Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Unstructured mesh”

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.

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

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Optimal Inlet Shape Design of N2B Hybrid Wing Body Configuration

The N2B hybrid wing body aircraft was conceptually designed to meet environmental and performance goals for the N+2 generation transport set by the Subsonic Fixed Wing project of NASA Fundamental Aeronautics Program. In the present study, flow simulations are conducted around the N2B configuration by a Reynolds-averaged Navier-Stokes flow solver using unstructured meshes. Boundary conditions at engine fan face and nozzle exhaust planes are provided by the NPSS thermodynamic engine cycle model. The flow simulations reveal challenging design issues arising from boundary layer ingestion offset inlet and airframe-propulsion integration. Adjoint-based optimal designs are then conducted for the inlet shape to minimize the airframe drag force and flow distortion at fan faces. Design surfaces are parameterized by NURBS, and the cowl lip geometry is modified by a spring analogy approach. By the drag minimization design, flow separation on the cowl surfaces are almost removed, and shock wave strength got remarkably reduced. For the distortion minimization design, a circumferential distortion indicator DPCP(sub avg) is adopted as the design objective and diffuser bottom and side wall surfaces are perturbed for the design. The distortion minimization results in a 12.5 % reduction in the objective function.

Kim, Hyoungjin↗
NASA NTRS2013

Optimal Shape Design of Mail-Slot Nacelle on N3-X Hybrid Wing-Body Configuration

System studies show that a N3-X hybrid wing-body aircraft with a turboelectric distributed propulsion system using a mail-slot inlet/nozzle nacelle can meet the environmental and performance goals for N+3 generation transports (three generations beyond the current air transport technology level) set by NASA's Subsonic Fixed Wing Project. In this study, a Navier-Stokes flow simulation of N3-X on hybrid unstructured meshes was conducted, including the mail-slot propulsor. The geometry of the mail-slot propulsor was generated by a CAD (Computer-Aided Design)-free shape parameterization. A novel body force model generation approach was suggested for a more realistic and efficient simulation of the flow turning, pressure rise and loss effects of the fan blades and the inlet-fan interactions. Flow simulation results of the N3-X demonstrates the validity of the present approach. An optimal Shape design of the mail-slot nacelle surface was conducted to reduce strength of shock waves and flow separations on the cowl surface.

Kim, Hyoungjin↗
NASA NTRS2016

Improving Fidelity of Launch Vehicle Liftoff Acoustic Simulations

Launch vehicles experience high acoustic loads during ignition and liftoff affected by the interaction of rocket plume generated acoustic waves with launch pad structures. Application of highly parallelized Computational Fluid Dynamics (CFD) analysis tools optimized for application on the NAS computer systems such as the Loci/CHEM program now enable simulation of time-accurate, turbulent, multi-species plume formation and interaction with launch pad geometry and capture the generation of acoustic noise at the source regions in the plume shear layers and impingement regions. These CFD solvers are robust in capturing the acoustic fluctuations, but they are too dissipative to accurately resolve the propagation of the acoustic waves throughout the launch environment domain along the vehicle. A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed to improve such liftoff acoustic environment predictions. The framework combines the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate discontinuous Galerkin (DG) solver, Loci/THRUST, developed in the same computational framework. Loci/THRUST employs a low dissipation, high-order, unstructured DG method to accurately propagate acoustic waves away from the source regions across large distances. The DG solver is currently capable of solving up to 4th order solutions for non-linear, conservative acoustic field propagation. Higher order boundary conditions are implemented to accurately model the reflection and refraction of acoustic waves on launch pad components. The DG solver accepts generalized unstructured meshes, enabling efficient application of common mesh generation tools for CHEM and THRUST simulations. The DG solution is coupled with the CFD solution at interface boundaries placed near the CFD acoustic source regions. Both simulations are executed simultaneously with coordinated boundary condition data exchange.

Liever, Peter↗
NASA NTRS2016

Validation of High-Fidelity CFD/CAA Framework for Launch Vehicle Acoustic Environment Simulation against Scale Model Test Data

A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed for launch vehicle liftoff acoustic environment predictions. The framework couples the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate Discontinuous Galerkin solver developed in the same production framework, Loci/THRUST, to accurately resolve and propagate acoustic physics across the entire launch environment. Time-accurate, Hybrid RANS/LES CFD modeling is applied for predicting the acoustic generation physics at the plume source, and a high-order accurate unstructured mesh Discontinuous Galerkin (DG) method is employed to propagate acoustic waves away from the source across large distances using high-order accurate schemes. The DG solver is capable of solving 2nd, 3rd, and 4th order Euler solutions for non-linear, conservative acoustic field propagation. Initial application testing and validation has been carried out against high resolution acoustic data from the Ares Scale Model Acoustic Test (ASMAT) series to evaluate the capabilities and production readiness of the CFD/CAA system to resolve the observed spectrum of acoustic frequency content. This paper presents results from this validation and outlines efforts to mature and improve the computational simulation framework.

Liever, Peter A.↗
NASA NTRS2017

Computational Analysis of a Wing Designed for the X-57 Distributed Electric Propulsion Aircraft

A computational study of the wing for the distributed electric propulsion X-57 Maxwell airplane configuration at cruise and takeoff/landing conditions was completed. Two unstructured-mesh, Navier-Stokes computational fluid dynamics methods, FUN3D and USM3D, were used to predict the wing performance. The goal of the X-57 wing and distributed electric propulsion system design was to meet or exceed the required lift coefficient 3.95 for a stall speed of 58 knots, with a cruise speed of 150 knots at an altitude of 8,000 ft. The X-57 Maxwell airplane was designed with a small, high aspect ratio cruise wing that was designed for a high cruise lift coefficient (0.75) at angle of attack of 0deg. The cruise propulsors at the wingtip rotate counter to the wingtip vortex and reduce induced drag by 7.5 percent at an angle of attack of 0.6deg. The unblown maximum lift coefficient of the high-lift wing (with the 30deg flap setting) is 2.439. The stall speed goal performance metric was confirmed with a blown wing computed effective lift coefficient of 4.202. The lift augmentation from the high-lift, distributed electric propulsion system is 1.7. The predicted cruise wing drag coefficient of 0.02191 is 0.00076 above the drag allotted for the wing in the original estimate. However, the predicted drag overage for the wing would only use 10.1 percent of the original estimated drag margin, which is 0.00749.

Deere, Karen A.↗
NASA NTRS2018

Computational Component Build-Up for the X-57 Distributed Electric Propulsion Aircraft

A computational study of the wing for the distributed electric propulsion X-57 Maxwell airplane configuration at cruise and takeoff/landing conditions was completed. Three unstructured-mesh, Navier-Stokes computational fluid dynamics methods, FUN3D, USM3D and Kestrel, were used to predict the performance buildup of components to the full X-57 configuration. The goal of the X-57 wing and distributed electric propulsion system design was to meet or exceed the required lift coefficient of 3.95 for a stall speed of 58 knots. The X-57 Maxwell airplane was designed with a small, high aspect ratio cruise wing that was designed for a high cruise lift coefficient of 0.75 at a cruise speed of 150 knots and altitude of 8,000 ft, with an angle of attack of approximately 0deg. The computational data indicates that the X-57 full aircraft drag would meet the cruise drag goal with a 25 count drag margin. The cruise configuration maximum lift coefficient is 2.07 and without including the stabilator is 1.86 at an angle of attack of 14 deg, predicted with the USM3D flow solver using the Spalart-Allmaras turbulence model. The maximum lift coefficient for the high-lift wing (with the 30deg flap deflection) without the stabilator contribution is 2.60 at an angle of attack of 13 deg. For high-lift blowing conditions with 13.7 hp/prop, the maximum lift coefficient excluding the stabilator is 4.426 at (alpha) = 13 deg. Therefore, the lift augmentation from the high-lift propellers is 1.7 and the total lift augmentation from the high-lift system (30 deg flap deflection and the high-lift blowing) is 2.38. The drag for the high-lift wing with 30 deg flap deflection is much higher than the cruise wing configuration, but the high-lift system is used only during a small portion of the flight envelope. The pitching moment is relatively constant for both blown and unblown conditions when the stabilator is excluded. Modeling the full geometry has indicated some adverse effects from the fuselage on the wing and stabilator. At high angles of attack, the solutions with the USM3D flow solver using the Spalart-Allmaras turbulence model indicates large flow separation on the wing upper surface between the two high-lift nacelles near the fuselage, and also a reduction in sectional lift on the stabilator in the first 50 percent of the stabilator semispan. However, the large flow separation near the fuselage is mostly eliminated in the solutions predicted with two codes, USM3D and Kestrel, using Hybrid Reynolds-averaged Navier Stokes/Large Eddy Simulation turbulence models.

Deere, Karen A.↗
NASA NTRSDate not supplied

Overview of Ablative TPS Modeling at NASA Ames

Over the past decade, NASA has invested in efforts to build predictive thermal protection system (TPS) material models from the micro-scale to the macro-scale. To complement the mission design cycle process and reduce the need for extensive testing, NASA is developing modeling and simulation tools that enable characterizing material properties and response to hot plasma experienced during atmospheric entry. Traditional material response and ablation modeling tools, such as the heritage code FIAT, and its multidimensional siblings, TITAN and 3dFIAT, are being complemented with newly developed software such as Icarus and PATO. Both of these programs are three-dimensional, finite-volume solvers that use unstructured meshes and 21st century programming paradigms to allow for efficient parallel simulations. FIAT and Icarus are also used for TPS sizing purposes. Today, these traditional tools are being supplemented with computational materials models at the atomistic level. The scales of interest range from computational chemistry (Density Functional Theory [DFT]), to atomistic simulations (Molecular Dynamics [MD]), to the microscale with the Porous Microstructure Analysis (PuMA) software that was recently awarded the 2022 NASA Software of the Year award. Finally, thermo-structural modeling is also of interest to the TPS Materials branch and done using commercial tools such as MSC MARC, MENTAT, NASTRAN and PATRAN. The present talk will also link the use of these computational tools to current NASA missions and projects associated with challenging and complex vehicles entries/reentries.

materials modeling↗
NASA NTRSDate not supplied

Combustor-Turbine Interactions By Using the Open National Combustion Code (OpenNCC) and the Glenn-HT Code

We develop the methodology of coupling two different computational fluid dynamic (CFD) codes, OpenNCC and Glenn-HT, in order to investigate the unsteady flow fields inside the combustor and around the first-stage stator of a high-pressure turbine (HPT) from the energy efficient engine (E 3 ) program. In our coupling strategy, OpenNCC, a time accurate unstructured mesh multi-phase combustion CFD code, is applied to the combustor region and Glenn-HT, a structured mesh CFD code designed for turbine applications, is utilized inside the HPT region. As a proof of concept, we first simulate the three-dimensional airflow over the backward facing step and compared the predicted pressure coefficient against experimental data. We then considered a Jet-A/Air combustor with the NASA single learn direct injector (LDI) as a reacting flow test case. Here, Glenn-HT is used in the downstream of the combustor and assumes that the working fluid is a single gas (i.e., air) where the properties of the gas are taken from time- and area-averaged values at the combustor exit. A fully coupled combustor-turbine simulation using both OpenNCC and Glenn-HT was conducted on the E 3 combustor and a detailed analysis done pertaining to how a realistic combustor outflow affects migration of hot-streaks and its impact on the aerodynamic behavior inside the HPT. It is found that the combustion dynamics (i.e., the switching main and pilot flame strength) significantly alters the aerodynamic behavior inside the HPT including hot-streak migration. Variations of the temperature and the velocity magnitude in the passage could be up to ±75 and ±15. These large variations are an important part of the combustor-turbine interactions, which are overlooked by a single component simulation of the HPT while imposing the steady inflow boundary condition at the HPT inlet. Finally, it is observed the strong density gradient associated with the hot-streaks and the pressure gradient at the passage significantly enhances the baroclinic torque, affecting the vorticity field.

CFD hot-streaks↗
NASA NTRSDate not supplied

Simulation of Dynamic Crushing Behavior of Simulated Carbon/Epoxy Stanchions Using MAT58 and MAT213 in LS-DYNA

Carbon fiber-reinforced polymer (CFRP) composites have shown promise as a material for structures designed to absorb energy in crush-style impact loading. In complementing the lightweight and tailorable characteristics of CFRP structures, the benefits of impact energy absorption are particularly interesting in aerospace vehicles that require excellent crashworthiness performance. However, simulating the behavior of CFRP structures in dynamic, crushing-style impact loading is challenging because of the many damage and failure modes that are essential to capture in the model. For the present investigation, CFRP stanchions were tested using a crash sled experimental test rig. The stanchions were designed by the Composite Materials Handbook-17 (CMH-17) Crashworthiness Working Group for the purpose of comparing experimental crash sled tests to corresponding simulations of the tests. The stanchions are C-channel shaped and represent a geometry common in the interior of aerospace vehicle structures. Explicit simulations in LSDYNA were performed using a well-established composite material model (MAT58) and a next-generation material model (MAT213). Fully integrated shell elements were utilized instead of 3D solid elements to limit computation time. In all models, each of the sixteen plies were represented with individual layers of shell elements with tiebreak contact between each adjacent ply pair to simulate interlaminar fracture. Simulating the crushing of the stanchions occurred in two phases. First, the material models were calibrated using flat specimens that were manufactured with the same layup as the stanchions. While the original goal was calibration of material-related properties, meshdependent behavior was observed in simulations with either material model, and an unstructured mesh was selected to remediate undesirable mesh-dependent failure modes. Additionally, for both the MAT58 and MAT213 models, it was found that either the crush force or the failure mode could be modeled accurately, but no set of parameters could be identified to attain both results in the same model. Once satisfactory calibration was achieved, the same material parameters were applied to the stanchion crush simulations. The stanchion simulations showed that MAT213 more accurately predicted the experimentally determined crush force, and both material models predicted key aspects of the experimentally observed failure modes.

Composite Materials↗
NASA NTRSDate not supplied

Radiative Heat Transfer Capability Implemented in OpenNCC for Conjugate Heat Transfer Applications

Thermal efficiency of gas turbine engine increases as the temperature and pressure at the combustor increases. Consequently, the materials used inside a combustor must survive an increasingly challenging environment. For this reason, accurate assessment of heat transfer is crucial for combustor design. While all three modes of heat transfer are present inside a combustor, the focus of this paper is the thermal radiation. Radiative heat transfer in a gas turbine combustors are particularly interesting from three reasons. Firstly, the radiative heat loss from the combustion region may affect the emission performance. Secondly, the cooling air will protect the liner from convection but not necessary from radiation. Finally, it is less frequently incorporated in CFD analysis than other forms of heat transfer. In this work, radiative heat transfer using discrete ordinate method has been incorporated in OpenNCC (a publicly releasable version of the National Combustion Code) developed at NASA Glenn Research Center. Aside from massively parallel computation capability using MPI and the ability to utilize unstructured mesh, the current implementation includes two types of spectral models, namely, the weighted some of gray gas model and the full spectrum correlated k-distribution model. After presenting the theory and the strategy of implementation, results of validation cases for gray gas and spectral models will be presented. While the implementation of the radiation solver is intended for gas turbine application, the radiation solver can run independently from the convection/combustion solver and the same theory can be applied to other application.

OpenNCC↗
NASA NTRSDate not supplied

Radiative Heat Transfer Capability Implemented in OpenNCC for Conjugate Heat Transfer Applications

Thermal efficiency of gas turbine engine increases as the temperature and pressure at the combustor increases. Consequently, the materials used inside a combustor must survive an increasingly challenging environment. For this reason, accurate assessment of heat transfer is crucial for combustor design. While all three modes of heat transfer are present inside a combustor, the focus of this paper is the thermal radiation. Radiative heat transfer in a gas turbine combustors are particularly interesting from three reasons. Firstly, the radiative heat loss from the combustion region may affect the emission performance. Secondly, the cooling air will protect the liner from convection but not necessary from radiation. Finally, it is less frequently incorporated in CFD analysis than other forms of heat transfer. In this work, radiative heat transfer using discrete ordinate method has been incorporated in OpenNCC (a publicly releasable version of the National Combustion Code) developed at NASA Glenn Research Center. Aside from massively parallel computation capability using MPI and the ability to utilize unstructured mesh, the current implementation includes two types of spectral models, namely, the weighted some of gray gas model and the full spectrum correlated k-distribution model. After presenting the theory and the strategy of implementation, results of validation cases for gray gas and spectral models will be presented. While the implementation of the radiation solver is intended for gas turbine application, the radiation solver can run independently from the convection/combustion solver and the same theory can be applied to other application.

OpenNCC↗
NASA NTRSDate not supplied

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

Introduction The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.

Tomography↗
NASA NTRSDate not supplied

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.

Tomography↗
NASA NTRSDate not supplied

Aerothermodynamic Analysis of a Flexible Thermal Protection System under Reentry Loads

The Carryall Block 1 reentry vehicle being developed by Outpost Space utilizes a strut supported semirigid deployable heatshield. This consists of a flexible thermal protection system, a heat-resistant fabric stack, stretched over actuated spars. The advantages of a deployable heatshield include reduced heat loading and earlier deceleration in the trajectory. However, the nature of the flexible thermal protection system necessitates considering the loaded shape of the heat shield. The flexible thermal protection system will deflect under reentry loads leading to areas of higher heating rates as well as a reduced axial coefficient as compared to the nominal shape. The Carryall Block 1 is analyzed using NASA’s FUN3D and DPLR CFD solvers with a deflected shape based on the catenary equations. The aerodynamic results are found to be within a percent for both solvers and both structured and unstructured mesh types. Fluid Structure Interaction (FSI) analysis is currently a work in progress, using file I/O to communicate between FUN3D and LS-DYNA, a commercial nonlinear structural solver. Challenges in deforming the geometry, mesh, and initial results are presented here.

thermal protection system↗
NASA NTRS1993

Unstructured 3D Delaunay mesh generation applied to planes, trains and automobiles

Technical issues associated with domain-tessellation production, including initial boundary node triangulation and volume mesh refinement, are presented for the 'TGrid' 3D Delaunay unstructured grid generation program. The approach employed is noted to be capable of preserving predefined triangular surface facets in the final tessellation. The capabilities of the approach are demonstrated by generating grids about an entire fighter aircraft configuration, a train, and a wind tunnel model of an automobile.

Blake, Kenneth R.↗
NASA NTRS1996

A User's Guide to AMR1D: An Instructional Adaptive Mesh Refinement Code for Unstructured Grids

This report documents the code AMR1D, which is currently posted on the World Wide Web (http://sdcd.gsfc.nasa.gov/ESS/exchange/contrib/de-fainchtein/adaptive _mesh_refinement.html). AMR1D is a one-dimensional finite element fluid-dynamics solver, capable of adaptive mesh refinement (AMR). It was written as an instructional tool for AMR on unstructured mesh codes. It is meant to illustrate the minimum requirements for AMR on more than one dimension. For that purpose, it uses the same type of data structure that would be necessary on a two-dimensional AMR code (loosely following the algorithm described by Lohner).

deFainchtein, Rosalinda↗
NASA NTRS1989

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, Dimitri J.↗
NASA NTRS1990

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗