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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 NTRS2003

Slotting Fins of Heat Exchangers to Provide Thermal Breaks

Heat exchangers that include slotted fins (in contradistinction to continuous fins) have been invented. The slotting of the fins provides thermal breaks that reduce thermal conduction along flow paths (longitudinal thermal conduction), which reduces heat-transfer efficiency. By increasing the ratio between transverse thermal conduction (the desired heat-transfer conduction) and longitudinal thermal conduction, slotting of the fins can be exploited to (1) increase heat-transfer efficiency (thereby reducing operating cost) for a given heat-exchanger length or to (2) reduce the length (thereby reducing the weight and/or cost) of the heat exchanger needed to obtain a given heat transfer efficiency. By reducing the length of a heat exchanger, one can reduce the pressure drop associated with the flow through it. In a case in which slotting enables the use of fins with thermal conductivity greater than could otherwise be tolerated on the basis of longitudinal thermal conduction, one can exploit the conductivity to make the fins longer (in the transverse direction) than they otherwise could be, thereby making it possible to make a heat exchanger that contains fewer channels and therefore, that weighs less, contains fewer potential leak paths, and can be constructed from fewer parts and, hence, reduced cost.

Scull, Timothy D.↗

NASA NTRS1994

Ignition and combustion characteristics of metallized propellants, phase 2

Experimental and analytical investigations focusing on aluminum/hydrocarbon gel droplet secondary atomization and its effects on gel-fueled rocket engine performance are being conducted. A single laser sheet sizing/velocimetry diagnostic technique, which should eliminate sizing bias in the data collection process, has been designed and constructed to overcome limitations of the two-color forward-scatter technique used in previous work. Calibration of this system is in progress and the data acquisition/validation code is being written. Narrow-band measurements of radiant emission, discussed in previous reports, will be used to determine if aluminum ignition has occurred in a gel droplet. A one-dimensional model of a gel-fueled rocket combustion chamber, described in earlier reports, has been exercised in conjunction with a two-dimensional, two-phase nozzle code to predict the performance of an aluminum/hydrocarbon fueled engine. Estimated secondary atomization effects on propellant burnout distance, condensed particle radiation losses to the chamber walls, and nozzle two phase flow losses are also investigated. Calculations indicate that only modest secondary atomization is required to significantly reduce propellant burnout distances, aluminum oxide residual size, and radiation heat losses. Radiation losses equal to approximately 2-13 percent of the energy released during combustion were estimated, depending on secondary atomization intensity. A two-dimensional, two-phase nozzle code was employed to estimate radiation and nozzle two phase flow effects on overall engine performance. Radiation losses yielded a one percent decrease in engine Isp. Results also indicate that secondary atomization may have less effect on two-phase losses than it does on propellant burnout distance and no effect if oxide particle coagulation and shear induced droplet breakup govern oxide particle size. Engine Isp was found to decrease from 337.4 to 293.7 seconds as gel aluminum mass loading was varied from 0-70 wt percent. Engine Isp efficiencies, accounting for radiation and two phase flow effects, on the order of 0.946 were calculated for a 60 wt percent gel, assuming a fragmentation ratio of five.

Mueller, D. C.↗

NASA NTRS1982

Numerical analysis of confined turbulent flow

The considered investigation is concerned with the development of an efficient computational method for obtaining a physical understanding of an internal turbulent field. The employed approach makes use of a 'two equation' type model for the turbulence to obtain the numerical solution of a two-dimensional confined turbulent flow. The mean flow governing equations are considered along with the governing equation of the mean temperature and concentrations, and the boundary conditions. The numerical procedure for solving the turbulent flow is discussed, taking into account an approximation to the nonlinear terms, and the inner and outer coupling. Attention is given to a stability convergence analysis, the stability characteristics, and computational examples.

Lin, A.↗

DOE OSTI2024

Early Exploration of a Flexible Framework for Efficient Quantum Linear Solvers in Power Systems

The rapid integration of renewable energy resources presents formidable challenges in managing power grids. While advanced computing and machine learning techniques offer some solutions for accelerating grid modeling and simulation, there remain complex problems that classical computers cannot effectively address. Quantum computing, a promising technology, has the potential to fundamentally transform how we manage power systems, especially in scenarios with a higher proportion of renewable energy sources. One critical aspect is solving linear systems of equations, crucial for power system applications like power flow analysis, for which the Harrow-Hassidim-Lloyd (HHL) algorithm is a well-known quantum solution. However, HHL quantum circuits often exhibit excessive depth, making them impractical for current Noisy-Intermediate-Scale-Quantum (NISQ) devices. In this paper, we introduce a versatile framework, powered by NWQSim, that bridges the gap between power system applications and quantum linear solvers available in Qiskit. This framework empowers researchers to efficiently explore power system applications using quantum linear solvers. Through innovative gate fusion strategies, reduced circuit depth, and GPU acceleration, our simulator significantly enhances resource efficiency. Power flow case studies have demonstrated up to a eight-fold speedup compared to Qiskit Aer, all while maintaining comparable levels of accuracy.

quantum computing, Harrow-Hassidim-Lloyd, high-per↗

DOE OSTI2021

Insights into scale translation of methane transport in nanopores

Accurate prediction of flow behavior in shale matrix is critical for efficient development of shale gas reservoirs. In these systems, the majority of pores are in the nano-size range. As a result, continuum-based approaches may not be appropriate to simulate flow in such systems. Molecular dynamics (MD) simulations are capable of capturing the relevant microscale physics. Their relatively high computational expense, however, restricts MD simulations to rather small systems and domains. This limitation creates a gap between computational need of macroscale systems and capabilities of MD simulations. The lattice Boltzmann method (LBM) is a suitable candidate to bridge this gap. In this work, the multiple-relaxation-time (MRT)-LBM is used to study methane transport in nano-size pores. Adsorption effects near solid boundaries, as well as non-ideal behavior of fluids, are accounted for via incorporating appropriate force terms in LBM. In this work, parameters associated with the force terms in the equation of state are studied in detail, and a workflow is proposed to determine optimal values of these parameters for gas flow in slit pores. Specifically, we establish these parameters such that the range of density values that the model is able to simulate is maximized. We demonstrate this workflow by simulating gas flow where velocity and density profiles from MD simulations are used as reference data. Results from LBM simulations are in good agreement with MD reference data for pores that are 4 nm in width or larger. Moreover, we propose a preconditioning scheme to improve the stability of LBM in dealing with complex geometries. The robustness of this scheme is demonstrated by simulating several roughness geometries. This work motivates the use of LBM in scale translation of the physics of mass transport in more complex permeable media.

03 NATURAL GAS↗

DOE OSTI2025

Comparison of wind farm control strategies under realistic offshore wind conditions: turbine quantities of interest

Abstract. Wind farm flow control is a strategy to increase the efficiency and therefore lower the levelized cost of energy of a wind farm. This is done using turbine settings such as the yaw angle, blade pitch angles, or generator torque to manipulate the flow behind the turbine, affecting downstream turbines in the farm. Two inherently different wind farm flow control methods have been identified in the literature: wake steering and wake mixing. This paper focuses on comparing the turbine quantities of interest between these methods for a simple two-turbine wind farm setup, while a companion article (Brown et al., 2025) focuses on the wake quantities of interest for a single wind turbine setup. Both papers use the same set of wind farm simulations based on high-fidelity large-eddy simulations (LESs) coupled with OpenFAST turbine models. First, precursor simulations are executed in order to match wind conditions measured with lidars in an offshore wind farm off the east coast of the USA. These measurements show general wind conditions that exhibit substantially higher vertical wind shear and veer than any of the LES studies performed with wind farm flow control strategies currently available in the literature. The precursors are used to evaluate the effectiveness of the control methods. In the LES, the wind veer leads to highly skewed wakes, which have considerable influence on the power uplift of wind farm flow control strategies. In addition to a baseline controller, four different control strategies, each of which uses either pitch or yaw control, are performed on the upstream turbine of a simple two-turbine wind farm. Assuming that the wind direction is known and constant over time, the simulations show that wake steering is generally the superior wind farm flow control strategy, considering both wind farm power production and turbine damage equivalent loads when substantial wind veer is present. This result is consistent over different wind speeds and wind directions. On the other hand, for similar wind conditions with lower veer, wake mixing was found to yield the highest power production, although at the expense of generally higher loads. This leads us to conclude that the effect of wind veer, which has so far not usually been considered, can not be neglected when determining the optimal wind farm flow control strategy.

17 WIND ENERGY↗

NASA NTRS1994

Effect of Porosity on Surface Catalytic Efficiency

This paper describes the effect of surface porosity of thermal protection materials on surface catalytic efficiency using test data taken from both arc-jet and side-arm reactor facilities. Relative surface porosity of the samples varied from 6% to 50%. Surface porosity was measured using a flow apparatus and Bernoulli equation. The surface catalytic efficiency of the materials was calculated using aerothermodynamic, and kinetic theories. The catalytic efficiency of the materials are compared at surface temperatures between room temperature and 2500 F. The data are presented in the form of graphs and tables.

Stewart, David A.↗

NASA NTRS1987

A numerical method for the solution of three dimensional, incompressible, viscous flows over slender bodies

A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.

Rosenfeld, Moshe↗

NASA NTRS1993

Convergence acceleration of implicit schemes in the presence of high aspect ratio grid cells

The performance of Navier-Stokes codes are influenced by several phenomena. For example, the robustness of the code may be compromised by the lack of grid resolution, by a need for more precise initial conditions or because all or part of the flowfield lies outside the flow regime in which the algorithm converges efficiently. A primary example of the latter effect is the presence of extended low Mach number and/or low Reynolds number regions which cause convergence deterioration of time marching algorithms. Recent research into this problem by several workers including the present authors has largely negated this difficulty through the introduction of time-derivative preconditioning. In the present paper, we employ the preconditioned algorithm to address convergence difficulties arising from sensitivity to grid stretching and high aspect ratio grid cells. Strong grid stretching is particularly characteristic of turbulent flow calculations where the grid must be refined very tightly in the dimension normal to the wall, without a similar refinement in the tangential direction. High aspect ratio grid cells also arise in problems that involve high aspect ratio domains such as combustor coolant channels. In both situations, the high aspect ratio cells can lead to extreme deterioration in convergence. It is the purpose of the present paper to address the reasons for this adverse response to grid stretching and to suggest methods for enhancing convergence under such circumstances. Numerical algorithms typically possess a maximum allowable or optimum value for the time step size, expressed in non-dimensional terms as a CFL number or vonNeumann number (VNN). In the presence of high aspect ratio cells, the smallest dimension of the grid cell controls the time step size causing it to be extremely small, which in turn results in the deterioration of convergence behavior. For explicit schemes, this time step limitation cannot be exceeded without violating stability restrictions of the scheme. On the other hand, for implicit schemes, which are typically unconditionally stable, there appears to be room for improvement through careful tailoring of the time step definition based on results of linear stability analyses. In the present paper, we focus on the central-differenced alternating direction implicit (ADI) scheme. The understanding garnered from this analyses can then be applied to other implicit schemes. In order to systematically study the effects of aspect ratio and the methods of mitigating the associated problems, we use a two pronged approach. We use stability analyses as a tool for predicting numerical convergence behavior and numerical experiments on simple model problems to verify predicted trends. Based on these analyses, we determine that efficient convergence may be obtained at all aspect ratios by getting a combination of things right. Primary among these are the proper definition of the time step size, proper selection of viscous preconditioner and the precise treatment of boundary conditions. These algorithmic improvements are then applied to a variety of test cases to demonstrate uniform convergence at all aspect ratios.

Buelow, B. E. O.↗

NASA NTRS1995

Hypergolic oxidizer and fuel scrubber emissions

Hypergolic fuels and oxidizer are emitted to the environment during fueling and deservicing shuttle and other spacecraft. Such emissions are difficult to measure due to the intermittent purge flow and to the presence of suspended scrubber liquor. A new method for emissions monitoring was introduced in a previous paper. This paper is a summary of the results of a one-year study of shuttle launch pads and orbiter processing facilities (OPF's) which proved that emissions can be determined from field scrubbers without direct measurement of vent flow rate and hypergol concentration. This new approach is based on the scrubber efficiency, which was measured during normal operations, and on the accumulated weight of hypergol captured in the scrubber liquor, which is part of the routine monitoring data of scrubber liquors. To validate this concept, three qualification tests were performed, logs were prepared for each of 16 hypergol scrubbers at KSC, the efficiencies of KSC scrubbers were measured during normal operations, and an estimate of the annual emissions was made based on the efficiencies and the propellant buildup data. The results have confirmed that the emissions from the KSC scrubbers can be monitored by measuring the buildup of hypergol propellant in the liquor, and then using the appropriate efficiency to calculate the emissions. There was good agreement between the calculated emissions based on outlet concentration and flow rate, and the emissions calculated from the propellant buildup and efficiency. The efficiencies of 12 KSC scrubbers, measured under actual servicing operations and special test conditions, were assumed to be valid for all subsequent operations until a significant change in hardware occurred. An estimate of the total emissions from 16 scrubbers for three years showed that 0.3 kg/yr of fuel and 234 kg/yr of oxidizer were emitted.

Parrish, Clyde F.↗

DOE OSTI2020

An embedded 3D fracture modeling approach for simulating fracture-dominated fluid flow and heat transfer in geothermal reservoirs

In this paper, we describe an efficient modeling approach, named embedded discrete fracture method (EDFM), for incorporating arbitrary 3D, discrete fractures, such as hydraulic fractures or faults, into modeling fracture-dominated fluid flow and heat transfer in fractured geothermal reservoirs. This technique allows 3D discrete fractures to be discretized independently from surrounding rock volume and inserted explicitly into a primary fracture/matrix grid, generated without including 3D discrete fractures in prior. An effective computational algorithm is developed to discretize these 3D discrete fractures and construct local connections between 3D fractures and fracture/matrix grid blocks representing the surrounding rock volume. The constructed gridding information on 3D fractures is then added to the primary grid. This embedded fracture modeling approach can be directly implemented into a developed geothermal reservoir simulator via the integral finite difference (IFD) method or with TOUGH2 technology. This embedded fracture modeling approach is very promising and computationally efficient to handle realistic 3D discrete fractures with complicated geometries, connections, and spatial distributions. Compared with other fracture modeling approaches, it avoids cumbersome 3D unstructured, local refining procedures, and increases computational efficiency by simplifying Jacobian matrix size and sparsity, while maintaining enough accuracy. Several numeral simulations are presented to demonstrate the utility and robustness of the proposed technique. Our numerical experiments show that this approach captures all the key patterns about fluid flow and heat transfer dominated by fractures in these cases. Thus, this approach is readily available to the simulation of fractured geothermal reservoirs with both artificial and natural fractures.

15 GEOTHERMAL ENERGY↗

NASA NTRS2000

A Unified Wall Boundary Treatment for Viscous and Inviscid Flows in the CE/SE Method

In the setting of the conservation element-solution element (CE/SE) method, a new and unified wall boundary treatment for the Navier-Stokes and Euler Equations is proposed. In essence, the shear stress exerted on the fluid by a wall is modeled as a source term as a part of local spacetime flux conservation in the vicinity of a wall boundary. When the fluid is inviscid, the source term vanishes and the boundary condition reduces to the usual 'slip' condition. On the other hand, when the fluid is viscous, the source-term effect is consistent with the traditional no-slip condition. Numerical results show that the new treatment is robust, efficient, and accurate for viscous and inviscid flows.

Chang, Sin-Chung↗

DOE OSTI2020

An Online Search Method for Representative Risky Fault Chains Based on Reinforcement Learning and Knowledge Transfer

In the analysis of cascading outages and blackouts in power systems, risky cascading fault chains should be accurately identified in order to do further block or alleviate blackouts. However, the huge computational burden makes online analysis difficult. In this paper, an online search method for representative risky fault chains based on reinforcement learning and knowledge transfer is proposed. This method aims at promoting efficiency by exploiting similarities of adjacent power flow snapshots in operations. After the “representative risky fault chain” is defined, a framework of tree search based on Markov Decision Process and Q-learning is constructed. The knowledge in past runs is accumulated offline and then applied online, with a mechanism of knowledge transition and extension. The proposed learning based approach is verified on an illustrative 39-bus system with different loading levels, and simulations are carried out on a realworld 1000-bus power grid in China to show the effectiveness and efficiency of the proposed approach.

Blackout↗

DOE OSTI2022

Current state and future trends in boundary layer control on lifting surfaces

Successful flow control may bring numerous benefits, such as flow stabilization, flow reattachment, separation delay, drag reduction, lift increase, aerodynamic performance improvement, energy efficiency increase, shock delay or weakening, noise reduction, etc. For these purposes, many different flow control devices, which can be classified as passive, semi-active and active, have been designed and tested. This review paper aims to highlight the most promising and commonly employed boundary layer control methods as well as outline their potential in specific applications in aerospace and energy engineering. Referenced studies, performed on various geometries (flat plates, channels, airfoils, wings, blades, cylinders), are primarily numerical or experimental. Although enhanced aerodynamic performance is achieved in many cases, further research is required to draw general conclusions. This paper aims to demonstrate that, in the future, we may expect further developments of flow control actuators, as well as their increased application.

42 ENGINEERING↗

DOE OSTI2024

Photosynthetic Electron Flows and Networks of Metabolite Trafficking to Sustain Metabolism in Photosynthetic Systems

Photosynthetic eukaryotes have metabolic pathways that occur in distinct subcellular compartments. However, because metabolites synthesized in one compartment, including fixed carbon compounds and reductant generated by photosynthetic electron flows, may be integral to processes in other compartments, the cells must efficiently move metabolites among the different compartments. This review examines the various photosynthetic electron flows used to generate ATP and fixed carbon and the trafficking of metabolites in the green alga Chlamydomomas reinhardtii; information on other algae and plants is provided to add depth and nuance to the discussion. We emphasized the trafficking of metabolites across the envelope membranes of the two energy powerhouse organelles of the cell, the chloroplast and mitochondrion, the nature and roles of the major mobile metabolites that move among these compartments, and the specific or presumed transporters involved in that trafficking. These transporters include sugar-phosphate (sugar-P)/inorganic phosphate (Pi) transporters and dicarboxylate transporters, although, in many cases, we know little about the substrate specificities of these transporters, how their activities are regulated/coordinated, compensatory responses among transporters when specific transporters are compromised, associations between transporters and other cellular proteins, and the possibilities for forming specific ‘megacomplexes’ involving interactions between enzymes of central metabolism with specific transport proteins. Finally, we discuss metabolite trafficking associated with specific biological processes that occur under various environmental conditions to help to maintain the cell’s fitness. These processes include C4 metabolism in plants and the carbon concentrating mechanism, photorespiration, and fermentation metabolism in algae.

Plant Sciences↗

DOE OSTI2025

Even Higher-Level Synthesis: An Exploration of AI Hardware Accelerators using HLS4ML

With the rise of artificial intelligence, the popularization of deep learning, and a constantly evolving industry, the demand for flexible and efficient tools has never been greater. As algorithms grow more complex, their runtime and energy consumption increase exponentially. Customized hardware accelerators, long used for specific mathematical operations, remain essential for managing modern applications' computational and power demands. Hardware accelerators can speed up complex computations by orders of magnitude, but their manual design and verification processes are often challenging and time-consuming. High-Level Synthesis (HLS) provides a solution by transforming high-level algorithm descriptions, typically written in C++ or SystemC, into synthesizable RTL suitable for hardware implementation. This approach reduces development time for RTL engineers while offering flexibility beyond what traditional handwritten RTL can provide. We extended this capability to the machine-learning domain with the open-source framework hls4ml, which allows neural networks trained in Python frameworks like Tensorflow or PyTorch to be synthesized into efficient hardware representations for the traditional FPGA and ASIC flows. This breakthrough addresses the growing need for reduced design turnaround and easy verification of ML hardware accelerators with low latency and power efficiency constraints. During this tutorial, we will demonstrate how Python complements HLS by simplifying the ML design process, bridging the gap between software and hardware development. Attendees will explore how we translate neural networks modeled in Python into fixed-point C++ models suitable for HLS workflows. We will dive into strategies like Value-Range Analysis and Quantization-Aware Training, which optimize these designs for deployment and evaluate their accuracy, power consumption, and energy efficiency. To exemplify these concepts, experts from Fermilab will share their experiences applying this technology to high-energy physics experiments, where real-time, low-latency processing is critical. Over the years, Fermilab engineers have demonstrated how deep neural networks, optimized for hardware using hls4ml, can meet the stringent requirements of trigger systems at the CERN Large Hadron Collider. These systems rely on rapid decision-making to process immense data volumes while retaining only the most relevant events for further analysis. The application of hls4ml has also been extended to innovative technologies like smart pixel arrays. These smart pixels integrate ML inference capabilities directly into sensor devices, enabling localized data processing at the pixel level. This approach drastically reduces the need to transmit raw data to external processing units, significantly decreasing power consumption and latency. By embedding neural networks within the pixel architecture, the smart pixels can identify and prioritize relevant data in real time, providing a highly efficient solution for edge computing in scenarios such as particle detectors and imaging systems. Fermilab's work highlights the potential of hardware-accelerated ML in scenarios where both speed and power efficiency are mission-critical. Through this tutorial, attendees will gain valuable insights into the challenges and solutions of deploying ML in hardware. Understanding how HLS and hls4ml streamline the development of neural network-based hardware accelerators is fundamental for the industry's future. Participants will learn how these technologies are shaping the future of AI and scientific computing.

Di Guglielmo, Giuseppe [Fermilab]↗

DOE OSTI2022

Enhancing Even Gas Distribution in Porous Media with Radial Flow

Packed beds, such as those used in thermal energy storage (TES) systems, typically use flow from one end to the other. This axial flow configuration leads to inefficiencies due to dispersion effects and high pressure drop. Instead of axial flow, this work proposes radial flow in packed beds, where a central tube provides flow that transports fluid from the center to the bed’s wall. Radial flow could be a promising solution to increase the efficiency of charging/discharging processes in TES systems. For instance, studies have been conducted on the thermal behavior during the charging process using radial flow and axial flow, and it was found that radial flow is better than axial flow in terms of thermal performance, where more energy can be stored in the storage tank during the charging process. However, the design of the radial pipe should be optimized to improve even flow distribution. In this work, numerical investigations on different designs were analyzed to enhance even flow gas distribution in the porous media when using this radial technique. This work shows the impact of different parameters on the even flow distribution into the packed bed for two different designs: 1) one radial tube at the center to provide the radial flow along with an annular tube at the wall to receive the flow, and 2) one radial tube at the center and four radial tubes at the wall. Air was used as fluid and 6 mm alumina beads as packing materials. Computational fluid dynamics (CFD) models in COMSOL Multiphysics were used to simulate the behavior of air flow through the piping and packed bed. It was found that the flow into the bed from the radial tube can be affected by different parameters: space between the holes, size/diameter of the holes, number of segments/zones, number of the holes in each zone and the length of each zone.

Beck, David M.↗

DOE OSTI2020

Direct numerical simulations of turbulent reacting flows with shock waves and stiff chemistry using many-core/GPU acceleration

Compressible reacting flows may display sharp spatial variation related to shocks, contact discontinuities or reactive zones embedded within relatively smooth regions. The presence of such phenomena emphasizes the relevance of shock-capturing schemes such as the weighted essentially non-oscillatory (WENO) scheme as an essential ingredient of the numerical solver. However, these schemes are complex and have more computational cost than the simple high-order compact or non-compact schemes. In this paper, we present the implementation of a seventh-order, minimally-dissipative mapped WENO (WENO7M) scheme in a newly developed direct numerical simulation (DNS) code called KAUST Adaptive Reactive Flows Solver (KARFS). In order to make efficient use of the computer resources and reduce the solution time, without compromising the resolution requirement, the WENO routines are accelerated via graphics processing unit (GPU) computation. The performance characteristics and scalability of the code are studied using different grid sizes and block decomposition. Furthermore, the performance portability of KARFS is demonstrated on a variety of architectures including NVIDIA Tesla P100 GPUs and NVIDIA Kepler K20X GPUs. In addition, the capability and potential of the newly implemented WENO7M scheme in KARFS to perform DNS of compressible flows is also demonstrated with model problems involving shocks, isotropic turbulence, detonations and flame propagation into a stratified mixture with complex chemical kinetics.

97 MATHEMATICS AND COMPUTING↗