of the applications considered; for example, fourth-order spatial accuracy in fluid velocity, pressure, and interface location is demonstrated for surface tension-driven two phase flow in 2D and 3D. Specific application examples include: vortex shedding in nontrivial geometry, capillary wave dynamics revealing fine-scale flow features, falling rigid bodies tumbling in unsteady flow, and free surface flow over a submersed obstacle, as well as high Reynolds number soap bubble oscillation dynamics and vortex shedding induced by a type of Plateau–Rayleigh instability in water ripple free surface flow. In conclusion, these last two examples compare numerical results with experimental data and serve as an additional means of validation; they also reveal physical phenomena not visible in the experiments, highlight how small-scale interfacial features develop and affect macroscopic dynamics, and demonstrate the wide range of spatial scales often at play in interfacial fluid flow.
We present a general framework for compressing unstructured scientific data with known local connectivity. A common application is simulation data defined on arbitrary finite element meshes. The framework employs a greedy topology preserving reordering of original nodes which allows for seamless integration into existing data processing pipelines. This reordering process depends solely on mesh connectivity and can be performed offline for optimal efficiency. However, the algorithm’s greedy nature also supports on-the-fly implementation. The proposed method is compatible with any compression algorithm that leverages spatial correlations within the data. The effectiveness of this approach is demonstrated on a large-scale real dataset using several compression methods, including MGARD, SZ, and ZFP.
Abstract We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC–AE) has been shown to capture nonlinear solution manifolds but fails to perform adequately when linear subspace approaches such as proper orthogonal decomposition (POD) would be optimal. Besides, most DL-ROM models rely on convolutional layers, which might limit its application to only a structured mesh. The proposed framework in this study relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning, where BT maximizes the information content of the embedding with the latent space through a joint embedding architecture. Through a series of benchmark problems of natural convection in porous media, BT–AE performs better than the previous DL-ROM framework by providing comparable results to POD-based approaches for problems where the solution lies within a linear subspace as well as DL-ROM autoencoder-based techniques where the solution lies on a nonlinear manifold; consequently, bridges the gap between linear and nonlinear reduced manifolds. We illustrate that a proficient construction of the latent space is key to achieving these results, enabling us to map these latent spaces using regression models. The proposed framework achieves a relative error of 2% on average and 12% in the worst-case scenario (i.e., the training data is small, but the parameter space is large.). We also show that our framework provides a speed-up of $$7 \times 10^{6}$$ 7 × 10 6 times, in the best case, and $$7 \times 10^{3}$$ 7 × 10 3 times on average compared to a finite element solver. Furthermore, this BT–AE framework can operate on unstructured meshes, which provides flexibility in its application to standard numerical solvers, on-site measurements, experimental data, or a combination of these sources.
A series of scale-resolving simulations of flow over the ONERA OAT15A airfoil have been performed at an angle of attack of 3.5◦, just past the onset of buffet. The focus of this study is to document the sensitivity of the wall-modeled large eddy simulation (WMLES) methodology for curvilinear structured overset grids within the Launch, Ascent, and Vehicle Aerodynamics (LAVA) framework to mesh spacing, mesh distribution, and domain size. A secondary purpose of the study is to compare the results from WMLES to unsteady Reynolds-averaged Navier Stokes (URANS) simulations and hybrid RANS-LES (HRLES) within the same LAVA solver framework. The study provides a unique perspective regarding comparisons between different turbulence modeling approaches, time-integration methods, and computational performance since many of the same numerical routines are used for all three types of simulations. The results are compared with experiments and previous numerical studies of the same geometry and flow conditions.
Here, we introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multiphysical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp gradients of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after remeshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal values and directions are projected onto smooth fields interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator in general leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the remeshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain.
The Oak Ridge Leadership Computing Facility (OLCF) has been preparing the nation's first exascale system, Frontier, for production and end users. Frontier is based on HPE Cray's new EX architecture and Slingshot interconnect and features 74 cabinets of optimized 3rd Gen AMD EPYC CPUs for HPC and AI and AMD Instinct 250X accelerators. As a part of this preparation, “real-world” user codes have been selected to help assess the functionality, performance, and usability of the system. This article describes early experiences using the system in collaboration with the Hamburg Observatory for two selected codes, which have since been adopted in the OLCF test harness. Experiences discussed include efforts to resolve performance variability and per-cycle slowdowns. Results are shown for a performance portable astrophysical magnetohydronamics code, AthenaPK, and a mini-application stressing the core functionality of a performance portable block-structured adaptive mesh refinement framework, Parthenon-Hydro. Here, these results show good scaling characteristics to the full system. At the largest scale, the Parthenon-Hydro miniapp reaches a total of $1.7$ $\times$ $10^{13}$ zone-cycles/s on 9216 nodes (73,728 logical GPUs) at ≈92% weak scaling parallel efficiency (starting from a single node using a second-order, finite-volume method).
The ExaStar project aims to deliver an efficient, versatile, and portable software ecosystem for multi-physics astrophysics simulations run on exascale machines. The code suite is a component-based multi-physics toolkit, built on the capabilities of current simulation codes (in particular Flash-X and Castro), and based on the massively parallel adaptive mesh refinement framework AMReX. It includes modules for hydrodynamics, advanced radiation transport, thermonuclear kinetics, and nuclear microphysics. The code will reach exascale efficiency by building upon current multi- and many-core packages integrated into an orchestration system that uses a combination of configuration tools, code translators, and a domain-specific asynchronous runtime to manage performance across a range of platform architectures. The target science includes multi-physics simulations of astrophysical explosions (such as supernovae and neutron star mergers) to understand the cosmic origin of the elements and the fundamental physics of matter and neutrinos under extreme conditions.
Interactions of flows of partially ionized, magnetized plasma are frequently accompanied by the presence of both thermal and non-thermal (pickup) ion components. Such interactions cannot be modeled using traditional MHD equations and require more advanced approaches to treat them. If a nonthermal component of ions is formed due to charge exchange and collisions between the thermal (core) ions and neutrals, it experiences the action of magnetic field, its distribution function is isotropized, and it soon acquires the velocity of the ambient plasma without being thermodynamically equilibrated. This situation, e. g., takes place in the outer heliosphere –- the part of interstellar space beyond the solar system whose properties are determined by the solar wind interaction with the local interstellar medium. This is also possible in laboratory, at million degrees and above, when plasma is conducting electricity far too well, which makes Ohmic heating ineffective. To attain the target temperatures one needs additional heating eventually playing a dominant role. Among such sources is a so-called neutral particle beam heating. This is a wide-spread technique (Joint European Torus and International Thermonuclear Experimental Reactor experiments) based on the injection of powerful beams of neutral atoms into ohmically preheated plasma. In this project we have investigated the energy and density separation between the thermal and nonthermal components in the solar wind and interstellar plasmas. A new model has been developed in which we solve the ideal MHD equations for mixture of all ions and the kinetic Boltzmann equation to describe the transport of neutral atoms. As a separate capability, we can treat the flow of neutral atoms in a multi-component fashion, where neutral atoms born in each thermodynamically distinct region are governed by the Euler gas dynamic equations. We also describe the behavior of pickup ions either kinetically, using the Fokker--Planck equation, or as a separate fluid. Our numerical simulations have demonstrated that pickup ions play a major role in the interaction of the solar wind and (partially ionized) interstellar medium plasmas. Our teams have investigated the stability of the surface (the heliopause) that separates the solar wind from the local interstellar medium, the transport of galactic cosmic rays, the properties of the heliotail flow, and modifications to the bow wave in front of the heliopause due to charge exchange between the neutral H atoms born in the solar wind and interstellar ions. Modeling results have been validated against observational data, such as obtained by the Interstellar Boundary Explorer (IBEX), and made it possible to shed light on the structure of energetic neutral atom maps created by this spacecraft.. We have also demonstrated that charge-exchange modulated heliosphere is a source of anisotropy of the multi-TeV cosmic ray flux observed in a number of Earth-bound air shower experiments. Newly developed codes are implemented within a Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS), a publicly available code being developed by our team for over 12 years. MS-FLUKSS scales well up to 160,000 computing cores and has been ported on major supercomputers in the country. Efficient parallelization and data choreography in the continuum simulation modules are provided by Chombo, an adaptive mesh refinement framework managed by Phillip Colella's team at LBNL. We have implemented in-house, hybrid (MPI+OpenMP) parallelization of the kinetic modules that solve the Boltzmann equation with a Monte Carlo method. Currently, the kinetic modules are being rewritten to take advantage of the modern CPU-GPU supercomputer architecture. The scope of the project allowed us to enhance plasma research and education in such broad, multidisciplinary field as physics of partially ionized plasma and its application to space physics and fusion science. Besides the impact on the modeling of complex physical systems, our approach to computational resource management for complex codes utilizing multiple algorithm technologies appears to be a major advance on current approaches. The development of sophisticated resource management will be essential for all future modeling efforts that incorporate a diversity of scales and physical processes. Our effort provided leadership in promoting computational science and plasma physics within the UAH and FIT campuses and, through the training of a broad spectrum of scientists and engineers, fostering new technologies across the country.
Interactions of flows of partially ionized, magnetized plasma are frequently accompanied by the presence of both thermal and non-thermal (pickup) ion components. Such interactions cannot be modeled using traditional MHD equations and require more advanced approaches to treat them. If a nonthermal component of ions is formed due to charge exchange and collisions between the thermal (core) ions and neutrals, it experiences the action of magnetic field, its distribution function is isotropized, and it soon acquires the velocity of the ambient plasma without being thermodynamically equilibrated. This situation, e. g., takes place in the outer heliosphere - the part of interstellar space beyond the solar system whose properties are determined by the solar wind interaction with the local interstellar medium. This is also possible in laboratory, at million degrees and above, when plasma is conducting electricity far too well, which makes Ohmic heating ineffective. To attain the target temperatures one needs additional heating eventually playing a dominant role. Among such sources is a so-called neutral particle beam heating. This is a wide-spread technique (Joint European Torus and International Thermonuclear Experimental Reactor experiments) based on the injection of powerful beams of neutral atoms into ohmically preheated plasma. In this project we have investigated the energy and density separation between the thermal and nonthermal components in the solar wind and interstellar plasmas. A new model has been developed in which we solve the ideal MHD equations for mixture of all ions and the kinetic Boltzmann equation to describe the transport of neutral atoms. As a separate capability, we can treat the flow of neutral atoms in a multi-component fashion, where neutral atoms born in each thermodynamically distinct regions are governed by the Euler gas dynamic equations. We also describe the behavior of pickup ions either kinetically, using the Fokker–Planck equation, or as a separate fluid. Our numerical simulations have demonstrated that pickup ions play a major role in the interaction of the solar wind and (partially ionized) interstellar medium plasmas. Our teams have investigated the stability of the surface (the heliopause) that separates the solar wind from the local interstellar medium, the transport of galactic cosmic rays, the properties of the heliotail flow, and modifications to the bow wave in front of the heliopause due to charge exchange between the neutral H atoms born in the solar wind and interstellar ions. Modeling results have been validated against observational data, such as obtained by the Interstellar Boundary Explorer (IBEX), and made it possible to shed light on the structure of energetic neutral atom maps created by this spacecraft.. We have also demonstrated that charge-exchange modulated heliosphere is a source of anisotropy of the multi-TeV cosmic ray flux observed in a number of Earth-bound air shower experiments. Newly developed codes are implemented within a Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS), a publicly available code being developed by our team for over 12 years. MS-FLUKSS scales well up to 160,000 computing cores and has been ported on major supercomputers in the country. Efficient parallelization and data choreography in the continuum simulation modules are provided by Chombo, an adaptive mesh refinement framework managed by Phillip Colella’s team at LBNL. We have implemented in-house, hybrid (MPI+OpenMP) parallelization of the kinetic modules that solve the Boltzmann equation with a Monte Carlo method. Currently, the kinetic modules are being rewritten to take advantage of the modern CPU-GPU supercomputer architecture. The scope of the project allowed us to enhance plasma research and education in such broad, multidis- ciplinary field as physics of partially ionized plasma and its application to space physics and fusion science. Besides the impact on the modeling of complex physical systems, our approach to computational resource management for complex codes utilizing multiple algorithm technologies appears to be a major advance on current approaches. The development of sophisticated resource management will be essential for all future modeling efforts that incorporate a diversity of scales and physical processes. Our effort provided leadership in promoting computational science and plasma physics within the UAH and FIT campuses and, through the training of a broad spectrum of scientists and engineers, foster new technologies across the country.