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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Exascale models of stellar explosions: Quintessential multi-physics simulation

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.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Collaborative Research: A Model of Partially Ionized Plasma Flows with Kinetic Treatment of Neutral Atoms and Nonthermal Ions

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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Collaborative Research: A Model of Partially Ionized Plasma Flows with Kinetic Treatment of Neutral Atoms and Nonthermal Ions

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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A Moving Embedded Boundary Approach for the Compressible Navier-Stokes Equations in a Block-Structured Adaptive Refinement Framework

A computational technique has been developed to perform compressible flow simulations involving moving boundaries using an embedded boundary approach within the block-structured adaptive mesh refinement (SAMR) framework of AMReX [1], [91], [92]. We leverage the SAMR capability to obtain quantitatively accurate results whilst using robust, second-order finite volume schemes. A conservative, unsplit, cut-cell approach is utilized and a ghost-cell approach is developed for computing the flux on the moving, embedded boundary faces. A third-order least-squares formulation has been developed to compute the wall velocity gradients, and was found to significantly improve the performance of the solver in terms of the quantitative comparison of surface quantities such as the skin friction coefficient. Various test cases are performed to validate the method, and compared with analytical, experimental, and other numerical results in literature. Inviscid and viscous test cases are performed that span a wide regime of flow speeds - acoustic (harmonically pulsating sphere), smooth flows (expansion fan created by a receding piston) and flows with shocks (shock-cylinder interaction, shock-wedge interaction, pitching NACA 0012 airfoil and shock-cone interaction). A closed system with moving boundaries - an oscillating piston in a cylinder, showed that the percentage error in mass within the system decreases with refinement, demonstrating that the numerical scheme is conservative with grid refinement, but is not discretely conservative. Viscous test cases involve that of a horizontally moving cylinder at Re = 40, an inline oscillating cylinder at Re = 100, and a transversely oscillating cylinder at Re = 185. The judicious use of adaptive mesh refinement with appropriate refinement criteria to capture the regions of interest leads to well-resolved flow features, and good quantitative comparison is observed with the results available in literature.

adaptive refinement↗
DOE OSTI2020

Xcompact3D: An open-source framework for solving turbulence problems on a Cartesian mesh

Xcompact3D is a Fortran 90–95 open-source framework designed for fast and accurate simulations of turbulent flows, targeting CPU-based supercomputers. It is an evolution of the flow solver Incompact3D which was initially designed in France in the mid-90’s for serial processors to solve the incompressible Navier–Stokes equations. Incompact3D was then ported to parallel High Performance Computing (HPC) systems in the early 2010’s. Very recently the capabilities of Incompact3D have been extended so that it can now tackle more flow regimes (from incompressible flows to compressible flows at low Mach numbers), resulting in the design of a new user-friendly framework called Xcompact3D. The present manuscript presents an overview of Xcompact3D with a particular focus on its functionalities, its ready-to-run simulations and a few case studies to demonstrate its impact.

17 WIND ENERGY↗
DOE OSTI2019

A data-driven framework for error estimation and mesh-model optimization in system-level thermal-hydraulic simulation

We report over the past decades, several computer codes have been developed for simulation and analysis of thermal-hydraulics and system response in nuclear reactors under operating, abnormal transient, and accident conditions. However, simulation errors and uncertainties still inevitably exist even while these codes have been extensively assessed and used. In this work, a data-driven framework (Optimal Mesh/Model Information System, OMIS) is formulated and demonstrated to estimate simulation error and suggest optimal selection of computational mesh size (i.e., nodalization) and constitutive correlations (e.g., wall functions and turbulence models) for low-fidelity, coarse-mesh thermal-hydraulic simulation, in order to achieve accuracy comparable to that of high-fidelity simulation. Using results from high-fidelity simulations and experimental data with many fast-running low-fidelity simulations, an error database is built and used to train a machine learning model that can determine the relationship between local simulation error and local physical features. This machine learning model is then used to generate insight and help correct low-fidelity simulations for similar physical conditions. The OMIS framework is designed as a modularized six-step procedure and accomplished with state-of-the-art methods and algorithms. A mixed-convection case study was performed to illustrate the entire framework.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Adaptive mesh refinement in stress-constrained topology optimization

We present a topology structural optimization framework with adaptive mesh refinement and stress-constraints. Finite element approximation and geometry representation benefit from such refinement by enabling more accurate stress field predictions and greater resolution of the optimal structural boundaries. We combine a volume fraction filter to impose a minimum design feature size, the RAMP penalization to generate “black-and-white designs” and a RAMP-like stress definition to resolve the “stress singularity problem.” Regions with stress concentrations dominate the optimized design. As such, rigorous simulations are required to accurately approximate the stress field. To achieve this goal, we invoke a threshold operation and mesh refinement during the optimization. We do so in an optimal fashion, by applying adaptive mesh refinement techniques that use error indicators to refine and coarsen the mesh as needed. In this way, we obtain more accurate simulations and greater resolution of the design domain. We present results in two dimensions to demonstrate the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

AMRIC: A Novel In Situ Lossy Compression Framework for Efficient I/O in Adaptive Mesh Refinement Applications

As supercomputers advance towards exascale capabilities, computational intensity increases significantly, and the volume of data requiring storage and transmission experiences exponential growth. Adaptive Mesh Refinement (AMR) has emerged as an effective solution to address these two challenges. Concurrently, error-bounded lossy compression is recognized as one of the most efficient approaches to tackle the latter issue. Despite their respective advantages, few attempts have been made to investigate how AMR and error-bounded lossy compression can function together. To this end, this study presents a novel in-situ lossy compression framework that employs the HDF5 filter to improve both I/O costs and boost compression quality for AMR applications. We implement our solution into the AMReX framework and evaluate on two real-world AMR applications, Nyx and WarpX, on the Summit supercomputer. Experiments with 512 cores demonstrate that AMRIC improves the compression ratio by 81X and the I/O performance by 39X over AMReX's original compression solution.

Wang, Daoce↗
DOE OSTI2026

PDE-constrained high-order mesh optimization

Here, we present a novel framework for PDE-constrained r-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality metric and a measure of the accuracy of the PDE solution obtained via finite element discretization. The proposed formulation achieves optimized, well-defined high-order meshes by integrating mesh quality control, PDE solution accuracy, and robust gradient regularization. We adopt the Target-Matrix Optimization Paradigm to control geometric properties across the mesh, independent of the PDE of interest. To incorporate the accuracy of the PDE solution, we introduce error measures that control the finite element discretization error. The implicit dependence of these error measures on the mesh nodal positions is accurately captured by adjoint sensitivity analysis. Additionally, a convolution-based gradient regularization strategy is used to ensure stable and effective adaptation of high-order meshes. We demonstrate that the proposed framework can improve mesh quality and reduce the error by up to 10 times for the solution of Poisson and linear elasto-static problems. The approach is general with respect to the dimensionality, the order of the mesh, the types of mesh elements, and can be applied to any PDE that admits well-defined adjoint operators.

Computer science↗
DOE OSTI2019

A new micromechanics based full field numerical framework to simulate the effects of dynamic recrystallization on the formability of HCP metals

This work presents a new full-field, efficient and mesh-free numerical framework to model microstructure evolution, dynamic recrystallization (DRX) and formability in hexagonal closed-packed (HCP) metals such as magnesium alloys at warm temperatures. A rate tangent-fast Fourier transform-based elasto-viscoplastic crystal plasticity constitutive model for HCP metals (RTCP-FFT-HCP) is coupled with a probabilistic cellular automata (CA) approach to model DRX (CA-DRX). Furthermore, this new model is coupled with the Marciniak-Kuczynski (M-K) approach to model formability of magnesium alloys at elevated temperatures. The RTCP-FFT-HCP model computes macro stress-strain, twinning volume fraction, micromechanical fields, texture evolution and local dislocation density. Nucleation of new grains and their subsequent growth is modeled using the cellular automata approach with probabilistic state switching rule. First, the proposed RTCP-FFT-HCP model is validated by comparing the predicted stress-strain responses and texture evolution under uniaxial tension and compression with experimental measurements for AZ31 sheet alloy at room temperature. The coupled CA-RTCPFFT-HCP model is further validated by comparing the predicted stress-strain responses and texture evolution in uniaxial compression with experimental measurements at 100 °C, 200 °C and 300 °C for the AZ31 sheet alloy. Next, the forming limit diagrams (FLDs) with and without including the effects of DRX are simulated at 100 °C, 200 °C and 300 °C for AZ31 sheet alloy. The predicted FLDs with DRX show very good agreement with the experimental measurements and clearly demonstrate the need for an accurate DRX model. The study reveals that the DRX strongly affects the deformed grain structure, grain size and texture evolution and also highlights the importance accounting for DRX during FLD simulations at high temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2023

High-Order Mesh hr-adaptivity for Surface Fitting to Implicit Geometries

We present an ℎ𝑟-adaptivity framework for morphing a given mesh to fit a target surface prescribed as the zero isocontour of a discrete function. In this framework, high-order meshing is posed as a variational minimization problem that depends on the mesh quality prescribed via the target matrix optimization paradigm (TMOP) and position of a subset of mesh nodes with respect to the target surface. The proposed formulation ensures that the variational problem is converged and mesh quality degradation near the surface is limited, even when the mesh topology is incompatible with the target surface. Additionally, a mesh subset-based approach and ℎ-refinement is introduced to efficiently increase fitting accuracy while reducing the computational cost of the mesh morphing problem. The ℎ𝑟-adaptivity technique extends to different element types in two- and three-dimensions, and can be used in existing finite element and spectral element frameworks to obtain high-order body-fitted meshes. Various numerical experiments demonstrate the robustness and accuracy of the fitting approach for problems of practical interest such as Lagrangian hydrodynamics and topology optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

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↗
DOE OSTI2019

The Target-Matrix Optimization Paradigm for High-Order Meshes

Here, we describe a framework for controlling and improving the quality of high-order finite element meshes based on extensions of the Target-Matrix Optimization Paradigm (TMOP) of [P. Knupp, Eng. Comput., 28 (2012), pp. 419--429]. This approach allows high-order applications to have a very precise control over local mesh quality, while still improving the mesh globally. We address the adaption of various TMOP components to the settings of general isoparametric element mappings, including the mesh quality metric in 2D and 3D, the selection of sample points and the solution of the resulting mesh optimization problem. We also investigate additional practical concerns, such as tangential relaxation and restricting the deviation from the original mesh. The benefits of the new high-order TMOP algorithms are illustrated on a number of test problems and examples from a high-order arbitrary Lagrangian--Eulerian (ALE) application [BLAST: High-order curvilinear finite elements for shock hydrodynamics, http://www.llnl.gov/CASC/blast]. Our implementation is freely available in an open-source library form [MFEM: Modular parallel finite element methods library, http://mfem.org].

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A hybrid finite volume method and smoothed particle hydrodynamics approach for efficient and accurate blast simulations

Modeling strong shock waves in fluids remains a persistent challenge in computational physics. Essential to research efforts in industry and defense, numerous methods have been devised to improve the accuracy and efficiency of shock simulations. A novel, hybrid Finite Volume Method (FVM)-Smoothed Particle Hydrodynamics (SPH) approach is capable of further improving efficiency and retaining accuracy by exploiting the favorable characteristics of each respective method. This hybrid approach is presented for shock capturing in compressible fluids. The Python framework Pyro2 is employed to simulate a coarse FVM mesh, while the Python framework PySPH is utilized to model the fluid in regions with high gradients through SPH particles. The performance of the hybrid FVM-SPH scheme, compared to the individual FVM and SPH methods, is assessed in 1 kt and 10 kt blast simulations. Our results indicate that the hybrid approach offers higher computational efficiency than SPH while preserving its accuracy and characteristics. The hybrid approach had a relative speedup of 11.3x and 22.3x over the FVM and SPH approaches for the 1 kt simulation and a relative speedup of 14.7x and 20.9x over the FVM and SPH approaches for the 10 kt simulation. The hybrid SPH algorithm enables future compressible fluid simulations with more extensive capabilities than grid-based methods alone, presenting potential applications in modeling fluid-structure interactions and solid deformation and fracturing in blast simulations.

Myers, Conner↗
DOE OSTI2019

Towards improved mesh-designing techniques of spark-ignition engines in the framework of spectral element methods

In the current paper we present an advanced meshing technique to perform high-fidelity numerical simulations in spark ignition (SI) engines. The design of the mesh is critical towards generating physically consistent, high fidelity data especially in regions of complex boundaries inside the cylinder, e.g., near the spark plugs. This is primarily due to the mesh deformation caused by the motion of the valve near the plug and also finer mesh sizes in the spark plug region. In the current work, we demonstrate the use of an overlapping grid (overset) methodology to design the mesh in the spark-plug region in a 2D SI engine-like geometry for a high-order simulation, based on the spectral element method (SEM). The data in the overlapping region is exchanged between the spark-plug geometry and the geometry containing rest of the objects like the piston, cylinder head, valve etc., using a high order spectral interpolation technique. The numerical simulations have been further compared against the standard, single (non-overset) grid, meshing technique for the whole 2D domain. The results further illustrate the capability of overlapping grid methodology in handling mesh deformation compared to the standard grid case and also the ability to capture the flow dynamics with a similar level of fidelity as the standard one

overlapping grids↗
DOE OSTI2021

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method (FEM) for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. We numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular and square meshes where the method coincides with the P 1 - P 0 Scott-Vogelius scheme, which is well-known to be unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. Finally, we numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular meshes, where the method coincides with the $\mathbb{P}_1$ – $\mathbb{P}_0$ Scott-Vogelius scheme, and on square meshes, which are situations that are well-known to be unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

Here, a high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation, and an exact Riemann solver is employed to compute the numerical flux at the interface between dissimilar materials with general anisotropic properties. The space-discretized equations are then advanced in time using explicit high-order Runge–Kutta algorithms. Several two- and three-dimensional numerical tests including dynamic adaptive mesh refinement are presented to demonstrate the high-order accuracy and the capability of the method in the elastodynamic analysis of single- and bi-phases solids containing complex geometries.

42 ENGINEERING↗