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At least 253 records · Page 14

Embedded mesh solution of the 2-D Euler equations - Evaluation of interface formulations

Solution of the steady 2-D Euler equations using mesh embedding, or local grid refinement, with a cell-centered finite volume scheme is investigated. Embedded regions which are topologically similar to the global grid are considered. An isoenergetic model for the governing equations is used in Jameson's finite volume multistage scheme with modifications to the boundary conditions and smoothing. A detailed study of the embedding interface flux and smoothing formulations is conducted. Taylor expansion analysis reveals that local second order spatial accuracy is not possible if a conservative interface flux formulation is used. The analysis also gives constraints for local first order accuracy. An energy stability analysis indicates that downwind weighting of interface fluxes causes local instabilities. Analysis shows that conservative interface smoothing formulations must have a locally convective component, but that correct interface formulations allow globally dissipative smoothing. Embedded mesh solutions obtained with this scheme are presented for a transonic airfoil. They show that if embedding interfaces are close to the shocks, then small modifications in the interface location can have large effects on converge and solution accuracy.

Allmaras, S. R.↗

Annual Research Briefs - 1996, Center for Turbulence Research

Partial contents include: (1) Simulation of jet impingement heat transfer with the k-e-V2 model; (2) A new methodology for turbulence modelers using Direct Numerical Simulation (DNS) database analysis; (3) A particle representation model for the deformation of homogeneous turbulence; (4) Modeling of inhomogeneous compressible turbulence using a two-scale statistical theory; (5) Lewis number effects on partially premixed flames; (6) Conditional moment closure of mixing and reaction in turbulent non-premixed combustion; (7) Dynamic models for LES of turbulent front propagation with a spectral method; (8) Jet noise using large eddy simulation; (9) Towards numerical simulations of trailing-edge aeroacoustics; (10) A model for the onset of vortex breakdown; (11) Compressing an elliptic vortex: transition to turbulence by tumble breakdown; (12) A new method for the adaptive control of vortex-wall interactions; (13) Symmetries in turbulent boundary layer flows; (14) Near-wall models in large eddy simulations of flow behind a backward-facing step; (15) Assessment of the subgrid-scale models at low and high Reynolds numbers; (16) Large-eddy simulations of flow around a NACA 4412 airfoil using unstructured grids; (17) Progress on LES of flow past a circular cylinder; (18) Experimental investigation of flow through an asymmetric plane diffuser; (19) Progress in the large-eddy simulation of an asymmetric plane diffuser; (20) A numerical study of self-similarity in a turbulent plane wake using large-eddy simulation; (21) On the generation of turbulent inflow conditions for boundary layer simulations, and (22) A new class of finite difference schemes.

COMPUTATIONAL FLUID DYNAMICS↗

Dynamics of Active Separation Control at High Reynolds Numbers

A series of active flow control experiments were recently conducted at high Reynolds numbers on a generic separated configuration. The model simulates the upper surface of a 20% thick Glauert-Goldschmied type airfoil at zero angle of attack. The flow is fully turbulent since the tunnel sidewall boundary layer flows over the model. The main motivation for the experiments is to generate a comprehensive data base for validation of unsteady numerical simulation as a first step in the development of a CFD design tool, without which it would not be possible to effectively utilize the great potential of unsteady flow control. This paper focuses on the dynamics of several key features of the baseline as well as the controlled flow. It was found that the thickness of the upstream boundary layer has a negligible effect on the flow dynamics. It is speculated that separation is caused mainly by the highly convex surface while viscous effects are less important. The two-dimensional separated flow contains unsteady waves centered on a reduced frequency of 0.8, while in the three dimensional separated flow, frequencies around a reduced frequency of 0.3 and 1 are active. Several scenarios of resonant wave interaction take place at the separated shear-layer and in the pressure recovery region. The unstable reduced frequency bands for periodic excitation are centered on 1.5 and 5, but these reduced frequencies are based on the length of the baseline bubble that shortens due to the excitation. The conventional swept wing-scaling works well for the coherent wave features. Reproduction of these dynamic effects by a numerical simulation would provide benchmark validation.

Pack, LaTunia G.↗

Dynamics of Active Separation Control at High Reynolds Numbers

A series of active flow control experiments were recently conducted at high Reynolds numbers on a generic separated configuration. The model simulates the upper surface of a 20% thick Glauert-Goldschmied type airfoil at zero angle of attack. The flow is fully turbulent since the tunnel sidewall boundary layer flows over the model. The main motivation for the experiments is to generate a comprehensive data base for validation of unsteady numerical simulation as a first step in the development of a CFD design tool, without which it would not be possible to effectively utilize the great potential of unsteady flow control. This paper focuses on the dynamics of several key features of the baseline as well as the controlled flow. It was found that the thickness of the upstream boundary layer has a negligible effect on the flow dynamics. It is speculated that separation is caused mainly by the highly convex surface while viscous effects are less important. The two-dimensional separated flow contains unsteady waves centered on a reduced frequency of 0.9, while in the three dimensional separated flow, frequencies around a reduced frequency of 0.3 and 1 are active. Several scenarios of resonant wave interaction take place at the separated shear-layer and in the pressure recovery region. The unstable reduced frequency bands for periodic excitation are centered on 1.5 and 5, but these reduced frequencies are based on the length of the baseline bubble that shortens due to the excitation. The conventional works well for the coherent wave features. Reproduction of these dynamic effects by a numerical simulation would provide benchmark validation.

Pack, LaTunia G.↗

Benchmark Problems Used to Assess Computational Aeroacoustics Codes

The field of computational aeroacoustics (CAA) encompasses numerical techniques for calculating all aspects of sound generation and propagation in air directly from fundamental governing equations. Aeroacoustic problems typically involve flow-generated noise, with and without the presence of a solid surface, and the propagation of the sound to a receiver far away from the noise source. It is a challenge to obtain accurate numerical solutions to these problems. The NASA Glenn Research Center has been at the forefront in developing and promoting the development of CAA techniques and methodologies for computing the noise generated by aircraft propulsion systems. To assess the technological advancement of CAA, Glenn, in cooperation with the Ohio Aerospace Institute and the AeroAcoustics Research Consortium, organized and hosted the Fourth CAA Workshop on Benchmark Problems. Participants from industry and academia from both the United States and abroad joined to present and discuss solutions to benchmark problems. These demonstrated technical progress ranging from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The results are documented in the proceedings of the workshop. Problems were solved in five categories. In three of the five categories, exact solutions were available for comparison with CAA results. A fourth category of problems representing sound generation from either a single airfoil or a blade row interacting with a gust (i.e., problems relevant to fan noise) had approximate analytical or completely numerical solutions. The fifth category of problems involved sound generation in a viscous flow. In this case, the CAA results were compared with experimental data.

Dahl, Milo D.↗

Mars Science Helicopter: Conceptual Design of the Next Generation of Mars Rotorcraft

Robotic planetary aerial vehicles increase the range of terrain that can be examined, compared to traditional landers and rovers, and have more near-surface capability than orbiters. Aerial mobility is a promising possibility for planetary exploration as it reduces the challenges that difficult obstacles pose to ground vehicles. The first use of a rotorcraft for a planetary mission will be in 2021, when the Ingenuity Mars helicopter technology demonstrator will be deployed via the Perseverance rover. NASA’s Jet Propulsion Laboratory and NASA Ames Research Center are exploring possibilities for a Mars Science Helicopter, a second-generation Mars rotorcraft with the capability of conducting science investigations independently of a lander or rover (although this type of vehicle could also be used to assist rovers or landers in future missions). Two, large rotorcraft configurations are described: a hexacopter and a co-axial helicopter with a payload in the range of two to three kilograms and an overall vehicle mass of approximately twenty kilograms. Additionally, advancements in technology over the course of the study are applied to a rotorcraft of the same size and form as Ingenuity. Initial estimates of weight and performance were based on the capabilities of Ingenuity. Rotorcraft designs for Mars are constrained by the dimensions of the aeroshell and lander for the trip to the planet, constraining maximum rotor dimensions and, hence, overall performance potential. The effects of airfoils designed specifically for the low Reynolds number and high Mach number inherent to operation on Mars were studied. Rotor structural designs were developed that met blade frequency and weight targets, subject to material stress limits. The final designs are representative of the vehicle configurations required for a large range of future missions and will require relatively minor adaptations once science tasks are chosen. These designs will be compared to Ingenuity to demonstrate technology advancements developed during the study.

Mars Science Helicopter↗

Efficient Use of Distributed Systems for Scientific Applications

Distributed computing has been regarded as the future of high performance computing. Nationwide high speed networks such as vBNS are becoming widely available to interconnect high-speed computers, virtual environments, scientific instruments and large data sets. One of the major issues to be addressed with distributed systems is the development of computational tools that facilitate the efficient execution of parallel applications on such systems. These tools must exploit the heterogeneous resources (networks and compute nodes) in distributed systems. This paper presents a tool, called PART, which addresses this issue for mesh partitioning. PART takes advantage of the following heterogeneous system features: (1) processor speed; (2) number of processors; (3) local network performance; and (4) wide area network performance. Further, different finite element applications under consideration may have different computational complexities, different communication patterns, and different element types, which also must be taken into consideration when partitioning. PART uses parallel simulated annealing to partition the domain, taking into consideration network and processor heterogeneity. The results of using PART for an explicit finite element application executing on two IBM SPs (located at Argonne National Laboratory and the San Diego Supercomputer Center) indicate an increase in efficiency by up to 36% as compared to METIS, a widely used mesh partitioning tool. The input to METIS was modified to take into consideration heterogeneous processor performance; METIS does not take into consideration heterogeneous networks. The execution times for these applications were reduced by up to 30% as compared to METIS. These results are given in Figure 1 for four irregular meshes with number of elements ranging from 30,269 elements for the Barth5 mesh to 11,451 elements for the Barth4 mesh. Future work with PART entails using the tool with an integrated application requiring distributed systems. In particular this application, illustrated in the document entails an integration of finite element and fluid dynamic simulations to address the cooling of turbine blades of a gas turbine engine design. It is not uncommon to encounter high-temperature, film-cooled turbine airfoils with 1,000,000s of degrees of freedom. This results because of the complexity of the various components of the airfoils, requiring fine-grain meshing for accuracy. Additional information is contained in the original.

Taylor, Valerie↗

Hydrodynamic Characteristics of Two Low-Drag Supercavitating Hydrofoils

An experimental investigation has been conducted in Langley tank no. 2 to determine the hydrodynamic characteristics of two low-drag supercavitating hydrofoils operating in a range of cavitation numbers from 0 to approximately 6. The hydrofoils had aspect ratios of 1 and 3, and the sections were derived by assuming five terms in the vorticity-distribution expansion of the equivalent airfoil. The aspect-ratio-1 hydrofoil was also tested at zero cavitation number with two sets of end plates having depths of 3/8 and 1/4 chords. Zero cavitation number was established by operating the hydrofoils near the water surface so that complete ventilation of the upper surfaces could be obtained. For those depths of submersion where complete ventilation was not obtained through vortex ventilation, two probes were used to introduce air to the upper surfaces of the hydrofoils and to induce complete ventilation. Data were obtained for a range of speeds from 20 to 80 fps, angles of attack from 2 to 20 deg, and ratios of depth of submersion to chord from 0 to 0.85. The experimental results obtained from the aspect-ratio-1 and aspect-ratio-3, five-term hydrofoils were compared with a three-dimensional zero-cavitation-number theory. The theoretical and experimental values of lift and center of pressure for the aspect-ratio-1 hydrofoil were in agreement, within engineering accuracy, for the range of lift coefficients investigated. The theoretical drag coefficients were lower, by a constant amount, than the experimental drag coefficients. The theoretical expressions derived for the lift, drag, and center of pressure of the aspect-ratio-3 hydrofoil were in agreement, within engineering accuracy, with the experimental values. The theoretical and experimental drag coefficients of the aspect-ratio-3 five-term hydrofoil were lower than the theoretical drag coefficients computed for a comparable Tulin-Burkart hydrofoil.

McGehee, John R.↗

Experience with advanced instrumentation in a hot section cascade

The Lewis Research Center gas turbine Hot Section Test Facility was developed to provide a real engine environment with known boundary conditions for the aerothermal performance evaluation and verification of computer design codes. This verification process requires experimental measurements in a hostile environment. The research instruments used in this facility are presented, and their characteristics and how they perform in this environment are discussed. The research instrumentation consisted of conventional pressure and temperature sensors, as well as thin-film thermocouples and heat flux gages. The hot gas temperature was measured by an aspirated temperature probe and by a dual-element, fast-response temperature probe. The data acquisition mode was both steady state and time dependent. These experiments were conducted over a wide range of gas Reynolds numbers, exit gas Mach numbers, and heat flux levels. This facility was capable of testing at temperatures up to 1600 K, and at pressures up to 18 atm. These corresponded to an airfoil exit Reynolds number range of 0.5 x 10(6) to 2.5 x 10(6) based on the airfoil chord of 5.55 cm. The results characterize the performance capability and the durability of the instrumentation. The challenge of making measurements in hostile environments is also discussed. The instruments exhibited more than adequate durability to achieve the measurement profile. About 70 percent of the thin-film thermocouples and the dual-element temperature probe survived several hundred thermal cycles and more than 35 hr at gas temperatures up to 1600 K. Within the experimental uncertainty, the steady-state and transient heat flux measurements were comparable and consistent over the range of Reynolds numbers tested.

Yeh, Frederick C.↗

Damping coefficients due to tail surfaces in aircraft

The object of the investigation described in this report was to compare the damping coefficients of an airfoil as calculated from a knowledge of the static characteristics of the section with those obtained experimentally with an oscillation. The damping coefficients as obtained, according to the conventional notation, can be considered either as due to pitching or as due to yawing, the oscillation in these experiments being so arranged that the surfaces oscillate about a vertical axis. This is in reality the case when the influence is yawing about the standard Z-axis, but it can also be considered as a pitching motion when the model is so rigged that its standard Y-axis becomes vertical. The horizontal oscillation has the advantage of eliminating the gravity action and avoiding the use of counterweights, whose presence in the wind tunnel is undesirable because of their interference with the air flow. The real point of the investigation was to separate the damping due to rotation from that due to translation. By varying the distance between the center of pressure and the center of rotation on the oscillator, the variation of damping moment can be observed and the rotational and translational effects can be separated.

Chu, Lynn↗

Overview of High Speed Close-Up Imaging in an Icing Environment

The Icing Branch and Imaging Technology Center at NASA Glenn Research Center have recently been involved in several projects where high speed close-up imaging was used to investigate water droplet impact/splash, and also ice particle impact/bounce in an icing wind tunnel. The combination of close-up and high speed imaging capabilities were required because the particles being studied were relatively small (d < 1 mm in diameter), and the impact process occurred in a very short time period (t(sub impact) << 1 sec). High speed close-up imaging was utilized to study the dynamics of droplet impact and splash in simulated Supercooled Large Droplet (SLD) icing conditions. The objective of this test was to evaluate the capability of a ultra high speed camera system to acquire quantitative information about the impact process (e.g., droplet size, velocity). Imaging data were obtained in an icing wind tunnel for spray cloud MVD > 50 m. High speed close-up imaging was also utilized to characterize the impact of ice particles on an airfoil with a thermally protected leading edge. The objective of this investigation was to determine whether ice particles tend to "stick" or "bounce" after impact. Imaging data were obtained for cases where the airfoil surface was heated and unheated. Based on the results from this test, follow on tests were conducted to investigate ice particle impact on the sensing elements of water content measurement devices. This paper will describe the use of the imaging systems to support these experimental investigations, present some representative results, and summarize what was learned about the use of these systems in an icing environment.

Miller, Dean R.↗

NASA Tech Briefs, January 2014

Topics include: Multi-Source Autonomous Response for Targeting and Monitoring of Volcanic Activity; Software Suite to Support In-Flight Characterization of Remote Sensing Systems; Visual Image Sensor Organ Replacement; Ultra-Wideband, Dual-Polarized, Beam-Steering P-Band Array Antenna; Centering a DDR Strobe in the Middle of a Data Packet; Using a Commercial Ethernet PHY Device in a Radiation Environment; Submerged AUV Charging Station; Habitat Demonstration Unit (HDU) Vertical Cylinder Habitat; Origami-Inspired Folding of Thick, Rigid Panels; A Novel Protocol for Decoating and Permeabilizing Bacterial Spores for Epifluorescent Microscopy; Method and Apparatus for Automated Isolation of Nucleic Acids from Small Cell Samples; Enabling Microliquid Chromatography by Microbead Packing of Microchannels; On-Command Force and Torque Impeding Devices (OC-FTID) Using ERF; Deployable Fresnel Rings; Transition-Edge Hot-Electron Microbolometers for Millimeter and Submillimeter Astrophysics; Spacecraft Trajectory Analysis and Mission Planning Simulation (STAMPS) Software; Cross Support Transfer Service (CSTS) Framework Library; Arbitrary Shape Deformation in CFD Design; Range Safety Flight Elevation Limit Calculation Software; Frequency-Modulated, Continuous-Wave Laser Ranging Using Photon-Counting Detectors; Calculation of Operations Efficiency Factors for Mars Surface Missions; GPU Lossless Hyperspectral Data Compression System; Robust, Optimal Subsonic Airfoil Shapes; Protograph-Based Raptor-Like Codes; Fuzzy Neuron: Method and Hardware Realization; Kalman Filter Input Processor for Boresight Calibration; Organizing Compression of Hyperspectral Imagery to Allow Efficient Parallel Decompression; and Temperature Dependences of Mechanisms Responsible for the Water-Vapor Continuum Absorption.

Source record↗

Validation of a Node-Centered Wall Function Model for the Unstructured Flow Code FUN3D

In this paper, the implementation of two wall function models in the Reynolds averaged Navier-Stokes (RANS) computational uid dynamics (CFD) code FUN3D is described. FUN3D is a node centered method for solving the three-dimensional Navier-Stokes equations on unstructured computational grids. The first wall function model, based on the work of Knopp et al., is used in conjunction with the one-equation turbulence model of Spalart-Allmaras. The second wall function model, also based on the work of Knopp, is used in conjunction with the two-equation k-! turbulence model of Menter. The wall function models compute the wall momentum and energy flux, which are used to weakly enforce the wall velocity and pressure flux boundary conditions in the mean flow momentum and energy equations. These wall conditions are implemented in an implicit form where the contribution of the wall function model to the Jacobian are also included. The boundary conditions of the turbulence transport equations are enforced explicitly (strongly) on all solid boundaries. The use of the wall function models is demonstrated on four test cases: a at plate boundary layer, a subsonic di user, a 2D airfoil, and a 3D semi-span wing. Where possible, different near-wall viscous spacing tactics are examined. Iterative residual convergence was obtained in most cases. Solution results are compared with theoretical and experimental data for several variations of grid spacing. In general, very good comparisons with data were achieved.

Carlson, Jan-Renee↗

Overview of numerical codes developed for predicted electrothermal deicing of aircraft blades

An overview of the deicing computer codes that have been developed at the University of Toledo under sponsorship of the NASA-Lewis Research Center is presented. These codes simulate the transient heat conduction and phase change occurring in an electrothermal deicier pad that has an arbitrary accreted ice shape on its surface. The codes are one-dimensional rectangular, two-dimensional rectangular, and two-dimensional with a coordinate transformation to model the true blade geometry. All modifications relating to the thermal physics of the deicing problem that have been incorporated into the codes will be discussed. Recent results of reformulating the codes using different numerical methods to increase program efficiency are described. In particular, this reformulation has enabled a more comprehensive two-dimensional code to run in much less CPU time than the original version. The code predictions are compared with experimental data obtained in the NASA-Lewis Icing Research Tunnel with a UH1H blade fitted with a B. F. Goodrich electrothermal deicer pad. Both continuous and cyclic heater firing cases are considered. The major objective in this comparison is to illustrate which codes give acceptable results in different regions of the airfoil for different heater firing sequences.

Keith, Theo G.↗

Progress Toward Efficient Laminar Flow Analysis and Design

A multi-fidelity system of computer codes for the analysis and design of vehicles having extensive areas of laminar flow is under development at the NASA Langley Research Center. The overall approach consists of the loose coupling of a flow solver, a transition prediction method and a design module using shell scripts, along with interface modules to prepare the input for each method. This approach allows the user to select the flow solver and transition prediction module, as well as run mode for each code, based on the fidelity most compatible with the problem and available resources. The design module can be any method that designs to a specified target pressure distribution. In addition to the interface modules, two new components have been developed: 1) an efficient, empirical transition prediction module (MATTC) that provides n-factor growth distributions without requiring boundary layer information; and 2) an automated target pressure generation code (ATPG) that develops a target pressure distribution that meets a variety of flow and geometry constraints. The ATPG code also includes empirical estimates of several drag components to allow the optimization of the target pressure distribution. The current system has been developed for the design of subsonic and transonic airfoils and wings, but may be extendable to other speed ranges and components. Several analysis and design examples are included to demonstrate the current capabilities of the system.

Campbell, Richard L.↗

Development of Computational Aeroacoustics Code for Jet Noise and Flow Prediction

Accurate prediction of jet fan and exhaust plume flow and noise generation and propagation is very important in developing advanced aircraft engines that will pass current and future noise regulations. In jet fan flows as well as exhaust plumes, two major sources of noise are present: large-scale, coherent instabilities and small-scale turbulent eddies. In previous work for the NASA Glenn Research Center, three strategies have been explored in an effort to computationally predict the noise radiation from supersonic jet exhaust plumes. In order from the least expensive computationally to the most expensive computationally, these are: 1) Linearized Euler equations (LEE). 2) Very Large Eddy Simulations (VLES). 3) Large Eddy Simulations (LES). The first method solves the linearized Euler equations (LEE). These equations are obtained by linearizing about a given mean flow and the neglecting viscous effects. In this way, the noise from large-scale instabilities can be found for a given mean flow. The linearized Euler equations are computationally inexpensive, and have produced good noise results for supersonic jets where the large-scale instability noise dominates, as well as for the tone noise from a jet engine blade row. However, these linear equations do not predict the absolute magnitude of the noise; instead, only the relative magnitude is predicted. Also, the predicted disturbances do not modify the mean flow, removing a physical mechanism by which the amplitude of the disturbance may be controlled. Recent research for isolated airfoils' indicates that this may not affect the solution greatly at low frequencies. The second method addresses some of the concerns raised by the LEE method. In this approach, called Very Large Eddy Simulation (VLES), the unsteady Reynolds averaged Navier-Stokes equations are solved directly using a high-accuracy computational aeroacoustics numerical scheme. With the addition of a two-equation turbulence model and the use of a relatively coarse grid, the numerical solution is effectively filtered into a directly calculated mean flow with the small-scale turbulence being modeled, and an unsteady large-scale component that is also being directly calculated. In this way, the unsteady disturbances are calculated in a nonlinear way, with a direct effect on the mean flow. This method is not as fast as the LEE approach, but does have many advantages to recommend it; however, like the LEE approach, only the effect of the largest unsteady structures will be captured. An initial calculation was performed on a supersonic jet exhaust plume, with promising results, but the calculation was hampered by the explicit time marching scheme that was employed. This explicit scheme required a very small time step to resolve the nozzle boundary layer, which caused a long run time. Current work is focused on testing a lower-order implicit time marching method to combat this problem.

Keith, Theo G., Jr.↗

An Advanced Mars Helicopter Design

Ingenuity may be the first of many Mars aerial vehicles. Rotorcraft increase the range and speed that can be traveled to locations of interest. This enables mission concepts previously considered not viable on Mars, such as missions performing science investigations in regions of high elevation, steep terrain, caves/lava tubes, and surveys of the lower atmosphere. Recent work done at NASA Ames Research Center and NASA’s Jet Propulsion Laboratory (JPL) show that significant science can be performed by rotorcraft either independently or as assistants to rovers and landers. Small rotorcraft of Ingenuity’s general size can be potentially integrated into missions already scheduled for launch. Additionally, larger rotorcraft can support standalone novel mission concepts but are still be able to be sized and configured for deployment from heritage entry, descent, and landing (EDL) systems. One such mission concept of interest is to determine if organics are associated with clay-bearing or silica-rich soil. For such a mission, a small rotorcraft “robotic assistant” to a lander or rover could help determine if ancient sediment contains biosignatures in regions such as Mawrth Vallis. Ingenuity has demonstrated that rotorcraft can be developed relatively quickly and inexpensively and increase the types and amount of science that can be performed on any given mission. Recent research has suggested that rotorcraft of Ingenuity’s general size can have their performance characteristics significantly enhanced – increasing their range, speed, and payload capacity – by using new generation rotor blade airfoils optimized for Mars operating conditions. Rotorcraft could potentially be a standard adjunct to all future lander and rover missions. This paper presents an advanced Mars helicopter design that leverages significantly the design heritage of the Ingenuity Mars Helicopter Technology Demonstrator (MHTD).

Advanced↗

A multigrid method for steady Euler equations on unstructured adaptive grids

A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

Riemslagh, Kris↗