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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Fuselage Structure Response to Boundary Layer, Tonal Sound, and Jet Noise

Experiments have been conducted to study the response of curved aluminum and graphite-epoxy fuselage structures to flow and sound loads from turbulent boundary layer, tonal sound, and jet noise. Both structures were the same size. The aluminum structure was reinforced with tear stoppers, while the graphite-epoxy structure was not. The graphite-epoxy structure weighed half as much as the aluminum structure. Spatiotemporal intermittence and chaotic behavior of the structural response was observed, as jet noise and tonal sound interacted with the turbulent boundary layer. The fundamental tone distributed energy to other components via wave interaction with the turbulent boundary layer. The added broadband sound from the jet, with or without a shock, influenced the responses over a wider range of frequencies. Instantaneous spatial correlation indicates small localized spatiotemporal regions of convected waves, while uncorrelated patterns dominate the larger portion of the space. By modifying the geometry of the tear stoppers between panels and frame, the transmitted and reflected waves of the aluminum panels were significantly reduced. The response level of the graphite-epoxy structure was higher, but the noise transmitted was nearly equal to that of the aluminum structure. The fundamental shock mode is between 80 deg and 150 deg and the first harmonic is between 20 deg and 80 deg for the underexpanded supersonic jet impinging on the turbulent boundary layer influencing the structural response. The response of the graphite-epoxy structure due to the fundamental mode of the shock impingement was stabilized by an externally fixed oscillator.

Maestrello, L.↗
NASA NTRS1987

Vortex shedding in compressor blade wakes

The wakes of highly loaded axial compressor blades were often considered to be turbulent, unstructured flows. Recent work has suggested that the blade wakes are in fact dominated by a vortex street-like structure. The work on the wake structure at MIT is reviewed, the results of a viscous numerical simulation are presented, the blade wake vortices are compared to those shed from a cylinder, and the implications of the wake structure on compressor performance are discussed. In particular, a two-dimensional, time accurate, viscous calculation shows both a periodic wake structure and time variations in the passage shock strength. The numerical calculations are compared to laser anemometer and high frequency response probe data. The effect of the wake structure on the entropy production and apparent adiabatic efficiency of the compressor rotor is discussed.

Epstein, A. H.↗
NASA NTRS1981

Supersonic Stall Flutter of High Speed Fans

An analytical model is developed for predicting the onset of supersonic stall bending flutter in axial flow compressors. The analysis is based on a modified two dimensional, compressible, unsteady actuator disk theory. It is applied to a rotor blade row by considering a cascade of airfoils whose geometry and dynamic response coincide with those of a rotor blade element at 85 percent of the span height (measured from the hub). The rotor blades are assumed to be unshrouded (i.e., free standing) and to vibrate in their first flexural mode. The effects of shock waves and flow separation are included in the model through quasi-steady, empirical, rotor total-pressure-loss and deviation-angle correlations. The actuator disk model predicts the unsteady aerodynamic force acting on the cascade blading as a function of the steady flow field entering the cascade and the geometry and dynamic response of the cascade. Calculations show that the present model predicts the existence of a bending flutter mode at supersonic inlet Mach numbers. This flutter mode is suppressed by increasing the reduced frequency of the system or by reducing the steady state aerodynamic loading on the cascade. The validity of the model for predicting flutter is demonstrated by correlating the measured flutter boundary of a high speed fan stage with its predicted boundary. This correlation uses a level of damping for the blade row (i.e., the log decrement of the rotor system) that is estimated from the experimental flutter data. The predicted flutter boundary is shown to be in good agreement with the measured boundary.

Adamczyk, J. J.↗
NASA NTRS1989

Transonic airfoil design for helicopter rotor applications

Despite the fact that the flow over a rotor blade is strongly influenced by locally three-dimensional and unsteady effects, practical experience has always demonstrated that substantial improvements in the aerodynamic performance can be gained by improving the steady two-dimensional charateristics of the airfoil(s) employed. The two phenomena known to have great impact on the overall rotor performance are: (1) retreating blade stall with the associated large pressure drag, and (2) compressibility effects on the advancing blade leading to shock formation and the associated wave drag and boundary-layer separation losses. It was concluded that: optimization routines are a powerful tool for finding solutions to multiple design point problems; the optimization process must be guided by the judicious choice of geometric and aerodynamic constraints; optimization routines should be appropriately coupled to viscous, not inviscid, transonic flow solvers; hybrid design procedures in conjunction with optimization routines represent the most efficient approach for rotor airfroil design; unsteady effects resulting in the delay of lift and moment stall should be modeled using simple empirical relations; and inflight optimization of aerodynamic loads (e.g., use of variable rate blowing, flaps, etc.) can satisfy any number of requirements at design and off-design conditions.

Hassan, Ahmed A.↗
NASA NTRS1985

The location of the subsolar bow shock of Venus - Implications for the obstacle shape

The rise in periapsis altitude with time has allowed the Pioneer Venus spacecraft to begin probing the subsolar Venus bow shock. This has allowed the altitude of the subsolar bow shock to be determined by in situ observations for the first time. The observed altitude of 2280 km at the nose together with the previously determined terminator altitude can be used to infer the shape of the obstacle using the gasdynamic model of the solar wind interaction with Venus. When this shape is compared to the measured locations of the Venus ionopause (defined as the point where the magnetosheath magnetic field pressure and ionospheric thermal pressures are equal), it is found that the observed ionopause position is too low to qualify as the obstacle. It is inferred that a layer of the mass loaded plasma in the magnetosheath forms the magnetic barrier.

Russell, C. T.↗
NASA NTRSDate not supplied

Coherence Analysis of the Space Launch System using Unsteady Pressure Sensitive Paint

Transonic buffet forces are a major source of unsteady loading on launch vehicles, thus requiring accurate estimation for efficient vehicle design. The state of the art in modeling these unsteady loads utilizes wind-tunnel tests where the fluctuating pressures are measured by pressure transducers (PTs) at discrete locations on a rigid buffet model. These pressures are then integrated over the surface of the vehicle to yield a series of orthogonal centerline loads called buffet forcing functions (BFFs). Typically, the PT layout aims at resolving the pressure correlation along the longitudinal axis of the vehicle. As a result, the distribution of azimuthal correlation and its impact on the estimated BFFs are not well known. To fill these gaps, extremely high-spatial-resolution uPSP data were collected for three different configurations of the Space Launch System in the NASA Ames Research Center 11-Foot Transonic Unitary Plan Wind Tunnel. The spatio-temporal behavior of the pressure correlation on these vehicles is analyzed and flow features of interest are investigated. It is shown that terminal shocks interacting with turbulence are a source of increased azimuthal coherence, especially when the shock develops at a junction. Vortex shedding off the forward attachment hardware that connects the core stage to the solid rocket boosters (SRBs) is the most severe buffet environment on the vehicle. The associated fluctuating pressures are shown to be highly coherent as far as the vehicle tail and up to 40 degrees away from the boosters. For selected areas of the vehicle, factoring the azimuthal coherence into the attenuation of discrete-measurements-based BFFs results in under prediction relative to the BFFs obtained from full integration of the uPSP data.

buffet↗
NASA NTRS1983

The prediction of the noise of supersonic propellers in time domain - New theoretical results

In this paper, a new formula for the prediction of the noise of supersonic propellers is derived in the time domain which is superior to the previous formulations in several respects. The governing equation is based on the Ffowcs Williams-Hawkings (FW-H) equation with the thickness source term replaced by an equivalent loading source term derived by Isom (1975). Using some results of generalized function theory and simple four-dimensional space-time geometry, the formal solution of the governing equation is manipulated to a form requiring only the knowledge of blade surface pressure data and geometry. The final form of the main result of this paper consists of some surface and line integrals. The surface integrals depend on the surface pressure, time rate of change of surface pressure, and surface pressure gradient. These integrals also involve blade surface curvatures. The line integrals which depend on local surface pressure are along the trailing edge, the shock traces on the blade, and the perimeter of the airfoil section at the inner radius of the blade. The new formulation is for the full blade surface and does not involve any numerical observer time differentiation. The method of implementation on a computer for numerical work is also discussed.

Farassat, F.↗
NASA NTRS1995

Vibrational and Electronic Energy Transfer and Dissociation of Diatomic Molecules by Electron Collisions

At high altitudes and velocities equal to or greater than the geosynchronous return velocity (10 kilometers per second), the shock layer of a hypersonic flight will be in thermochemical nonequilibrium and partially ionized. The amount of ionization is determined by the velocity. For a trans atmospheric flight of 10 kilometers per second and at an altitude of 80 kilometers, a maximum of 1% ionization is expected. At a velocity of 12 - 17 kilometer per second, such as a Mars return mission, up to 30% of the atoms and molecules in the flow field will be ionized. Under those circumstances, electrons play an important role in determining the internal states of atoms and molecules in the flow field and hence the amount of radiative heat load and the distance it takes for the flow field to re-establish equilibrium. Electron collisions provide an effective means of transferring energy even when the electron number density is as low as 1%. Because the mass of an electron is 12,760 times smaller than the reduced mass of N2, its average speed, and hence its average collision frequency, is more than 100 times larger. Even in the slightly ionized regime with only 1% electrons, the frequency of electron-molecule collisions is equal to or larger than that of molecule-molecule collisions, an important consideration in the low density part of the atmosphere. Three electron-molecule collision processes relevant to hypersonic flows will be considered: (1) vibrational excitation/de-excitation of a diatomic molecule by electron impact, (2) electronic excitation/de-excitation, and (3) dissociative recombination in electron-diatomic ion collisions. A review of available data, both theory and experiment, will be given. Particular attention will be paid to tailoring the molecular physics to the condition of hypersonic flows. For example, the high rotational temperatures in a hypersonic flow field means that most experimental data carried out under room temperatures are not applicable. Also, the average electron temperature is expected to be between 10,000 and 20,000 K. Thus only data for low energy electrons are relevant to the model.

Huo, Winifred M.↗
DOE OSTI2022

Physics Guided Simulation of Electrostatic Discharge: Technical Report

Triboelectrically-charged objects may create threshold sparks, electrostatic discharge (ESD) events, to equilibrate charge between themselves and other relatively charged objects. ESD events exhibit many complex physical phenomena. They are a nexus of several fields of physics with disparate characteristic scales: plasma physics, chemical kinetics, hydrodynamics, circuit models, etc. These scales can span many orders of magnitude from the varied collisions thermalizing information within a plasma on the $\mathcal{O}(fs/ps)$ to the physical size of the plasma channel on the $\mathcal{O}(100µm)$, to the speed of a nonlinear hydrodynamic wave propagating at $\mathcal{O}(µm, ns)$. These threshold ESD events may occur in situations of programmatic importance, delivering energy and power profiles to a “victim load” generating deleterious consequences. To predict and mitigate these consequences we must answer questions about the spark’s energy budget: how much energy goes into producing the spark channel; how much gets radiated away; how much energy is advected away into the hydrodynamics; and how much energy is delivered to a victim load. An ESD simulation toolset has been created and evolved in order to answer these questions. An appropriate, physics guided implementation for simulation can be done by gaining insight into its constituent physics and leveraging that intuition to choose a suitable numerical operator. We examine in detail the chemical kinetics, circuit discharge, and hydrodynamics to deter mine dominant regimes, values, timescales, and interactions to uncover the underlying physical dynamics. We also examine and propose model reduction schemes for high-dimensional chemical kinetics. We use past and current work with experimentally validated and theoretically-verified hydrodynamics to calculate applicability limits of the non-ionizing strong shock limit. We quantify the energy budget from a hydrodynamic perspective and demonstrate that a significant fraction of the stored energy is “earmarked” for hydrodynamic advection as an energy terminus. Lastly, we combine the constituent physics of an ESD event (chemical kinetics, circuit model, and hydrodynamics) into a cohesive, actionable toolset and obtain promising results from an isothermal test case. We then propose a viable, modular evolution of the ESD toolset based upon the performed examination of the physics uncovering dominant physical scales and the stiffness of the compositional differential system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2016

Passive Rocket Diffuser Theory: A Re-Examination of Minimum Second Throat Size

Second-throat diffusers serve to isolate rocket engines from the effects of ambient back pressure during testing without using active control systems. Among the most critical design parameters is the relative area of the diffuser throat to that of the nozzle throat. A smaller second throat is generally desirable because it decreases the stagnation-to-ambient pressure ratio the diffuser requires for nominal operation. There is a limit, however. Below a certain size, the second throat can cause pressure buildup within the diffuser and prevent it from reaching the start condition that protects the nozzle from side-load damage. This paper presents a method for improved estimation of the minimum second throat area which enables diffuser start. The new 3-zone model uses traditional quasi-one-dimensional compressible flow theory to approximate the structure of two distinct diffuser flow fields observed in Computational Fluid Dynamics (CFD) simulations and combines them to provide a less-conservative estimate of the second throat size limit. It is unique among second throat sizing methods in that it accounts for all major conical nozzle and second throat diffuser design parameters within its limits of application. The performance of the 3-zone method is compared to the historical normal shock and force balance methods, and verified against a large number of CFD simulations at specific heat ratios of 1.4 and 1.25. Validation is left as future work, and the model is currently intended to function only as a first-order design tool.

Jones, Daniel R.↗
NASA NTRS2003

Transonic Unsteady Aerodynamics of the F/A-18E at Conditions Promoting Abrupt Wing Stall

A transonic wind tunnel test of an 8% F/A-18E model was conducted in the NASA Langley Research Center (LaRC) 16-Foot Transonic Tunnel (16-Ft TT) to investigate the Abrupt Wing Stall (AWS) characteristics of this aircraft. During this test, both steady and unsteady measurements of balance loads, wing surface pressures, wing root bending moments, and outer wing accelerations were performed. The test was conducted with a wide range of model configurations and test conditions in an attempt to reproduce behavior indicative of the AWS phenomenon experienced on full-scale aircraft during flight tests. This paper focuses on the analysis of the unsteady data acquired during this test. Though the test apparatus was designed to be effectively rigid. model motions due to sting and balance flexibility were observed during the testing, particularly when the model was operating in the AWS flight regime. Correlation between observed aerodynamic frequencies and model structural frequencies are analyzed and presented. Significant shock motion and separated flow is observed as the aircraft pitches through the AWS region. A shock tracking strategy has been formulated to observe this phenomenon. Using this technique, the range of shock motion is readily determined as the aircraft encounters AWS conditions. Spectral analysis of the shock motion shows the frequencies at which the shock oscillates in the AWS region, and probability density function analysis of the shock location shows the propensity of the shock to take on a bi-stable and even tri-stable character in the AWS flight regime.

Schuster, David M.↗
NASA NTRS1991

Periodic blade loads of a high speed propeller at small angle of attack

A code has been developed to predict the periodic aerodynamic loads of an advanced turboprop propeller. The analytical formulation accounts for flow three-dimensionality and flow periodicity due to the propeller inclination. The flow past the blade sections is computed using a thin layer Navier-Stokes solver. An iterative procedure is used to account for the induced axial and rotational velocities. The viscous periodic results are obtained for an eight-bladed Hamilton Standard SR-7L advanced propeller at a cruise Mach number of 0.813 and 35,000 ft. altitude. The results are shown for flow field quantities and performance parameters during the blade passage in the plane of rotation illustrating the periodic nature of blade flow separation and shocks. The time averaged coefficients of thrust and power are computed and compared with available flight test data. The results obtained show excellent agreement at cruise conditions for small nacelle angles of attack.

Takallu, M. A.↗
NASA NTRS1954

Analytical investigation of off-design performance of a transonic turbine

The off-design performance and a breakdown of the losses of a transonic turbine were determined by an analytical method that was previously developed for turbines of more conservative design. The analytically obtained performance map is compared with the performance map obtained from an experimental investigation of the turbine. The rotor hub conditions of incidence angle, relative Mach number, and reaction calculated from the analytical results are compared with those calculated from experimental data. The loss breakdown obtained for the transonic turbine did not differ substantially from that previously obtained from a turbine of more conservative design, except that large stator-exit shock losses were predicted for the transonic turbine at low speeds. The trends of the rotor hub incidence angle, relative Mach number, and reaction calculated from the analytical results agreed well with those calculated from the experimental data over the performance range. These trends indicate that, compared with a turbine of more conservative design, the transonic turbine operated over a much smaller range of incidence angle, a much wider range of rotor relative Mach number, and at a considerably lower level of reaction. Good over-all agreement was obtained between the analytically predicted performance and the experimental performance, except at 40-percent design speed, where in the analysis the stator reached limiting loading before the rotor choked. Since this discrepancy resulted from errors in the simplifying assumptions used in the analysis, it is regarded as a limitation in the analytical method as applied to a transonic turbine.

Whitney, Warren J↗
NASA NTRS2018

Modeling and Flight Performance of Supersonic Disk-Gap-Band Parachutes in Slender Body Wakes

NASA's ASPIRE (Advanced Supersonic Parachute Inflation Research and Experiments) project is investigating the supersonic deployment and inflation of full-scale parachutes. To achieve Mars-relevant conditions, the parachutes are deployed at high altitudes over Earth on a sounding rocket platform. During the flight test, Disk-Gap-Band parachutes of 21.5 meter diameter are deployed behind a slender payload 1/6th the diameter of the blunt Mars2020 capsule. Due to the differences in leading body geometry between the test flight and a parachute deployment at Mars, high fidelity numerical simulations of slender and blunt bodywakes, and of rigid parachutes behind them, were used to understand differences and similarities in the flow and the effect on parachute drag. The slender body wake is thinner, closes earlier, and presents a smaller wake deficit. Thus, a parachute deployed in the wake of a slender body is more likely to see a higher dynamic pressure than a parachute deployed behind a blunt body. In the presence of a parachute, the interaction of the unsteady wake with the parachute bow shock is stronger behind the blunt body. Simulations yield highly unsteady forces on the parachute, which was modeled as a rigid body. The mean parachute force behind a slender body is between 3 and 12 percent higher than behind a blunt body, depending on the angle of the parachute with the flow. As the angle of incidence increases, more of the parachute moves out of the leading body wakes, decreasing the sensitivity to leading body shape. To compare the flow past parachutes in Earth's and Mars' atmospheres, simulations were also performed in CO2. At the Mach number considered (1.75), the shock standoff distance ahead of the parachute, post-shock jump conditions, and the resulting parachute forces were found to be very similar in both air and CO2, indicating that a high altitude test is a good proxy for a Mars descent. The results of these numerical simulations and available data on past flight and wind tunnel tests of supersonic Disk-Gap-Band parachutes behind slender bodies were used to generate a parachute drag model for ASPIRE, which in turn was used to help design the flight test. The first flight test occurred in October 2017. The parachute was successfully deployed at Mach 1.77 and an altitude of 42 kilometers. Test instrumentation provided the atmospheric conditions, test vehicle trajectory, and the loads on the parachute along with detailed high-resolution imagery of the inflation process. Reconstruction of the flight test indicated that the measured forces on the parachute were within the model's bounds, although the model over-predicted the parachute force during the first few seconds. The parachute forces during the long subsonic period were well-predicted by the ASPIRE drag model.

Muppidi, Suman↗
NASA NTRS2016

Flat H Frangible Joint Evolution

Space vehicle staging and separation events require pyrotechnic devices. They are single-use mechanisms that cannot be tested, nor can failure-tolerant performance be demonstrated in actual flight articles prior to flight use. This necessitates the implementation of a robust design and test approach coupled with a fully redundant, failure-tolerant explosive mechanism to ensure that the system functions even in the event of a single failure. Historically, NASA has followed the single failure-tolerant (SFT) design philosophy for all human-rated spacecraft, including the Space Shuttle Program. Following the end of this program, aerospace companies proposed building the next generation human-rated vehicles with off-the-shelf, non-redundant, zero-failure-tolerant (ZFT) separation systems. Currently, spacecraft and launch vehicle providers for both the Orion and Commercial Crew Programs (CCPs) plan to deviate from the heritage safety approach and NASA's SFT human rating requirements. Both programs' partners have base-lined ZFT frangible joints for vehicle staging and fairing separation. These joints are commercially available from pyrotechnic vendors. Non-human-rated missions have flown them numerous times. The joints are relatively easy to integrate structurally within the spacecraft. In addition, the separation event is debris free, and the resultant pyro shock is lower than that of other design solutions. It is, however, a serious deficiency to lack failure tolerance. When used for critical applications on human-rated vehicles, a single failure could potentially lead to loss of crew (LOC) or loss of mission (LOM)). The Engineering and Safety & Mission Assurance directorates within the NASA Johnson Space Center took action to address this safety issue by initiating a project to develop a fully redundant, SFT frangible joint design, known as the Flat H. Critical to the ability to retrofit on launch vehicles being developed, the SFT mechanisms must fit within the same three-dimensional envelope as current designs as well as meet structural loads requirements. There is increased mass associated with the redundant design, and the goal is to minimize the weight impact as much as possible. These requirements presented significant challenges, both technically and financially; these challenges will be explored in this paper. Perhaps greater than the technical issues confronted during this design process, were the financial considerations. These were a significant part of the story of this design and development plan. Insufficient financial and labor resources were formidable barriers to completing this project. Nevertheless, JSC personnel successfully conducted several test series at JSC with very useful results. The many lessons learned drove design improvements, performance efficiency, and increased functional reliability. This paper examines the significant technical and financial challenges that these requirements posed to the project team. It discusses the evolution of the SFT frangible joint design, including optimization, testing, and successful partnering of the Johnson Space Center (JSC) engineering and JSC safety organizations, to enhance the flight safety margin for America's next generation of human-rated space vehicles.

Diegelman, Thomas E.↗
NASA NTRS1992

Physiologically constrained aerocapture for manned Mars missions

Aerobraking has been proposed as a critical technology for manned missions to Mars. The variety of mission architectures currently under consideration presents aerobrake designers with an enormous range of potential entry scenarios. Two of the most important considerations in the design of an aerobrake are the required control authority (lift-to-drag ratio) and the aerothermal environment which the vehicle will encounter. Therefore, this study examined the entry corridor width and stagnation-point heating rate and load for the entire range of probable entry velocities, lift-to-drag ratios, and ballistic coefficients for capture at both Earth and Mars. To accomplish this, a peak deceleration limit for the aerocapture maneuvers had to be established. Previous studies had used a variety of load limits without adequate proof of their validity. Existing physiological and space flight data were examined, and it was concluded that a deceleration limit of 5 G was appropriate. When this load limit was applied, numerical studies showed that an aerobrake with an L/D of 0.3 could provide an entry corridor width of at least 1 degree for all Mars aerocaptures considered with entry velocities up to 9 km/s. If 10 km/s entries are required, an L/D of 0.4 to 0.5 would be necessary to maintain a corridor width of at least 1 degree. For Earth return aerocapture, a vehicle with an L/D of 0.4 to 0.5 was found to provide a corridor width of 0.7 degree or more for all entry velocities up to 14.5 km/s. Aerodynamic convective heating calculations were performed assuming a fully catalytic, 'cold' wall; radiative heating was calculated assuming that the shock layer was in thermochemical equilibrium. Heating rates were low enough for selected entries at Mars that a radiatively cooled thermal protection system might be feasible, although an ablative material would be required for most scenarios. Earth return heating rates were generally more severe than those encountered by the Apollo vehicles, and would require ablative heat shields in all cases.

Lyne, James Evans↗
NASA NTRS1973

High-Tip-Speed, Low-Loading Transonic Fan Stage. Part 1: Aerodynamic and Mechanical Design

A high-tip-speed, low-loading transonic fan stage was designed to deliver an overall pressure ratio of 1.5 with an adiabatic efficiency of 86 percent. The design flow per unit annulus area is 42.0 pounds per square foot. The fan features a hub/tip ratio of 0.46, a tip diameter of 28.74 in. and operates at a design tip speed of 1600 fps. For these design conditions, the rotor blade tip region operates with supersonic inlet and supersonic discharge relative velocities. A sophisticated quasi-three-dimensional characteristic section design procedure was used for the all-supersonic sections and the inlet of the midspan transonic sections. For regions where the relative outlet velocities are supersonic, the blade operates with weak oblique shocks only.

Wright, L. C.↗
DOE OSTI2026

A cell-centered AMR-ALE framework for 3D multi-material hydrodynamics. Part I: Lagrangian and indirect Euler AMR algorithms

Many applications of physics and engineering involve wide ranges of time and spatial scales. The numerical simulation of localized small scales such as shock waves and material interfaces requires a large number of computational cells in these regions. For these applications, Lagrangian and Arbitrary-Lagrangian-Eulerian (ALE) related methods are engaging since the moving mesh feature naturally brings mesh cells on shock discontinuities and material interfaces are carefully captured. In addition, Adaptive-Mesh-Refinement (AMR) strategies aim to optimize computational resources by concentrating finer mesh cells only in areas of interest while using coarser cells elsewhere. A key but challenging AMR requirement consists in efficiently distributing the computational effort to achieve high accuracy without the prohibitive computational costs associated with uniformly fine grids. Here, in this document, the coupling of the p4est AMR library with a cell-centered Lagrangian scheme is presented with the goal to perform reliable 3D Lagrangian-AMR and indirect Euler-AMR multi-material simulations. In particular, it is shown that starting from a 3D indirect ALE code, the memory management and load balancing requirements can be delegated to an external library (here the p4est library) to unlock ALE-AMR capabilities. First, we present a strategy to transcribe the octant-based connectivity of the 3D AMR framework with that of an unstructured mesh of polygonal cells used in Lagrangian hydrodynamics. Then, we show how refinement and coarsening operations must be adapted to the particular Lagrangian framework to ensure the conservation of volume during those steps. Finally, several numerical test cases are presented that demonstrate the capabilities of the Lagrangian-AMR and indirect Euler-AMR algorithms.

3D cell-centered Lagrangian numerical scheme↗