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A problem-adaptive solution procedure for improving the reliability of finite element solutions to geometrically nonlinear shell-type problem is presented. The strategy incorporates automatic error detection and control and includes an iterative procedure which utilizes the solution at the same load step on a more refined model. Representative nonlinear shell problem are solved.
A robust rocket engine combustor design and development process must include tools which can accurately predict the multi-dimensional thermal environments imposed on solid surfaces by the hot combustion products. Currently, empirical methods used in the design process are typically one dimensional and do not adequately account for the heat flux rise rate in the near-injector region of the chamber. Computational Fluid Dynamics holds promise to meet the design tool requirement, but requires accuracy quantification, or validation, before it can be confidently applied in the design process. This effort presents the beginning of such a validation process for the Loci- CHEM CPD code. The model problem examined here is a gaseous oxygen (GO2)/gaseous hydrogen (GH2) shear coaxial single element injector operating at a chamber pressure of 5.42 MPa. The GO2/GH2 propellant combination in this geometry represents one the simplest rocket model problems and is thus foundational to subsequent validation efforts for more complex injectors. Multiple steady state solutions have been produced with Loci-CHEM employing different hybrid grids and two-equation turbulence models. Iterative convergence for each solution is demonstrated via mass conservation, flow variable monitoring at discrete flow field locations as a function of solution iteration and overall residual performance. A baseline hybrid grid was used and then locally refined to demonstrate grid convergence. Solutions were also obtained with three variations of the k-omega turbulence model.
When computing the response of an ablating thermal protection system during entry, the aerothermal environment and material response are traditionally computed independently, with the introduction of a blowing correction term in the material response model to account for the outgassing of char and pyrolysis gases. This study presents an approach, where the pyrolysis blowing gases, calculated within the PATO material response code [1], are integrated into the DPLR hypersonic CFD code [2] via a blowing boundary condition. This methodology employs an iterative process, whereby the blown pyrolysis gas products from PATO are incorporated into DPLR, refining surface heating predictions. The NEQAIR code is used to compute radiative heating [3]. The method is applied in computing 3D material response of the Mars 2020 entry. When compared with uncoupled material response, the coupled simulations show a lower surface heat flux initially and a higher heat flux at peak heating as shown in Fig. 1. This is in agreement with previous work using a sphere case with environments from MSL [4].
When computing the response of an ablating thermal protection system during entry, the aerothermal environment and material response are traditionally computed independently, with the introduction of a blowing correction term in the material response model to account for the outgassing of char and pyrolysis gases. This study presents an approach, where the pyrolysis blowing gases, calculated within the PATO material response code, are integrated into the DPLR hypersonic CFD code via a blowing boundary condition. This methodology employs an iterative process, whereby the blown pyrolysis gas products from PATO are incorporated into DPLR, refining surface heating predictions. The NEQAIR code is used to compute radiative heating. The method is applied in computing 3D material response of the Mars 2020 entry. When compared with uncoupled material response, the coupled simulations show a lower surface heat flux initially and a higher heat flux at peak heating as shown in Fig. 1. This is in agreement with previous work using a sphere case with environments from MSL.
The capability of the HL-20 lifting body spacecraft to perform an abort maneuver from the launch pad to a horizontal landing was studied at NASA Langley Research Center. This study involved both piloted and batch simulation models of the vehicle. A point-mass model of the vehicle was used for trajectory optimization studies. The piloted simulation was performed in the Visual Motion Simulator in fixed-base mode. A candidate maneuver was developed and refined for the worst-case launch-pad-to-landing-site geometry using an iterative procedure of off-line maneuver analysis followed by piloted evaluations and heuristic improvements to the candidate maneuver. The resulting maneuver demonstrates the launch site abort capability of the HL-20 and dictates requirements for nominal abort motor performance. The sensitivity of the maneuver to variations in several design parameters was documented.
The capability of the HL-20 lifting body to perform an abort maneuver from the launch pad to a horizontal landing was studied. The study involved both piloted and batch simulation models of the vehicle. A point-mass model of the vehicle was used for trajectory optimization studies. The piloted simulation was performed in the Langley Visual/Motion Simulator in the fixed-base mode. A candidate maneuver was developed and refined for the worst-case launch-pad-to-landing-site geometry with an iterative procedure of off-line maneuver analysis followed by piloted evaluations and heuristic improvements to the candidate maneuver. The resulting maneuver demonstrates the launch-site abort capability of the HL-20 and dictates requirements for nominal abort-motor performance. The sensitivity of the maneuver to variations in several design parameters was documented.
Abstract Plasma edge simulations with codes like SOLPS-ITER are widely employed to interpret fusion experiments. However, numerical errors appearing in such simulations are rarely investigated, despite their potential large impact on simulation results. These errors consist of the statistical error and the bias, both resulting from the finite number of employed EIRENE Monte Carlo particles and incomplete convergence, and the discretization error due to the finite resolution of the computational grids. In this contribution, the resulting numerical errors on simulations of pure deuterium and neon seeded H-mode EAST discharges are examined. The statistical error can be kept small compared to other numerical error contributions by averaging the plasma profiles. This allows investigating the bias and discretization errors using Richardson extrapolation. It is shown that grid refinement and the number of employed Monte Carlo particles have the largest influence on the result, in agreement with similar studies of an ITER deuterium case. For the first time, numerical error bars on the entire simulated target profiles are determined showing that the largest numerical error is 17.9%, mainly due to the plasma grid discretization. On top, also numerical errors on simulated neutral pressures are investigated in detail, for which the statistical error is dominant. The analysis demonstrates which setup is needed to keep numerical errors limited: the SOLPS-ITER averaging procedure should be employed including enough EIRENE particles, and the involved grids should be sufficiently refined to reduce discretization errors.
We study in detail the pressure stabilizing effects of the non-iterated fixed-stress splitting in poromechanical problems which are nearly undrained and incompressible. When applied in conjunction with a spatial discretization which does not satisfy the discrete inf–sup condition, namely a mixed piecewise linear–piecewise constant spatial discretization, the explicit fixed-stress scheme can have a pressure stabilizing effect in transient problems. This effect disappears, however, upon time step refinement or the attainment of steady state. The interpretation of the scheme as an Augmented Lagrangian method similar to Uzawa iteration for incompressible flow helps explain these results. Moreover, due to the slowly evolving solution within undrained seal regions, we show that the explicit fixed-stress scheme requires very large time steps to reveal its pressure stabilizing effect in examples of geologic CO 2 sequestration. We note that large time steps can result in large errors in drained regions, such as the aquifer or reservoir regions of these examples, and can prevent convergence of nonlinear solvers in the case of multiphase flows, which can make the explicit scheme an unreliable source of pressure stabilization. We conclude by demonstrating that pressure jump stabilization is as effective in the explicit fixed-stress setting as in the fully implicit setting for undrained problems, while maintaining the stability and convergence of the fixed-stress split for drained problems.
We present an iterative technique in which model checking and static analysis are combined to verify large software systems. The role of the static analysis is to compute partial order information which the model checker uses to reduce the state space. During exploration, the model checker also computes aliasing information that it gives to the static analyzer which can then refine its analysis. The result of this refined analysis is then fed back to the model checker which updates its partial order reduction. At each step of this iterative process, the static analysis computes optimistic information which results in an unsafe reduction of the state space. However we show that the process converges to a fired point at which time the partial order information is safe and the whole state space is explored.
Matching Pursuit Decomposition (MPD) is a powerful iterative algorithm for signal decomposition and feature extraction. MPD decomposes any signal into linear combinations of its dictionary elements or atoms . A best fit atom from an arbitrarily defined dictionary is determined through cross-correlation. The selected atom is subtracted from the signal and this procedure is repeated on the residual in the subsequent iterations until a stopping criterion is met. The reconstructed signal reveals the waveform structure of the original signal. However, a sufficiently large dictionary is required for an accurate reconstruction; this in return increases the computational burden of the algorithm, thus limiting its applicability and level of adoption. The purpose of this research is to improve the scalability and performance of the classical MPD algorithm. Correlation thresholds were defined to prune insignificant atoms from the dictionary. The Coarse-Fine Grids and Multiple Atom Extraction techniques were proposed to decrease the computational burden of the algorithm. The Coarse-Fine Grids method enabled the approximation and refinement of the parameters for the best fit atom. The ability to extract multiple atoms within a single iteration enhanced the effectiveness and efficiency of each iteration. These improvements were implemented to produce an improved Matching Pursuit Decomposition algorithm entitled MPD++. Disparate signal decomposition applications may require a particular emphasis of accuracy or computational efficiency. The prominence of the key signal features required for the proper signal classification dictates the level of accuracy necessary in the decomposition. The MPD++ algorithm may be easily adapted to accommodate the imposed requirements. Certain feature extraction applications may require rapid signal decomposition. The full potential of MPD++ may be utilized to produce incredible performance gains while extracting only slightly less energy than the standard algorithm. When the utmost accuracy must be achieved, the modified algorithm extracts atoms more conservatively but still exhibits computational gains over classical MPD. The MPD++ algorithm was demonstrated using an over-complete dictionary on real life data. Computational times were reduced by factors of 1.9 and 44 for the emphases of accuracy and performance, respectively. The modified algorithm extracted similar amounts of energy compared to classical MPD. The degree of the improvement in computational time depends on the complexity of the data, the initialization parameters, and the breadth of the dictionary. The results of the research confirm that the three modifications successfully improved the scalability and computational efficiency of the MPD algorithm. Correlation Thresholding decreased the time complexity by reducing the dictionary size. Multiple Atom Extraction also reduced the time complexity by decreasing the number of iterations required for a stopping criterion to be reached. The Course-Fine Grids technique enabled complicated atoms with numerous variable parameters to be effectively represented in the dictionary. Due to the nature of the three proposed modifications, they are capable of being stacked and have cumulative effects on the reduction of the time complexity.
The determination of physical parameters of celestial bodies provides critical navigational and scientific information. Determining the mass, rotation state, and density distribution is an important task of the navigation team on an operational mission. One representation of the internal density distribution, spherical harmonics, may be leveraged to compute the orientation of the principal axis frame of the celestial body, which in turn informs the dynamics of the body’s motion. Using data from NASA’s Dawn mission to the massive asteroids (1) Ceres and (4) Vesta, a method is proposed that refines the knowledge of the principal axis frame by utilizing estimated spherical harmonic coefficients. Applying an iterative rotation scheme to the solved-for body-fixed frame leads to convergence on a frame that is very close to the actual dynamical principal axis frame.
The capabilities of modern artificial intelligence (AI) as a “scientific collaborator” are explored by engaging it with three nuanced problems in quantum optics: state populations in optical pumping, resonant transitions between decaying states (the Burshtein effect), and degenerate mirrorless lasing. Through iterative dialogue, the authors observe that AI models–when prompted and corrected–can reason through complex scenarios, refine their answers, and provide expert-level guidance, closely resembling the interaction with an adept colleague. The findings highlight that AI can democratize access to sophisticated modeling and analysis, shifting the focus in scientific practice from technical mastery to the generation and testing of ideas, and reducing the time for completing research tasks from days to minutes.
Geological interpretations, earthquake source inversions and ground motion modeling, among other applications, require models that jointly resolve crustal and mantle structure. With the second generation of the Collaborative Seismic Earth Model (CSEM2), we present a global multi-resolution tomographic Earth model that serves this purpose. The model evolves through successive regional- and global-scale refinements. While the first generation aggregated regional models, with this study, we ensure consistency between all individual submodels, resulting in a model that accurately explains wave propagation across scales. Recent regional tomographic models were incorporated, comprising continental-scale inversions for Asia and Africa, as well as regional inversions for the Western US, Central Andes, Iran, and Southeast Asia. Across all regional refinements, over 793,000 source-receiver pairs contributed. Moreover, the long-wavelength Earth model (LOWE) introduces large-scale structures outside of pre-existing local refinements. A full-waveform inversion for global anisotropic P-and S-wave speed structure over a total of 194 iterations with a minimum period of 50 s on a large data set of 1 hr of waveform data from 2,423 earthquakes and over 6 million source-receiver pairs ensures that regional updates in the crust and uppermost mantle translate into updates of deeper, global-scale structure. To test the performance of CSEM2, we evaluate waveform fits between observed and synthetic seismograms at 50 s for an independent data set on the global scale, and on the regional scale for lower periods. We accurately simulate waveforms within and across regional refinements, maintaining the original resolution of the submodels embedded in the global framework.
We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.
An exact nonlinear mathematical model that accounts for three-dimensional cascade effects about the inner portions of the rotor blades and compressibility effects about the tip regions of the blades was derived. An artificially time dependent version was iteratively solved by a finite volume technique involving an artificial viscosity and a three-level consecutive mesh refinement. The exact boundary conditions were applied by generating a boundary conforming periodic computation mesh.
The air flow through a propeller-type wind turbine rotor is characterized by three-dimensional rotating cascade effects about the inner portions of the rotor blades and compressibility effects about the tip regions of the blades. In the case of large rotor diameter and/or increased rotor angular speed, the existence of small supersonic zones terminated by weak shocks is possible. An exact nonlinear mathematical model (called a steady Full Potential Equation - FPE) that accounts for the above phenomena has been rederived. An artificially time dependent version of FPE was iteratively solved by a finite volume technique involving an artificial viscosity and a three-level consecutive mesh refinement. The exact boundary conditions were applied by generating a boundary conforming periodic computation mesh.
An algorithm for automating correspondence detection between point clouds composed of multibeam sonar data is presented. This allows accurate initialization for point cloud alignment techniques even in cases where accurate inertial navigation is not available, such as iceberg profiling or vehicles with low-grade inertial navigation systems. Techniques from computer vision literature are used to extract, label, and match keypoints between "pseudo-images" generated from these point clouds. Image matches are refined using RANSAC and information about the vehicle trajectory. The resulting correspondences can be used to initialize an iterative closest point (ICP) registration algorithm to estimate accumulated navigation error and aid in the creation of accurate, self-consistent maps. The results presented use multibeam sonar data obtained from multiple overlapping passes of an underwater canyon in Monterey Bay, California. Using strict matching criteria, the method detects 23 between-swath correspondence events in a set of 155 pseudo-images with zero false positives. Using less conservative matching criteria doubles the number of matches but introduces several false positive matches as well. Heuristics based on known vehicle trajectory information are used to eliminate these.
Introduction: In-Situ Resource Utilization (ISRU) is the process of extracting local resources to produce commodities for propulsion, life support systems, and off-planet construction rather than transporting consumables from Earth. Molten Regolith Electrolysis (MRE) is a novel ISRU method of extracting oxygen gas and metal alloy from lunar regolith. The MRE process involves placing lunar regolith between two electrodes, through which current is passed, to melt the regolith and reduce the metal oxide constituents by direct electrolysis (e.g. FeO, SiO2, MgO, Al2O3) into oxygen gas and metal alloys. The oxygen is liquefied and used as propellant for landers, while the metals (e.g. Ferro-alloys) are further processed and used in structural building materials and parts manufacturing. A system model was developed that accounted for the major processes of an MRE plant (from excavation of raw materials to storage of products) to assess the feasibility of a lunar MRE plant. The System Engineering and Integration (SE&I) ISRU Modeling and Analysis (SIMA) team utilized its previously documented system sizing model, the Mission Analysis and Integration Tool (MAIT) [1] as framework of the system model. MAIT uses MATLAB/Simulink to integrate subsystem models into a complete system model of the MRE plant. Total mass, volume, and power requirements were computed for numerous iterations of a MRE plant. System Model: Figure 1: MRE Plant Block Diagram The regolith excavation model determines the mass and power needed to excavate sufficient regolith. The preheating auger initiates the regolith heating process before regolith enters the MRE re-actor to reduce the energy required to turn the solid into a molten liquid. The MRE reactor is modeled in COMSOL Multiphysics and based on the research by Dominguez, Sibille, and Schreiner [2, 3, 4]. This preliminary reactor model provides an accurate calculation of thermal equilibrium during electrochemical operation of the reactor system to assess the optimal mass and power required to process the inlet flow of regolith. The model also computes the outlet flowrates of oxygen and molten products. For this analysis, the primary components of the metal alloy considered were iron and silicon. The oxygen is then purified using an Yttrium Stabilized Zirconia (YSZ) electrode, followed by liquefaction using a 90K cryocooler to be stored as liquid oxygen in insulated cylindrical tanks. In future iterations of the system model, the molten metal tapped from the MRE reactor will undergo additional processing or refinement. However, downstream handling of metals is currently a technology gap that is missing a high TRL subsystem model. Therefore, for this analysis, the accumulated metal alloy stream terminates after leaving the MRE reactor. Study Goals: This analysis investigates multiple input variables to the system to determine the sensitivity of a (near) complete plant at full-scale. This preliminary investigation ran parametric sweeps on the MRE reactor geometry, electrical current supply, layers of multi-layer insulation (MLI) on the reactor, size of the electrodes in the oxygen purification model, and regolith composition (based on landing site location). Three production targets of oxygen (1,000, 10,000, and 50,000 kg/yr) were investigated for this analysis. The parametric sweeps conducted in this analysis provide valuable insight into the expected impact of the various model inputs on plant size. This information can be used to identify the most critical components of the plant and guide future decisions on allocating funding for research and development, providing subsystem developers with appropriate interfaces with downstream and upstream processes, and assessing the overall feasibility of MRE when compared to other ISRU plants. References: [1] Carlson, A. et al. (2024) ICES, ICES-2024-53. [2] Dominguez, D.A., and Sibille, L. (2011) AIAA, AIAA-2011-700. [3] Schreiner, S.S. (2015) MIT, Dissertation. [4] Schreiner, S.S. et al. (2016) ASR, 57(7), pp.1585-1603.