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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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NASA NTRS1990

Extension of a streamwise upwind algorithm to a moving grid system

A new streamwise upwind algorithm was derived to compute unsteady flow fields with the use of a moving-grid system. The temporally nonconservative LU-ADI (lower-upper-factored, alternating-direction-implicit) method was applied for time marching computations. A comparison of the temporally nonconservative method with a time-conservative implicit upwind method indicates that the solutions are insensitive to the conservative properties of the implicit solvers when practical time steps are used. Using this new method, computations were made for an oscillating wing at a transonic Mach number. The computed results confirm that the present upwind scheme captures the shock motion better than the central-difference scheme based on the beam-warming algorithm. The new upwind option of the code allows larger time-steps and thus is more efficient, even though it requires slightly more computational time per time step than the central-difference option.

Obayashi, Shigeru↗
NASA NTRS2000

Generational Analysis Reveals that TGF-Beta1 Inhibits the Rate of Angiogenesis in Vivo by Selective Decrease in the Number of New Vessels

Quantitative analysis of vascular generational branching demonstrated that transforming growth factor-beta1 (TGF-beta1), a multifunctional cytokine and angiogenic regulator, strongly inhibited angiogenesis in the arterial tree of the developing quail chorioallantoic membrane (CAM) by inhibition of the normal increase in the number of new, small vessels. The cytokine was applied uniformly in solution at embryonic day 7 (E7) to the CAMs of quail embryos cultured in petri dishes. After 24 h the rate of arterial growth was inhibited by as much as 105% as a function of increasing TGF-beta1 concentration. Inhibition of the rate of angiogenesis in the arterial tree by TGF-beta1 relative to controls was measured in digital images by three well-correlated, computerized methods. The first computerized method, direct measurement by the computer code VESGEN of vascular morphological parameters according to branching generations G(sub 1) through G(sub greater than or equal to 5), revealed that TGF-beta1 selectively inhibited the increase in the number density of small vessels, N(sub v greater than or equal to 5), (382 plus or minus 85 per square centimeter) for specimens treated with 1 microgram TGF-beta1/CAM for 24 h, compared to 583 plus or minus 99 per square centimeter for controls), but did not significantly affect other parameters such as average vessel length or vessel diameter. The second and third methods, the fractal dimension (D(sub f)) and grid intersection (rho (sub v)), are statistical descriptors of spatial pattern and density. According to D(sub f) and rho(sub v), arterial density increased in control specimens from 1.382 plus or minus 0.007 and 662 plus or minus 52 per square centimeters at E7 (0 h) to 1.439 plus or minus 0.013 and 884 plus or minus 55 per square centimeters at E8 (24 h), compared to 1.379 plus or minus 0.039 and 650 plus or minus 111 per square centimeter for specimens treated with 1 microgram TGF-beta1/CAM for 24 h. TGF-beta1 therefore regulates vascular pattern and the rate of angiogenesis in a unique fingerprint manner, as do other major angiogenic regulators that include VEGF, FGF-2 (bFGF), and angiostatin. TGF-beta1 did not stimulate angiogenesis significantly at low cytokine concentrations, which suggests that this quail CAM model of angiogenesis is not associated with an inflammatory response.

Parsons-Wingerter, Patricia↗
NASA NTRS1998

A Geometry Based Infra-Structure for Computational Analysis and Design

The computational steps traditionally taken for most engineering analysis suites (computational fluid dynamics (CFD), structural analysis, heat transfer and etc.) are: (1) Surface Generation -- usually by employing a Computer Assisted Design (CAD) system; (2) Grid Generation -- preparing the volume for the simulation; (3) Flow Solver -- producing the results at the specified operational point; (4) Post-processing Visualization -- interactively attempting to understand the results. For structural analysis, integrated systems can be obtained from a number of commercial vendors. These vendors couple directly to a number of CAD systems and are executed from within the CAD Graphical User Interface (GUI). It should be noted that the structural analysis problem is more tractable than CFD; there are fewer mesh topologies used and the grids are not as fine (this problem space does not have the length scaling issues of fluids). For CFD, these steps have worked well in the past for simple steady-state simulations at the expense of much user interaction. The data was transmitted between phases via files. In most cases, the output from a CAD system could go to Initial Graphics Exchange Specification (IGES) or Standard Exchange Program (STEP) files. The output from Grid Generators and Solvers do not really have standards though there are a couple of file formats that can be used for a subset of the gridding (i.e. PLOT3D data formats). The user would have to patch up the data or translate from one format to another to move to the next step. Sometimes this could take days. Specifically the problems with this procedure are:(1) File based -- Information flows from one step to the next via data files with formats specified for that procedure. File standards, when they exist, are wholly inadequate. For example, geometry from CAD systems (transmitted via IGES files) is defined as disjoint surfaces and curves (as well as masses of other information of no interest for the Grid Generator). This is particularly onerous for modern CAD systems based on solid modeling. The part was a proper solid and in the translation to IGES has lost this important characteristic. STEP is another standard for CAD data that exists and supports the concept of a solid. The problem with STEP is that a solid modeling geometry kernel is required to query and manipulate the data within this type of file. (2) 'Good' Geometry. A bottleneck in getting results from a solver is the construction of proper geometry to be fed to the grid generator. With 'good' geometry a grid can be constructed in tens of minutes (even with a complex configuration) using unstructured techniques. Adroit multi-block methods are not far behind. This means that a million node steady-state solution can be computed on the order of hours (using current high performance computers) starting from this 'good' geometry. Unfortunately, the geometry usually transmitted from the CAD system is not 'good' in the grid generator sense. The grid generator needs smooth closed solid geometry. It can take a week (or more) of interaction with the CAD output (sometimes by hand) before the process can begin. One way Communication. (3) One-way Communication -- All information travels on from one phase to the next. This makes procedures like node adaptation difficult when attempting to add or move nodes that sit on bounding surfaces (when the actual surface data has been lost after the grid generation phase). Until this process can be automated, more complex problems such as multi-disciplinary analysis or using the above procedure for design becomes prohibitive. There is also no way to easily deal with this system in a modular manner. One can only replace the grid generator, for example, if the software reads and writes the same files. Instead of the serial approach to analysis as described above, CAPRI takes a geometry centric approach. This makes the actual geometry (not a discretized version) accessible to all phases of the analysis. The connection to the geometry is made through an Application Programming Interface (API) and NOT a file system. This API isolates the top-level applications (grid generators, solvers and visualization components) from the geometry engine. Also this allows the replacement of one geometry kernel with another, without effecting these top-level applications. For example, if UniGraphics is used as the CAD package then Parasolid (UG's own geometry engine) can be used for all geometric queries so that no solid geometry information is lost in a translation. This is much better than STEP because when the data is queried, the same software is executed as used in the CAD system. Therefore, one analyzes the exact part that is in the CAD system. CAPRI uses the same idea as the commercial structural analysis codes but does not specify control. Software components of the CAD system are used, but the analysis suite, not the CAD operator, specifies the control of the software session. This also means that the license issues (may be) minimized and individuals need not have to know how to operate a CAD system in order to run the suite.

Haimes, Robert↗
NASA NTRS1995

Some Numerical Experiments on Detonation Wave Propagation

In this paper we present the results of a series of numerical experiments done on the propagation and initiation of a detonation wave. The calculations are performed in one-dimension, with considerable grid resolution. Of particular interest are the following questions: (1) the nature of periodic and chaotic instabilities generated by the wave; (2) the influence of the grid resolution on these instabilities; (3) the influence of the 'quality' of the numerical scheme; and (4) the influence of 'noise'. In the calculations, we use a second-order Total Variation Diminishing (TVD) scheme as the basic numerical method, with grid spacings as low as a fraction of a micron. Detonations waves are generated at the closed end of a tube, and allowed to propagate for approximately 20 cm. The required energy for successful initiation of the detonation will be measured for different cases of grid resolution and numerical schemes. A modified version of the TVD scheme has also been devised, which allows for much lower numerical diffusion of the radical species in the exponentially growing region behind the shock. The effect of this modification will be demonstrated. Oscillations in peak pressure and induction length are seen to develop in some cases: the oscillations can go through a sequence of modes, from a regular, high frequency mode to a low frequency mode with period doubling. A chaotic regime can also be obtained. General conclusions on the quality of algorithms will be presented. We will also discuss the performance of a version of the code developed on the IBM SP2 parallel computer.

Cambier, Jean-Luc↗
NASA NTRSDate not supplied

The NASA Ames Mars Global Climate Model: Benchmarking Publicly Released Source Code and Model Output

We have recently publicly released source code from the new NASA Ames Mars Global Climate Model (MGCM), which is based on NOAA/GFDL cubed-sphere finite volume (FV3-based) dynamical core (https://github.com/nasa/AmesGCM). We also we have a manuscript in preparation that aims to document the status of the new MGCM, and present selected simulations generated from it with interpretations and comparisons to both observations and the Ames Legacy MGCM. Output from our reference simulation will be made publicly available as well. One of our ongoing goals is to understand the underlying causes for differences between results produced with the new FV3-based dynamical core compared to the Legacy C-grid dynamical core. While the thermal and dynamical fields predicted with the new and Legacy GCMs are broadly similar for much of the year, there are key differences at low resolution when no external drag is applied to the new MGCM. This is particularly clear during a seasonal window of ~100 degrees of Ls surrounding southern summer solstice, when the predicted northern hemisphere polar warming is significantly over-predicted in the new MGCM. When we apply Rayleigh drag throughout much of the tropics and sub-tropics to the new MGCM, the simulated zonal mean structure of the atmosphere is much more consistent with both MCS observations and Legacy MGCM simulations. We note that the Kling et al. (2023; this meeting) study demonstrates that the behavior that we see with Rayleigh drag here can be recovered with high resolution simulations (in the horizontal and in the vertical) or with parameterized orographic and non-orographic gravity waves at lower resolution. While this work is still in progress, our preliminary conclusion is that the new dynamical core is less dissipative than the Legacy dynamical core. At low to moderate resolution, users of the new MGCM will need to be careful to use some sort of external drag, either in the form of gravity wave drag parameterizations or the simpler Rayleigh drag.

Melinda April Kahre↗
NASA NTRS1998

LSPRAY: Lagrangian Spray Solver for Applications With Parallel Computing and Unstructured Gas-Phase Flow Solvers

Sprays occur in a wide variety of industrial and power applications and in the processing of materials. A liquid spray is a phase flow with a gas as the continuous phase and a liquid as the dispersed phase (in the form of droplets or ligaments). Interactions between the two phases, which are coupled through exchanges of mass, momentum, and energy, can occur in different ways at different times and locations involving various thermal, mass, and fluid dynamic factors. An understanding of the flow, combustion, and thermal properties of a rapidly vaporizing spray requires careful modeling of the rate-controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as other phenomena. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on sprays to unstructured grids and parallel computing. LSPRAY, which was developed by M.S. Raju of Nyma, Inc., is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo probability density function (PDF) solver. The LSPRAY solver accommodates the use of an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements in the gas-phase solvers. It is used specifically for fuel sprays within gas turbine combustors, but it has many other uses. The spray model used in LSPRAY provided favorable results when applied to stratified-charge rotary combustion (Wankel) engines and several other confined and unconfined spray flames. The source code will be available with the National Combustion Code (NCC) as a complete package.

Raju, Manthena S.↗
NASA NTRS2007

Effective Inflow Conditions for Turbulence Models in Aerodynamic Calculations

The selection of inflow values at boundaries far upstream of an aircraft is considered, for one- and two-equation turbulence models. Inflow values are distinguished from the ambient values near the aircraft, which may be much smaller. Ambient values should be selected first, and inflow values that will lead to them after the decay second; this is not always possible, especially for the time scale. The two-equation decay during the approach to the aircraft is shown; often, the time scale has been set too short for this decay to be calculated accurately on typical grids. A simple remedy for both issues is to impose floor values for the turbulence variables, outside the viscous sublayer, and it is argued that overriding the equations in this manner is physically justified. Selecting laminar ambient values is easy, if the boundary layers are to be tripped, but a more common practice is to seek ambient values that will cause immediate transition in boundary layers. This opens up a wide range of values, and selection criteria are discussed. The turbulent Reynolds number, or ratio of eddy viscosity to laminar viscosity has a huge dynamic range that makes it unwieldy; it has been widely mis-used, particularly by codes that set upper limits on it. The value of turbulent kinetic energy in a wind tunnel or the atmosphere is also of dubious value as an input to the model. Concretely, the ambient eddy viscosity must be small enough to preserve potential cores in small geometry features, such as flap gaps. The ambient frequency scale should also be small enough, compared with shear rates in the boundary layer. Specific values are recommended and demonstrated for airfoil flows

Spalart, Philippe R.↗
NASA NTRS2017

Viscous Three-Dimensional Simulation of Flow in an Axial Low Pressure Compressor at Engine Icing Operating Points

Viscous three-dimensional simulations of the Honeywell ALF502R-5 low pressure compressor (sometimes called a booster) using the NASA Glenn code GlennHT have been carried out. A total of ten simulations were produced. Five operating points are investigated, with each point run with two different wall thermal conditions. These operating points are at, or near, points where engine icing has been determined to be likely. In the future, the results of this study will be used for further analysis such as predicting collection efficiency of ice particles and ice growth rates at various locations in the compressor. A mixing plane boundary condition is used between each blade row, resulting in convergence to steady state within each blade row. The k-omega turbulence model of Wilcox, combined with viscous grid spacing near the wall on the order of one, is used to resolve the turbulent boundary layers. For each of the operating points, heat transfer coefficients are generated on the blades and walls. The heat transfer coefficients are produced by running the operating point with two different wall thermal conditions and then solving simultaneously for the heat transfer coefficient and adiabatic wall temperature at each point. Average Nusselt numbers are calculated for the most relevant surfaces. The values are seen to scale with Reynolds number to approximately a power of 0.7. Additionally, images of surface distribution of Nusselt number are presented. Qualitative comparison between the five operating points show that there is relatively little change in the character of the distribution. The dominant observed effect is that of an overall scaling, which is expected due to Reynolds number differences. One interesting aspect about the Nusselt number distribution is observed on the casing (outer diameter) downstream of the exit guide vanes (EGVs). The Nusselt number is relatively high between the pairs of EGVs, with two lower troughs downstream of each EGV trailing edge. This is of particular interest since rather complex ice shapes have been observed in that region.

compressor↗
NASA NTRS1988

Adaptive computational methods for aerothermal heating analysis

The development of adaptive gridding techniques for finite-element analysis of fluid dynamics equations is described. The developmental work was done with the Euler equations with concentration on shock and inviscid flow field capturing. Ultimately this methodology is to be applied to a viscous analysis for the purpose of predicting accurate aerothermal loads on complex shapes subjected to high speed flow environments. The development of local error estimate strategies as a basis for refinement strategies is discussed, as well as the refinement strategies themselves. The application of the strategies to triangular elements and a finite-element flux-corrected-transport numerical scheme are presented. The implementation of these strategies in the GIM/PAGE code for 2-D and 3-D applications is documented and demonstrated.

Price, John M.↗
NASA NTRS1992

Theoretical studies of the outer envelopes of young stellar objects

With the Monte Carlo code developed by Whitney and Hartmann, a series of models was computed of scattering in disks around young stellar objects. The code calculates scattering by dust, including polarization, in arbitrary geometries. By computing model images, it was found that disk, by themselves, around young stellar objects would be very difficult to detect with present day imaging techniques. In comparing these images to observations of young stellar objects which show diffuse structure, little resemblance was found. A flared disk system will only give high polarization when viewed edge-on, and the position angle is always oriented perpendicular to the disk plane. This suggests that an envelope, perhaps the remnant infalling envelope, must be present to scatter more stellar light than a disk can, and obscure the star at many inclinations. A grid was computed of models of scattering in a disk+envelope system. Evidence is presented that the wind of the pre-main sequence object FU Orionis arises from the surface of the luminous prostellar accretion disk. A disk wind model calculated assuming radiative equilibrium explains the differential behavior of the observed asymmetrical absorption line profiles. The model predicts that strong lines should be asymmetric and blueshifted, while weak lines should be symmetric and doubled peaked due to disk rotation, in agreement with observations.

Hartmann, Lee↗
NASA NTRS1992

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 4: Advanced fan section aerodynamic analysis computer program user's manual

The computer program user's manual for the ADPACAPES (Advanced Ducted Propfan Analysis Code-Average Passage Engine Simulation) program is included. The objective of the computer program is development of a three-dimensional Euler/Navier-Stokes flow analysis for fan section/engine geometries containing multiple blade rows and multiple spanwise flow splitters. An existing procedure developed by Dr. J. J. Adamczyk and associates at the NASA Lewis Research Center was modified to accept multiple spanwise splitter geometries and simulate engine core conditions. The numerical solution is based upon a finite volume technique with a four stage Runge-Kutta time marching procedure. Multiple blade row solutions are based upon the average-passage system of equations. The numerical solutions are performed on an H-type grid system, with meshes meeting the requirement of maintaining a common axisymmetric mesh for each blade row grid. The analysis was run on several geometry configurations ranging from one to five blade rows and from one to four radial flow splitters. The efficiency of the solution procedure was shown to be the same as the original analysis.

Crook, Andrew J.↗
NASA NTRS1995

A guide to the use of the pressure disk rotor model as implemented in INS3D-UP

This is a guide for the use of the pressure disk rotor model that has been placed in the incompressible Navier-Stokes code INS3D-UP. The pressure disk rotor model approximates a helicopter rotor or propeller in a time averaged manner and is intended to simulate the effect of a rotor in forward flight on the fuselage or the effect of a propeller on other aerodynamic components. The model uses a modified actuator disk that allows the pressure jump across the disk to vary with radius and azimuth. The cyclic and collective blade pitch angles needed to achieve a specified thrust coefficient and zero moment about the hub are predicted. The method has been validated with experimentally measured mean induced inflow velocities as well as surface pressures on a generic fuselage. Overset grids, sometimes referred to as Chimera grids, are used to simplify the grid generation process. The pressure disk model is applied to a cylindrical grid which is embedded in the grid or grids used for the rest of the configuration. This document will outline the development of the method, and present input and results for a sample case.

Chaffin, Mark S.↗
NASA NTRS1995

TADS: A CFD-based turbomachinery and analysis design system with GUI. Volume 2: User's manual

The primary objective of this study was the development of a computational fluid dynamics (CFD) based turbomachinery airfoil analysis and design system, controlled by a graphical user interface (GUI). The computer codes resulting from this effort are referred to as the Turbomachinery Analysis and Design System (TADS). This document is intended to serve as a user's manual for the computer programs which comprise the TADS system. TADS couples a throughflow solver (ADPAC) with a quasi-3D blade-to-blade solver (RVCQ3D) in an interactive package. Throughflow analysis capability was developed in ADPAC through the addition of blade force and blockage terms to the governing equations. A GUI was developed to simplify user input and automate the many tasks required to perform turbomachinery analysis and design. The coupling of various programs was done in a way that alternative solvers or grid generators could be easily incorporated into the TADS framework.

Myers, R. A.↗
NASA NTRS2001

NASA National Combustion Code Simulations

A systematic effort is in progress to further validate the National Combustion Code (NCC) that has been developed at NASA Glenn Research Center (GRC) for comprehensive modeling and simulation of aerospace combustion systems. The validation efforts include numerical simulation of the gas-phase combustor experiments conducted at the Center for Turbulence Research (CTR), Stanford University, followed by comparison and evaluation of the computed results with the experimental data. Presently, at GRC, a numerical model of the experimental gaseous combustor is built to simulate the experimental model. The constructed numerical geometry includes the flow development sections for air annulus and fuel pipe, 24 channel air and fuel swirlers, hub, combustor, and tail pipe. Furthermore, a three-dimensional multi-block, multi-grid grid (1.6 million grid points, 3-levels of multi-grid) is generated. Computational simulation of the gaseous combustor flow field operating on methane fuel has started. The computational domain includes the whole flow regime starting from the fuel pipe and the air annulus, through the 12 air and 12 fuel channels, in the combustion region and through the tail pipe.

Iannetti, Anthony↗
NASA NTRS1985

A 3-dimensional Navier-Stokes-Euler code for blunt-body flow computations

The shock-layer flowfield is obtained with or without viscous and heat-conducting dissipations from the conservative laws of fluid dynamics equations using a shock-fitting implicity finite-difference technique. The governing equations are cast in curvilinear-orthogonal coordinates and transformed to the domain between the shock and the body. Another set of equations is used for the singular coordinate axis, which, together with a cone generator away from the stagnation point, encloses the computation domain. A time-dependent alternating direction implicit factorization technique is applied to integrate the equations with local-time increment until a steady solution is reached. The shock location is updated after the flowfield computation, but the wall conditions are implemented into the implicit procedure. Innovative procedures are introduced to define the initial flowfield, to treat both perfect and equilibrium gases, to advance the solution on a coarse-to-fine grid sequence, and to start viscous flow computations from their corresponding inviscid solutions. The results are obtained from a grid no greater than 28 by 18 by 7 and converged within 300 integration steps. They are of sufficient accuracy to start parabolized Navier-Stokes or Euler calculations beyond the nose region, to compare with flight and wind-tunnel data, and to evaluate conceptual designs of reentry spacecraft.

Li, C. P.↗
NASA NTRS1993

A parallel adaptive mesh refinement algorithm

Over recent years, Adaptive Mesh Refinement (AMR) algorithms which dynamically match the local resolution of the computational grid to the numerical solution being sought have emerged as powerful tools for solving problems that contain disparate length and time scales. In particular, several workers have demonstrated the effectiveness of employing an adaptive, block-structured hierarchical grid system for simulations of complex shock wave phenomena. Unfortunately, from the parallel algorithm developer's viewpoint, this class of scheme is quite involved; these schemes cannot be distilled down to a small kernel upon which various parallelizing strategies may be tested. However, because of their block-structured nature such schemes are inherently parallel, so all is not lost. In this paper we describe the method by which Quirk's AMR algorithm has been parallelized. This method is built upon just a few simple message passing routines and so it may be implemented across a broad class of MIMD machines. Moreover, the method of parallelization is such that the original serial code is left virtually intact, and so we are left with just a single product to support. The importance of this fact should not be underestimated given the size and complexity of the original algorithm.

Quirk, James J.↗
NASA NTRS2001

CFD Validation Studies for Hypersonic Flow Prediction

A series of experiments to measure pressure and heating for code validation involving hypersonic, laminar, separated flows was conducted at the Calspan-University at Buffalo Research Center (CUBRC) in the Large Energy National Shock (LENS) tunnel. The experimental data serves as a focus for a code validation session but are not available to the authors until the conclusion of this session. The first set of experiments considered here involve Mach 9.5 and Mach 11.3 N, flow over a hollow cylinder-flare with 30 deg flare angle at several Reynolds numbers sustaining laminar, separated flow. Truncated and extended flare configurations are considered. The second set of experiments, at similar conditions, involves flow over a sharp, double cone with fore-cone angle of 25 deg and aft-cone angle of 55 deg. Both sets of experiments involve 30 deg compressions. Location of the separation point in the numerical simulation is extremely sensitive to the level of grid refinement in the numerical predictions. The numerical simulations also show a significant influence of Reynolds number on extent of separation. Flow unsteadiness was easily introduced into the double cone simulations using aggressive relaxation parameters that normally promote convergence.

Gnoffo, Peter A.↗
NASA NTRS2001

CFD Validation Studies for Hypersonic Flow Prediction

A series of experiments to measure pressure and heating for code validation involving hypersonic, laminar, separated flows was conducted at the Calspan-University at Buffalo Research Center (CUBRC) in the Large Energy National Shock (LENS) tunnel. The experimental data serves as a focus for a code validation session but are not available to the authors until the conclusion of this session. The first set of experiments considered here involve Mach 9.5 and Mach 11.3 N2 flow over a hollow cylinder-flare with 30 degree flare angle at several Reynolds numbers sustaining laminar, separated flow. Truncated and extended flare configurations are considered. The second set of experiments, at similar conditions, involves flow over a sharp, double cone with fore-cone angle of 25 degrees and aft-cone angle of 55 degrees. Both sets of experiments involve 30 degree compressions. Location of the separation point in the numerical simulation is extremely sensitive to the level of grid refinement in the numerical predictions. The numerical simulations also show a significant influence of Reynolds number on extent of separation. Flow unsteadiness was easily introduced into the double cone simulations using aggressive relaxation parameters that normally promote convergence.

Gnoffo, Peter A.↗