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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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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Modelling the complex evaporated gas flow and its impact on particle spattering during laser powder bed fusion

The additive manufacturing (AM) of metals is becoming an increasingly important production process with the potential to replace traditional techniques such as casting. Laser Powder Bed Fusion (LPBF) is used in many applications to print metal parts from powder. The metal powder is heated locally with sufficient laser radiation that the liquid melt easily reaches its boiling temperature, which leads to a metallic vapour jet that can entrain both powder bed particles and molten droplets. The small size of laser-matter interaction site makes a detailed experimental analysis of the process challenging. Synchrotron X-ray imaging experiments are one of the few methods which can capture the dynamic melting and solidification processes. Comparing such experiments with computer simulations of the process is an important approach in order to better understand the manufacturing process and to analyse the influence of process parameters on the evaporated gas jet and the subsequent impact on particle ejection, leading to potentially reduced AM component quality. The melting and solidification of the metal powder is simulated using an Eulerian multiphase approach based on a control volume discretization of powder bed and substrate and a volume of liquid separation from melt and gas phase. The gas phase modelled as an ideal gas reaches velocities up to 100 m/s. Lagrangian particle tracking in the simulation demonstrates that the velocity fields calculated by the Eulerian multi-phase approach in combination with a standard drag-force model lead to particle accelerations in good agreement with those measured experimentally. In order to avoid numerical laborious Lagrangian calculations, a direct method to compare an Eulerian multiphase simulation with synchrotron X-ray experiments was introduced and validated. This approach is used to analyse the influence of process parameters including laser power and laser speed on the maximal acceleration of particles from the melt pool area. While the particle acceleration increases linearly with line energy in the conduction mode, a linear decrease of the acceleration with increasing line energy can be found in the transition mode before the accel-eration increases again with line energy in the keyhole mode.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Numerical investigation of laser-driven shock interaction with a deformable particle

A laser-driven shock propagating through an isolated particle embedded in a plastic (CH) target was studied using the radiation-hydrodynamic code FLASH. Preliminary simulations using IONMIX equations of state (EOS) showed significant differences in the shock Hugoniot of aluminum compared to experimental data in the low-pressure regime [O(10) GPa], resulting in higher streamwise compression and deformation of an aluminum particle. Hence, a simple modification to the ideal gas EOS was developed and employed to describe the target materials and examine the particle dynamics. The evolution of the pressure field demonstrated a complex wave interaction, resulting in a highly unsteady particle drag which featured two drag minima due to shock focusing at the rear end of the particle and rarefaction stretching due to laser shut-off. Although ~30% lateral expansion and ~25% streamwise compression were observed, the aluminum particle maintained considerable integrity without significant distortion. Additional simulations examined the particle response for a range of particle densities, sizes, and acoustic impedances. The data revealed that lighter particles such as aluminum gained significant momentum, reaching up to ~96% of the shocked CH's speed, compared to ~29% for the heavier tungsten particles. Despite the differences seen in the early stage of shock interaction, particles with varying acoustic impedances ultimately reached the same peak velocity. This identified particle-to-host density ratio is an important factor in determining the inviscid terminal velocity of the particle. In addition, the modified EOS model presented in this study could be used to approximate solid materials in hydrocodes that lack material strength models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Collaborative Research: Unravelling the Physics Associated with the Production of Extremely Dense Plasma States of Microscale (Final Report) Nanosecond-pulsed Discharges

The aim of this project is to study and establish the physical mechanisms that contribute to the formation of anomalously dense plasmas in high-pressure nanosecond-pulsed discharges. These discharges have a broad range of applications such as plasma-assisted combustion, plasma flow actuators, biomedical sterilization and exotic materials synthesis. The structure and formation of these discharges, producing high plasma densities of ~10 14 -10 15 cm -3 , are well-studied and understood. Fast-pulsed microscale high-pressure discharges can be driven to even higher densities of > 10 19 cm -3 , approaching warm dense matter conditions. The mechanisms that generate these plasmas have not been understood. Analysis of the warm dense matter state under laboratory conditions is an expensive and non-trivial endeavor. For instance, dense plasmas can be generated by electrical explosions of metal foils and wires. Plasmas generated after the explosion have a short lifetime and often present difficult conditions for diagnostics. Generation of dense plasmas was also achieved during high-voltage nanosecond pulsed discharges when the so-called explosive electron emission is obtained. Unfortunately, this process is very difficult to control for the studies of warm dense matter. In our recent study, we have shown that additional heating of plasma by lasers can further increase the density of plasma and even lead to the fully ionized state. This method, potentially, allows better control of the plasma parameters. In this work, we studied a second stage laser-heated micro-discharge using a self-consistent one-dimensional particle-in-cell Monte Carlo-collision (1D PIC-MCC) model coupled with Maxwell’s equations. We predicted the generation of a fully ionized plasma on the picosecond time scale. However, this model considered the plasma as an ideal gas despite the high pressure and the nearly fully ionized state. The ideal plasma model assumes that the dilute gas approximation is valid, where the inter-particle interactions are negligible. For charged particles this assumption holds as long as the shielded Coulomb potential assumption is valid. For very high plasma densities, this concept breaks down since the Debye sphere surrounding each charged particle no longer contains enough electrons to statistically provide the shielding of the single particle Coulomb interaction potential. At such densities, the plasma can no longer be described as ideal and non-ideal coupling effects need to be considered. In this report, we elucidate our recent work of developing a PIC-MCC model with improvements for non-ideal plasma conditions due to Coulomb coupling at high densities. In particular, we study the interaction of green light radiation and a dense microplasma, and explore the non-ideal plasma effects in this interaction. In this computational model, we implement the two most important non-ideal effects: ionization potential depression (IPD) and enhanced collision cross sections. Our primary goal is to study the physics associated with electromagnetic (EM) wave heating, also called the second-stage wave-heating, and establish the role of plasma non-ideality in this phenomenon. Our secondary goal is to improve the chemistry mechanism of the 1D PIC-MCC model by including a more detailed excited species collision treatment. At high pressures, stepwise ionization from excited species might play an important role in the ionization process. Previously, this ionization mechanism was neglected due to the excitation collision cross section of xenon being smaller than that of ionization. However, a preliminary study showed that the excited species density in the initial microplasma was an order of magnitude higher than the electron density. Therefore, my aim is to determine the significance of this additional ionization pathway to the plasma generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

PDC Modifications for Analysis of Gas-Cooled Reactors with Direct Helium Brayton Cycle

Capabilities of the Plant Dynamics Code (PDC) have been extended to allow steady-state and transient simulation of graphite-cooled reactors with direct helium Brayton cycle. On the cycle side, the most significant code modification is the addition of helium properties, in the format required by the code’s equations. Since the code was already formulated to handle more complex real gas properties, adding helium as working fluid that behaves like ideal gas was fairly straightforward. A reactor module was added to PDC to simulate a reactor cooled by the working fluid of the Brayton cycle. Two options are supported: channel type, typical for graphite gas-cooled reactors, and pin type, typical for light-water and liquid metal-cooled reactors. The reactor module is an extension of the electrical heater model and simulates heat deposition in the fuel and transfer of this heat from the fuel to the coolant through the matrix and tube materials. The new reactor module becomes the third option in PDC for modeling heat addition to the cycle, besides previously modeled heat addition heat exchanger and electrical heater. In addition to those changes, other minor code modifications and improvements were introduced during the work of expanding PDC to modeling of gas-cooled reactors. These modifications are summarized in the last chapter of this report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Pipeline Hydrogen Decarbonization and Repurposing Analyzers (P-HyDRAs)

The Pipeline Hydrogen Decarbonization and Repurposing Analyzers (P-HyDRAs) are a set of prototype computational tools for simulating and optimizing midstream natural gas pipeline system operations subject to location and time-dependent hydrogen blending. The models can accurately resolve dynamic gas flows through large-scale pipeline networks using non-ideal gas equations of state. The codes can be used as decision support for planning and design decisions involving intra-day energy flow schedules as well as spatiotemporal economic values of natural gas, hydrogen, and net energy delivered to consumers while ensuring that pipeline hydraulic limitations, gas compressor station constraints, operational factors, and pre-existing shipping contracts are satisfied. The inputs to the codes are a model of the pipeline system as well as time-series data that specify boundary conditions on the network. For optimization, the code module requires price and quantity offers for natural gas and hydrogen and price and quantity bids for energy, which are used as time-dependent constraints in an optimal control problem. The outputs are time-series data that provide a predictive simulation of gas flows, mass fractions, and pressures, or with additional degrees of freedom give an approximately optimal solution for gas injections/withdrawals, compressor settings, and sensitivities to the objective function that provide locational values of energy.

Zlotnik, Anatoly↗
DOE OSTI2021

Additively Manufactured Compliant Hybrid Gas Thrust Bearing for Supercritical Carbon Dioxide Turbomachinery: Experimental Evaluation and Fluid–Structure Model Predictions

This paper presents rotating test results and advances an analytical predictive fluid–structure model for a new type of gas-lubricated thrust bearing fabricated using direct metal laser melting. The bearing concept in this study is a compliant hybrid gas thrust bearing that uses external pressurization to increase load carrying capacity, where the testing campaign in this study was only focused on steady-state static performance. The need for the bearing concept comes from enabling highly efficient supercritical carbon dioxide (sCO2) turbomachinery by replacing oil-lubricated bearings with process gas lubrication. Leveraging the process gas of the turbomachine for bearing lubrication results in lowered bearing power loss, simplified mechanical design, and allows for novel oil-free hermetic drivetrains resulting in an efficient emission-free system. The new concept utilizes hydrostatic pressurization on individual tilting pads flexibly mounted with hermetic squeeze film dampers (HSFDs). This paper focuses on rotating tests of a 173 mm outer diameter gas thrust bearing in air up to 10 krpm and hydrostatic inlet pressures to 365 psi (2.52 MPa). The influence of thrust runner speed and bearing inlet pressure on force deflection characteristics and load carrying capability of the gas film were experimentally evaluated. This work also advances a predictive fluid–structure thrust bearing model using an isothermal ideal-gas-based compressible Reynolds flow equation directly coupled to a lumped stiffness element possessing axial and rotational degrees-of-freedom. The rotating testing demonstrated load capability of 1816 lbs (8.1 kN), which equates to a thrust bearing unit load of 67 psi (0.46 MPa). Gas film force–deflection curves reveal a nonlinear relationship between thrust load and film clearance. Comparison of film thickness values with the predictive model show good agreement under high load and inlet pressure, however deviate as load and pressure decrease. Load capability was shown to increase with increasing hydrostatic inlet pressure, while the increase in thrust runner speed revealed a small decrease in load capacity.

Engineering↗
DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems using MOOSE

As an increasing number of companies look toward commercial Inertial Fusion Energy (IFE) designs, there is a pressing need to understand the physics of thick-wall chamber gas dynamics. The thick liquid wall approach implements a renewable wall to mitigate the fusion target emissions, thereby reducing the radiation damage rate and significantly extending the lifetime of chamber structures, leading to increased plant availability and reduced waste streams in comparison to dry wall chamber designs. It is necessary, however, to assess the critical performance and safety aspects of these systems. For example, it is crucial to predict (1) where the mass ablated from the liquid walls will vent, which determines the placement of condensing surfaces; (2) debris propagation up the beam lines, which provides essential information for design and protection requirements; (3) peak pressures and impulse on chamber walls, which affect chamber structural design; and (4) momentum transfer to the liquid jets, which constrains the shape and positioning of the jets. In turn, the chamber design and its liquid walls affect shielding requirements, material activation, and tritium fuel cycle. Currently available simulation tools, however, are unable to accurately capture key thick-wall chamber dynamics. Significant assumptions are often made to simplify the system and reduce computational cost and modeling capability needs, but the impact of these assumptions on simulation predictions has not been evaluated. For example, no three-dimensional simulations can be found in the open literature to evaluate gas venting and momentum transfer to the jets with simulations using two-dimensional domains to represent complex three-dimensional geometries. Moreover, limited studies have been dedicated to jet breakup due to both turbulence and neutron heating, and no studies have been found that evaluate how jet breakup can impact shock-jet interaction. Furthermore, effects of radiative heat transfer have rarely been included for the hydrodynamic phase of shock propagation, and integration of proper equations of state in shock dynamics codes has been mostly exploratory. In this study, we use the flexible, high-fidelity Multiphysics Object-Oriented Simulation Environment (MOOSE) to model these complex phenomena and inform design and safety studies. Capabilities to model thick-wall chamber gas dynamics are being developed, and the impact of the assumptions listed above (i.e., two-dimensional vs three-dimensional, absence of jet breakout, no radiative heat transfer, and ideal gas behavior) are being quantified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems Using MOOSE-based Multiphysics Simulations

As an increasing number of companies look toward commercial Inertial Fusion Energy (IFE) designs, there is a pressing need to understand the physics of thick-wall chamber gas dynamics. The thick liquid wall approach implements a renewable wall to mitigate the fusion target emissions, thereby reducing the radiation damage rate and significantly extending the lifetime of chamber structures, leading to increased plant availability and reduced waste streams in comparison to dry wall chamber designs. It is necessary, however, to assess the critical performance and safety aspects of these systems. For example, it is crucial to predict (1) where the mass ablated from the liquid walls will vent, which determines the placement of condensing surfaces; (2) debris propagation up the beam lines, which provides essential information for design and protection requirements; (3) peak pressures and impulse on chamber walls, which affect chamber structural design; and (4) momentum transfer to the liquid jets, which constrains the shape and positioning of the jets. In turn, the chamber design and its liquid walls affect shielding requirements, material activation, and tritium fuel cycle. Currently available simulation tools, however, are unable to accurately capture key thick-wall chamber dynamics. Significant assumptions are often made to simplify the system and reduce computational cost and modeling capability needs, but the impact of these assumptions on simulation predictions has not been evaluated. For example, no three-dimensional simulations can be found in the open literature to evaluate gas venting and momentum transfer to the jets with simulations using two-dimensional domains to represent complex three-dimensional geometries. Moreover, limited studies have been dedicated to jet breakup due to both turbulence and neutron heating, and no studies have been found that evaluate how jet breakup can impact shock-jet interaction. Furthermore, effects of radiative heat transfer have rarely been included for the hydrodynamic phase of shock propagation, and integration of proper equations of state in shock dynamics codes has been mostly exploratory. In this study, we use the flexible, high-fidelity Multiphysics Object-Oriented Simulation Environment (MOOSE) to model these complex phenomena and inform design and safety studies. Capabilities to model thick-wall chamber gas dynamics are being developed, and the impact of the assumptions listed above (i.e., two-dimensional vs three-dimensional, absence of jet breakout, no radiative heat transfer, and ideal gas behavior) are being quantified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Modeling and optimization of steady flow of natural gas and hydrogen mixtures in pipeline networks

Here, we extend the canonical problems of simulation and optimization of steady-state gas flows in pipeline networks with compressors to the transport of mixtures of highly heterogeneous gases injected throughout a network. Our study is motivated by proposed projects to blend hydrogen generated using clean energy into existing natural gas pipeline systems as part of efforts to reduce the reliance of energy systems on fossil fuels. Flow in a pipe is related to endpoint pressures by a basic Weymouth equation model, with an ideal gas equation of state, where the wave speed depends on the hydrogen concentration. At vertices, in addition to mass balance, we also consider mixing of incoming flows of varying hydrogen concentrations. The problems of interest are the heterogeneous gas flow simulation (HGFS), which determines system pressures and flows given fixed boundary conditions and compressor settings, as well as the heterogeneous gas flow optimization (HGFO), which extremizes an objective by determining optimal boundary conditions and compressor settings. We examine conditions for uniqueness of solutions to the HGFS, as well as compare and contrast mixed-integer and continuous nonlinear programming formulations for the HGFO. We develop computational methods to solve both problems, and examine their performance using four test networks of increasing complexity.

08 HYDROGEN↗
DOE OSTI2019

Implications of real-gas behavior on refractive index calculations for optical diagnostics of fuel–air mixing at high pressures

Three models to compute the refractive index of gaseous mixtures at real gas conditions are presented with the purpose to improve the accuracy of state relationships between refractive index and thermodynamic properties. Models are compared with experimental data to determine one that is applicable to high pressure mixtures with non-ideal thermodynamic behavior near or above a fluids’ critical point. The optimal model is applied to analyze adiabatic thermal mixing of fuel and air at typical diesel engine conditions. Our results show that the ideal gas mixture law is appropriate in the vapor region, assuming it is known, for example, from experimental measurements. Finally, the model is applied for binary fuel-air mixing at supercritical conditions to demonstrate its full potential.

02 PETROLEUM↗
DOE OSTI2020

Investigation of Mixing Law Efficacy for Gaseous Hydrodynamic Simulations

A computational simulation of various mixing laws for gaseous equations of state using planar traveling shocks for multiple mixtures in three dimensions is analyzed against nominal experimental data. Numerical simulations utilize the Sandia National Laboratories shock hydrodynamic code CTH and other codes including the thermochemical equilibrium code TIGER and the uncertainty qualification and sensitivity analysis code DAKOTA. The mixtures are a 1:1 and a 1:3 molar mixture of helium and sulfur hexafluoride. The mixing laws to be analyzed are the ideal gas law, Amagat's Law, Dalton's Law, the BKW EOS, the EXP6 EOS, and the JCZ3 EOS. Examination of the experimental data with TIGER revealed that the shock strength should not be strong enough to turn the mixture non-ideal as the compressibility factor z was essentially unity (z ≈ 1.02). Experimental results show that none of the equations of state are able to accurately predict the properties of the shocked mixture; similar discrepancies have been observed in previous works. Kinetic molecular theory appears to introduce a parameter which offers an explanation regarding the discrepancies. Implementation of the KMT pararneter into the EOS is left for future work.

42 ENGINEERING↗
DOE OSTI2023

Static Self-Energy and Effective Mass of the Homogeneous Electron Gas from Quantum Monte Carlo Calculations

We discuss the methodology of quantum Monte Carlo calculations of the effective mass based on the static self-energy Σ(k,0). We then use variational Monte Carlo calculations of Σ(k,0) of the homogeneous electron gas at various densities to obtain results very close to perturbative G 0 W 0 calculations for values of the density parameter 1 ≤ r s ≤ 10. Here, the obtained values for the effective mass are close to diagrammatic Monte Carlo results and disagree with previous quantum Monte Carlo calculations based on a heuristic mapping of excitation energies to those of an ideal gas.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Optimization techniques in self-similar compressible flow

We investigate the one-dimensional (1D) inviscid compressible flow equations for an ideal gas through the lens of optimization techniques. It is the case that, to our knowledge, optimization analysis applied to the so-called “linear velocity” solutions of the Euler compressible flow equations has not been previously conducted. Through both gradient-based and variational techniques, new variants of well-studied flow scenarios, i.e., self-similar, 1D, linear velocity solution class to idealized inviscid compressible flow equations, are determined, as encoded in both the kinematic and thermodynamic properties of this self-similar solution class. With the kinematics of the said solutions being driven by a self-similar “scale radius” and the thermodynamics being driven separately through the appearance of an arbitrary function, a myriad of new solution classes is possible. Acting as a guide to more realistic physical circumstances as well as discovery, it is the hope that the presented cases serve as the framework for future investigations into the intersection of self-similarity and optimization techniques. Fields of study that may find this work to be of interest include aerodynamic design, flow control, inertial confinement fusion, physics-informed neural networks, and other related areas of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Modeling and simulation of gas separations with spiral–wound membranes

Models for gas separations with spiral–wound membranes are developed and found to exhibit good agreement with experiments performed on N 2 /O 2 mixtures. The two–dimensional (2D) model can be accurately approximated by a one–dimensional (1D) surrogate model when the spacer widths are chosen to make the channel pressure drops small. Subsequently, the separation of propane/propylene mixtures from the recycle purge stream of a polypropylene reactor is investigated. Assuming ideal gas is found to lead to significant overestimations in membrane stage cuts (sometimes more than 10%), an extent comparable to that associated with extrapolating constant olefin permeance from a low–pressure condition. While olefin permeance can change significantly with pressure, using a constant–permeance formulation can result in a small (< 2.5%) underprediction in stage cut if the value for the permeance is taken from the feed condition. Finally, membrane properties and costs necessary for a viable separation process are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Generalized definition of the isothermal compressibility in (2+1)-flavor QCD

We introduce a generalized definition of the isothermal compressibility ($𝜅_{𝑇,𝜎{^2_𝑄}}$) calculable by keeping net conserved charge fluctuations rather than total number densities constant. We present lattice QCD results for this isothermal compressibility, expressed in terms of fluctuations of conserved charges that are related to baryon (𝐵), electric charge (𝑄), and strangeness (𝑆) quantum numbers. This generalized isothermal compressibility is compared with hadron resonance gas model calculations as well as with heavy-ion collision data obtained at RHIC and the LHC. We find $𝜅_{𝑇,𝜎{^2_𝑄}}$ = 13.8⁢(1.3) fm 3 /GeV at $𝑇_{\textrm{pc},0}$ =156.5⁢(1.5) MeV and $\hat{𝜇}_𝐵$ = 0. This finding is consistent with the rescaled result of the ALICE Collaboration, where we replaced the number of charged hadrons (𝑁 ch ) by the total number of hadrons (𝑁 tot ) at freeze-out. Normalizing this result with the QCD pressure (𝑃) we find that the isothermal compressibility on the pseudocritical line stays close to that of an ideal gas, i.e., $𝑃⁢𝜅_{𝑇,𝜎{^2_𝑄}} ≃$ 1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Influence of Real Gas Effects on Chemical Kinetics in Oxycombustion in Supercritical Carbon Dioxide

Oxycombustion in supercritical carbon dioxide is an integral part of the Allam Cycle, a technology that enables carbon-neutral use of fossil-fuels and carbon-negative use of biofuels. We simulate oxycombustion in a realistic combustor geometry for two sets of fuel conditions: pure methane, and a 40 percent methane/60 percent carbon dioxide blend, both at 343.15 K. The fuel jet mixes with a preheated swirler of 20 percent oxygen and 80 percent carbon dioxide at 1005.35 K, with a 100 percent carbon dioxide coflow at 783.15 K. The entire system operates at a pressure of 300 bar, putting the entire system above the critical temperature and pressure of carbon dioxide. Simulations are performed using PeleC, a compressible block-structured adaptive-mesh refinement (AMR) reacting flow code. Direct comparison of results using thermodynamically self-consistent implementations of the ideal gas equation of state and the Soave-Redlich-Kwong (SRK) equation of state allow quantification of the real gas impacts on combustion kinetics, flow temperatures, and pollutant formation.

carbon dioxide↗
DOE OSTI2021

A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Herein, we present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.

97 MATHEMATICS AND COMPUTING↗