SEARCH · Search NASA

Results for “simulation types and techniques”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 541 records · Page 30

All sources NASA NTRS DOE OSTI

NASA NTRS2014

Quantification of In-flight Physical Changes: Anthropometry and Neutral Body Posture

Currently, NASA does not have sufficient in-flight anthropometric data gathered to assess the impact of physical body shape and size changes on suit sizing. For developing future planetary and reduced gravity suits, NASA needs to quantify the impacts of microgravity on anthropometry, body posture, and neutral body postures (NBP) to ensure optimal crew performance, fit, and comfort. To obtain these impacts, anthropometric data, circumference, length, height, breadth, and depth for body segments (i.e. chest, waist, bicep, thigh, calf) from astronauts for pre, in-, and postflight conditions needs to be collected. Once this data has been collected, a comparison between pre, in-, and postflight anthropometric values will be analyzed, yielding microgravity factors. The NBP will be used to determined body posture (joint angle) changes between subjects throughout the duration of a mission. Data collection, starting with Increments 37/38, is still in progress with the completion of 3 out of 12 subjects. NASA suit engineers and NASA's Extravehicular Activity (EVA) Project Office have identified that suit fit in microgravity could become an issue. It has been noted that crewmembers often need to adjust their suit sizing once they are in orbit. This adjustment could be due to microgravity effects on anthropometry and postural changes, and is necessary to ensure optimal crew performance, fit, and comfort in space. To date, the only data collected to determine the effects of microgravity on physical human changes have been during Skylab, STS-57, and a recent HRP study on seated height changes due to spinal elongation (Spinal Elongation, Master Task List [MTL] #221). The Skylab and the STS-57 studies found that there is a distinct neutral body posture (NBP) based on photographs. The still photographs showed that there is a distinguishable posture with the arms raised and the shoulder abducted; and, in addition, the knees were flexed with noticeable hip flexion and the foot plantar flexed [1,2]. This is the one standard set of body joint angles for a NBP in microgravity. A recent simulated microgravity NBP study [3] has shown an individual variability and inconsistencies in defining NBP. This variation may be influenced by spinal growth, the type of suit fit, and other potential anthropometry factors such as spinal curvature, age, and gender. The variation aspect of this essential data is required for all kinds of space device designs (e.g. suits, habitat, mobility aids, etc.). The method proposed considers the dynamic nature of body movement and will use a measurement technique to continually monitor posture and develop a probability likelihood of the natural posture and how the NBP postures are affected by anthropometry. Additionally, Skylab studies found that crewmembers experienced a stature growth of up to 3%. The data included 3 crewmembers that showed that there is a bi-phasic stature growth once the crew enters into weightlessness. However, the Spinal Elongation study identified that the crewmembers could experience about a 6% growth in seated height and a 3% stature growth, when exposed to microgravity. The results prove that not all anthropometric measurements have the same microgravity percent growth factor. For EVA and suit engineers to properly update the sizing protocol for microgravity, they need additional anthropometric data from space missions. Hence, this study is aimed to gather additional in-flight anthropometric measurements, such as length, depth, breadth, and circumference, to determine the changes to body shape and size due to microgravity effects. It is anticipated that by recording the potential changes to body shape and size, a better suit sizing protocol will be developed for ISS and other space missions. In essence, this study will help NASA quantify the impacts of microgravity on anthropometry to ensure optimal crew performance, fit, and comfort. This study will use simplistic data collection techniques, 3D laser scanning, digital still, and video data, and perform photogrammetric analyses to determine the changes that occur to the body shape, size, and NBP when exposed to a microgravity environment.

Young, K. S.↗

DOE OSTI2024

Rare Earth Elements (REEs) Measurement in Coal and Rock Mineral Matrices

Although critical minerals including rare earth elements (REEs) can be analyzed in laboratory by some established and reliable laboratory based analytical techniques, their in-situ measurements in the field have always been challenging. For identification of REE-rich sites and REEs distribution measurement, portable field applicable technologies are paramount. As Laser-induced breakdown spectroscopy (LIBS) has enormous potential for field measurement, it has been explored for REEs measurements by many research groups. However, most of the studies are still dealing with simulated samples with traditional bench top experiments. In real world, REEs are available in various types of natural complex matrices in low content depending on the geographical locations. Considering this, LIBS has been evaluated for REE measurement in two different complex coal and rock mineral matrices representing some natural REE-rich sites. In addition, multiple samples collected from some natural sites in Wyoming, USA were experimented by using NETL’s bench top as well as miniaturized prototype setups for REE measurements.

Bhatt, Chet R.↗

NASA NTRS1981

A sensitivity model for energy consumption in buildings. Part 1: Effect of exterior environment

A simple analytical model is developed for the simulation of seasonal heating and cooling loads of any class of buildings to complement available computerized techniques which make hourly, daily, and monthly calculations. An expression for the annual energy utilization index, which is a common measure of rating buildings having the same functional utilization, is derived to include about 30 parameters for both building interior and exterior environments. The sensitivity of a general class building to either controlled or uncontrolled weather parameters is examined. A hypothetical office type building, located at the Goldstone Space Communication Complex, Goldstone, California, is selected as an example for the numerical sensitivity evaluations. Several expressions of variations in local outside air temperature, pressure, solar radiation, and wind velocity are presented.

Lansing, F. L.↗

NASA NTRS1990

Defining, modeling, and measuring system lag in virtual environments

In such real-time interactive computer environments as those used for virtual environments and simulators, system lag dramatically affects system usability. Attention is presently given to two types of lag: (1) transmission lag time, which is the difference between the moving of a sensing device and that device's motion on a graphic display, and (2) position lag, which is the difference between the actual position of a tracker in motion and the displayed position of a tracker at the same time. A method for measuring these types of lag using a video technique was developed for the NASA-Ames Virtual Interactive Environment Workstation. The position lag can be understood in terms of the transmission lag, so that optimizing a system for small transmission lag will also optimize for small position lag.

Bryson, Steve↗

NASA NTRS1996

Concurrent Probabilistic Simulation of High Temperature Composite Structural Response

A computational structural/material analysis and design tool which would meet industry's future demand for expedience and reduced cost is presented. This unique software 'GENOA' is dedicated to parallel and high speed analysis to perform probabilistic evaluation of high temperature composite response of aerospace systems. The development is based on detailed integration and modification of diverse fields of specialized analysis techniques and mathematical models to combine their latest innovative capabilities into a commercially viable software package. The technique is specifically designed to exploit the availability of processors to perform computationally intense probabilistic analysis assessing uncertainties in structural reliability analysis and composite micromechanics. The primary objectives which were achieved in performing the development were: (1) Utilization of the power of parallel processing and static/dynamic load balancing optimization to make the complex simulation of structure, material and processing of high temperature composite affordable; (2) Computational integration and synchronization of probabilistic mathematics, structural/material mechanics and parallel computing; (3) Implementation of an innovative multi-level domain decomposition technique to identify the inherent parallelism, and increasing convergence rates through high- and low-level processor assignment; (4) Creating the framework for Portable Paralleled architecture for the machine independent Multi Instruction Multi Data, (MIMD), Single Instruction Multi Data (SIMD), hybrid and distributed workstation type of computers; and (5) Market evaluation. The results of Phase-2 effort provides a good basis for continuation and warrants Phase-3 government, and industry partnership.

Abdi, Frank↗

NASA NTRS2012

Functional Near Infrared Spectroscopy: Watching the Brain in Flight

Functional Near Infrared Spectroscopy (fNIRS) is an emerging neurological sensing technique applicable to optimizing human performance in transportation operations, such as commercial aviation. Cognitive state can be determined via pattern classification of functional activations measured with fNIRS. Operational application calls for further development of algorithms and filters for dynamic artifact removal. The concept of using the frequency domain phase shift signal to tune a Kalman filter is introduced to improve the quality of fNIRS signals in realtime. Hemoglobin concentration and phase shift traces were simulated for four different types of motion artifact to demonstrate the filter. Unwanted signal was reduced by at least 43%, and the contrast of the filtered oxygenated hemoglobin signal was increased by more than 100% overall. This filtering method is a good candidate for qualifying fNIRS signals in real time without auxiliary sensors

Harrivel, Angela↗

DOE OSTI2023

Comparison of FAST Experiments to BISON Simulations

The Fission Accelerated Steady-State Test (FAST) experiments utilize the effects of scaling to accelerate the burnup experienced by the fuel. This experimental technique offers a unique opportunity to evaluate the effects of scaling on fuel and cladding material modelling. Currently, models used in the BISON fuel performance code for metallic fuel performance are calibrated for EBR-II conditions and geometries. Comparing BISON simulations to FAST experimental data will allow for the identification of shortcomings in the models for conditions outside the EBR-II paradigm. FAST experiments have been performed on U-Zr and U-10Mo fuel types with HT9 cladding. Initial comparisons of simulated cladding strains to experimental results show that the BISON simulations consistently overpredict cladding strain in the fuel region but underpredict the cladding strain in the plenum region. This indicates potential issues with the simulation of swelling and gas pressure at smaller geometries. Further comparison with fission gas release measurements is planned as data becomes available.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Scalable preconditioning for the stabilized contact mechanics problem

We present a family of preconditioning strategies for the contact problem in fractured and faulted porous media. We combine low-order continuous finite elements to simulate the bulk deformation with piecewise constant Lagrange multipliers to impose the frictional contact constraints. This formulation is not uniformly inf-sup stable and requires stabilization. We improve previous work by Franceschini et al. (2020) by introducing a novel jump stabilization technique that requires only local geometrical and mechanical properties. We then design scalable preconditioning strategies that take advantage of the block structure of the Jacobian matrix using a physics-based partitioning of the unknowns by field type, namely displacement and Lagrange multipliers. The key to the success of the proposed preconditioners is a pseudo-Schur complement obtained by eliminating the Lagrange multiplier degrees of freedom, which can then be efficiently solved using an optimal multigrid method. Numerical results, including complex real-world problems, are presented to illustrate theoretical properties, scalability and robustness of the preconditioner. A comparison with other approaches available in the literature is also provided.

58 GEOSCIENCES↗

NASA NTRS1989

Tools for 3D scientific visualization in computational aerodynamics

The purpose is to describe the tools and techniques in use at the NASA Ames Research Center for performing visualization of computational aerodynamics, for example visualization of flow fields from computer simulations of fluid dynamics about vehicles such as the Space Shuttle. The hardware used for visualization is a high-performance graphics workstation connected to a super computer with a high speed channel. At present, the workstation is a Silicon Graphics IRIS 3130, the supercomputer is a CRAY2, and the high speed channel is a hyperchannel. The three techniques used for visualization are post-processing, tracking, and steering. Post-processing analysis is done after the simulation. Tracking analysis is done during a simulation but is not interactive, whereas steering analysis involves modifying the simulation interactively during the simulation. Using post-processing methods, a flow simulation is executed on a supercomputer and, after the simulation is complete, the results of the simulation are processed for viewing. The software in use and under development at NASA Ames Research Center for performing these types of tasks in computational aerodynamics is described. Workstation performance issues, benchmarking, and high-performance networks for this purpose are also discussed as well as descriptions of other hardware for digital video and film recording.

Bancroft, Gordon↗

NASA NTRS1998

Testing and Troubleshooting Automatically Generated Source Code

Tools allowing engineers to model the real-time behavior of systems that control many types of NASA systems have become widespread. These tools automatically generate source code that is compiled, linked, then downloaded into computers controlling everything from wind tunnels to space flight systems. These tools save hundreds of hours of software development time and allow engineers with thorough application area knowledge but little software development experience to generate software to control the systems they use daily. These systems are verified and validated by simulating the real-time models, and by other techniques that focus on the model or the hardware. The automatically generated source code is typically not subjected to rigorous testing using conventional software testing techniques. Given the criticality and safety issues surrounding these systems, the application of conventional and new software testing and troubleshooting techniques to the automatically generated will improve the reliability of the resulting systems.

Henry, Joel↗

NASA NTRS1983

Laboratory analysis of techniques for remote sensing of estuarine parameters using laser excitation

The theoretical concepts underlying remote sensing of estuarine parameters using laser excitation are examined. The concepts are extended to include Mie scattering as a measure of the total suspended solids and to develop the water Raman signal as an internal standard. Experimental validation of the theory was performed using backscattered laser light from a laboratory tank to simulate a remote-sensing geometry. Artificially prepared sediments and biological cultures were employed to check specific aspects of the theory under controlled conditions. Natural samples gathered from a variety of water types were also analyzed in the tank to further enhance the simulation. The results indicate that it should be possible to remotely quantify total suspended solids, dissolved organics, attenuation coefficient, chlorophyll a, and phycoerythrin in estuarine water using laser excitation.

Exton, R. J.↗

NASA NTRS1972

Study of dense aluminum plasmas

Studies directed toward the development of a computer program describing the penetration of a thin aluminum plate by a quartz sphere are reported. The aluminum simulates a bumper plate for micrometeoroids. The ablation of a rock sphere by penetrating a stack of paper sheets is described, and an equation for losses near the surface of the sphere is derived. The expansions of aluminum plasma sphere with initial energies of 44.45, 20.8, and 7.136 eV are investigated, including shock compression during penetration and adiabatic expansion. The equations of state were derived for aluminum and quartz, as well as one of the Mie-Grunesen type. A technique to determine momentum at the bottom surface of the thin plate, and the energy for hypervelocity separation of fragments of the aluminum plate are also considered.

Todd, F. C.↗

NASA NTRS1987

A piloted simulation of helicopter air combat to investigate effects of variations in selected performance and control response characteristics

A piloted simulation study investigating handling qualities and flight characteristics required for helicopter air to air combat is presented. The Helicopter Air Combat system was used to investigate this role for Army rotorcraft. Experimental variables were the maneuver envelope size (load factor and sideslip), directional axis handling qualities, and pitch and roll control-response type. Over 450 simulated, low altitude, one-on-one engagements were conducted. Results from the experiment indicate that a well damped directional response, low sideforce caused by sideslip, and some effective dihedral are all desirable for weapon system performance, good handling qualities, and low pilot workload. An angular rate command system was favored over the attitude type pitch and roll response for most applications, and an enhanced maneuver envelope size over that of current generation aircraft was found to be advantageous. Pilot technique, background, and experience are additional factors which had a significant effect on performance in the air combat tasks investigated. The implication of these results on design requirements for future helicopters is presented.

Lewis, Michael S.↗

NASA NTRS2012

Functional Near Infrared Spectroscopy: Watching the Brain in Flight

Functional Near Infrared Spectroscopy (fNIRS) is an emerging neurological sensing technique applicable to optimizing human performance in transportation operations, such as commercial aviation. Cognitive state can be determined via pattern classification of functional activations measured with fNIRS. Operational application calls for further development of algorithms and filters for dynamic artifact removal. The concept of using the frequency domain phase shift signal to tune a Kalman filter is introduced to improve the quality of fNIRS signals in real-time. Hemoglobin concentration and phase shift traces were simulated for four different types of motion artifact to demonstrate the filter. Unwanted signal was reduced by at least 43%, and the contrast of the filtered oxygenated hemoglobin signal was increased by more than 100% overall. This filtering method is a good candidate for qualifying fNIRS signals in real time without auxiliary sensors.

Harrivel, Angela↗

NASA NTRSDate not supplied

Autonomous Ocean World Exploration: Advancement of a Virtual Testbed

The search for life (extinct or extant) and potentially habitable bodies in our solar system and beyond is one of the 12 priority science questions outlined in the National Acadamies’ 2022 decadal survey [5]. Extraterrestrial destinations containing liquid water present an opportunity to search for life as we know it, and in recent years an increasing number of such locations have been discovered within our solar system. Several Jovian moons—Europa, Ganymede, and Callisto [10]—and the Saturnian moons Enceladus [8] and Titan [9] are known or suspected to harbor massive subsurface oceans. Of these "ocean worlds", Europa is the focus of at least one planned NASA orbiter mission, Europa Clipper [4], and an early lander mission concept, the Europa Lander [2, 3]. Whereas most robotic missions to the Moon and Mars (e.g. orbiters, rovers, landers) to date have had ground controllers on Earth tightly involved in mission operations, missions to more distant worlds will require a high degree of onboard autonomy due to long communication lags and blackouts, harsh environments (radiation, cold), and more limited battery and hardware life. The past decade has seen great advances in both AI technologies and computing scalability and performance that offer promising solutions for spacecraft autonomy and motivate the software system and research programs described in this paper. The Ocean Worlds Autonomy Testbed for Exploration, Research, and Simulation (OceanWATERS) [1], which has been in development at the NASA Ames Research Center since 2018, is a virtual environment for testing lander autonomy solutions. It is built on the Robot Operating System (ROS), runs on consumer-grade Linux workstations, and was released as open source in 2020. OceanWATERS provides a physical and visual simulation of a prototypical lander in a Europa-like environment (Figure 1). The lander was modeled after requirements and specifications made in JPL’s Europa Lander Study of 2016 [3]. Simulated lander systems include stereo cameras and spotlights mounted on an antenna mast that pans and tilts, a 6 degrees of freedom (DoF) robotic arm with a force-torque sensor and two interchangeable end effectors, and a battery pack power system. The environment consists of multiple terrain models including a highly detailed model sourced from the FROST dataset [11], simulation of surrounding planetary bodies based on an ephemeris model, and lighting from the sun with associated surface illumination, reflectance, and shadows. Operations supported by OceanWATERS include panoramic and directed imaging of the environment and lander workspace, Cartesian and joint-level arm commanding, grinding of the terrain surface (e.g. digging a trench), and scooping of ground material (Figure 2) which can be discarded or collected as science samples in a receptacle that can be emptied (science operations themselves are not simulated). These operations are realized as ROS Actions and are complimented by a wide selection of telemetry that is continually produced by each lander subsystem. The power system model is driven by the open-source Generic Software Architecture for Prognostics (GSAP) [11] that predicts the battery’s remaining useful life and other characteristics. As a testbed for high-level autonomy, OceanWATERS provides an execution framework based on PLEXIL [12], an open-source plan specification language and execution engine developed largely at Ames. NASA's initial development of OceanWATERS, as well the Ocean Worlds Lander Autonomy Testbed (OWLAT) [6], a complimentary physical testbed developed at JPL, was the first step in a plan for realizing candidate onboard autonomy solutions for such planetary landers. In 2020 NASA solicited applications for its Autonomous Robotics Research for Ocean Worlds (ARROW) program, and in 2021 the similar Concepts for Ocean worlds Life Detection Technology (COLDTech) program. Collectively six research teams, based in universities and companies across the United States, were awarded grants to develop and demonstrate autonomy solutions on OceanWATERS and OWLAT. These 1–2-year projects have now finished or are nearing completion, and a wide variety of autonomy challenges in ocean world surface missions were addressed. Prototyped and demonstrated solutions have included autonomous discovery, response and adaptation to system faults and unexpected environmental events, world model synthesis through perception, plan synthesis using learned models, methods to optimize sample target selection and prioritize science data transmission, extension of PLEXIL for stochastic decision-making, and an integration of a model of JPL’s mission-ready COLDArm [7]. Technologies used in these projects include many forms of machine learning, causal reasoning, automated planning, Markov decision processes, formal methods, and other advanced techniques. A more detailed summary of the ARROW and COLDTech projects is given herein. OceanWATERS has had significant enhancements since its open-source release in 2020. Many of its new features were driven or shaped by feedback from the ARROW and COLDTech teams and requirements of their projects. In support of enabling autonomous adaptation to spacecraft faults (a specific capability solicited by both programs), a fault injection and detection framework was developed that supports a wide and growing range of fault types such as locked joints, image loss, and battery failures. The power system model was completed and integrated into the simulator, starting as a single-cell battery model and later upgraded to a multi-cell model with associated faults such as cell disconnection. Arm/terrain interaction was improved by adding a force-torque sensor and associated faults, and an analytic dig force model based on the Balovnev bucket force equations. Environment fidelity was increased by modeling terrain deformation resulting from digging and scooping; visual improvements were made in textures, lighting, and shadows. To facilitate interoperation with OWLAT, a unified command and telemetry interface between the testbeds was developed at the ROS level, along with a PLEXIL interface. The number of lander operations was greatly expanded (e.g. with Cartesian-based arm and antenna movement), and a framework was designed for users to build their own lander actions. A GUI for PLEXIL plan selection was created (Figure 3), and an expansive set of plans were added, such as those that illustrate patterns for fault handling. This paper provides a self-contained high-level description of OceanWATERS, focusing on more detailed coverage of the aforementioned enhancements. It provides a high-level summary of the projects undertaken by participants in the ARROW and COLDTech programs and how these efforts have helped shape OceanWATERS. Finally, potential future work and directions for the testbed are listed, as likely informed by the recent planetary science decadal survey [5].

K Michael Dalal↗

NASA NTRS2000

A New Method for Accurate Treatment of Flow Equations in Cylindrical Coordinates Using Series Expansions

The motivation of this work is the ongoing effort at the Center for Turbulence Research (CTR) to use large eddy simulation (LES) techniques to calculate the noise radiated by jet engines. The focus on engine exhaust noise reduction is motivated by the fact that a significant reduction has been achieved over the last decade on the other main sources of acoustic emissions of jet engines, such as the fan and turbomachinery noise, which gives increased priority to jet noise. To be able to propose methods to reduce the jet noise based on results of numerical simulations, one first has to be able to accurately predict the spatio-temporal distribution of the noise sources in the jet. Though a great deal of understanding of the fundamental turbulence mechanisms in high-speed jets was obtained from direct numerical simulations (DNS) at low Reynolds numbers, LES seems to be the only realistic available tool to obtain the necessary near-field information that is required to estimate the acoustic radiation of the turbulent compressible engine exhaust jets. The quality of jet-noise predictions is determined by the accuracy of the numerical method that has to capture the wide range of pressure fluctuations associated with the turbulence in the jet and with the resulting radiated noise, and by the boundary condition treatment and the quality of the mesh. Higher Reynolds numbers and coarser grids put in turn a higher burden on the robustness and accuracy of the numerical method used in this kind of jet LES simulations. As these calculations are often done in cylindrical coordinates, one of the most important requirements for the numerical method is to provide a flow solution that is not contaminated by numerical artifacts. The coordinate singularity is known to be a source of such artifacts. In the present work we use 6th order Pade schemes in the non-periodic directions to discretize the full compressible flow equations. It turns out that the quality of jet-noise predictions using these schemes is especially sensitive to the type of equation treatment at the singularity axis. The objective of this work is to develop a generally applicable numerical method for treating the singularities present at the polar axis, which is particularly suitable for highly accurate finite-differences schemes (e.g., Pade schemes) on non-staggered grids. The main idea is to reinterpret the regularity conditions developed in the context of pseudo-spectral methods. A set of exact equations at the singularity axis is derived using the appropriate series expansions for the variables in the original set of equations. The present treatment of the equations preserves the same level of accuracy as for the interior scheme. We also want to point out the wider utility of the method, proposed here in the context of compressible flow equations, as its extension for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical coordinates with finite-differences schemes of various level of accuracy is straightforward. The robustness and accuracy of the proposed technique is assessed by comparing results from simulations of laminar forced-jets and turbulent compressible jets using LES with similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r = 0.

Constantinescu, G.S.↗

DOE OSTI2020

Neutrino Transport with Monte Carlo Method. I. Toward Fully Consistent Implementation of Nucleon Recoils in Core-collapse Supernova Simulations

The small energy exchange via nucleon recoils in neutrino–nucleon scattering is now supposed to be one of the important factors for successful explosions of core-collapse supernovae (CCSNe), as they can change neutrino spectra through accumulation of a large number of scatterings. In deterministic methods employed for neutrino transport in CCSN simulations, we normally cannot afford to deploy a large enough number of energy bins needed to resolve this small energy exchange, and subgrid techniques are employed one way or another. In this paper, we study quantitatively with the Monte Carlo (MC) method how well such a treatment performs. We first investigate the effects of nucleon recoils on the neutrino spectra and confirm that the average energy is reduced by ~15% for heavy-lepton neutrinos and much smaller amounts for other types of neutrinos in a typical postbounce situation. It is also observed that the nucleon scattering dominates the electron scattering in the thermalization of neutrino spectra in all flavors. We then study possible artifacts that the coarse energy grid may produce in the deterministic methods. In order to mimic the latter calculation, we redistribute MC particles in each energy bin after a certain interval in a couple of ways and study how the results are affected, depending on the energy resolution. We also discuss the possible implications of our results for the deterministic methods.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1996

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Molenaar, J.↗