Results for “Finite volume method” — Page 37

NASA NTRS2013

Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

Schwing, Alan M.↗

NASA NTRS1993

Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

Walker, Kevin P.↗

NASA NTRS1972

Three-dimensional plasma diffusion in a very strong magnetic field.

The thermal equilibrium coefficient of spatial diffusion transverse to a strong uniform dc magnetic field is calculated for a fully ionized plasma. The particles are assumed to move transverse to the field only as a consequence of the E x B drift, but to move freely parallel to it. The particles interact only electrostatically. The calculation is done at large, but fixed and finite, plasma volume. It is shown that, as magnetic field density approaches infinity, the leading term of the coefficient of transverse spatial diffusion falls off in a prescribed manner, but contains a multiplicative factor which goes to zero as the plasma volume becomes infinite. The method of calculation fails for unbounded plasmas.

Montgomery, D.↗

NASA NTRS1993

Computation of propulsion-related flowfields using unstructured adaptive meshes

In this paper, we describe a computational fluid dynamics (CFD) technique based on unstructured triangular/tetrahedral meshes. A finite-volume scheme is used in conjunction with a multi-stage Runge-Kutta algorithm. Convergence enhancements in the form of dual time-stepping and time-derivative preconditioning are used to overcome the limitations of conventional multi-stage schemes. The method is applied to propulsion-related flows and shown to perform satisfactorily.

Weiss, Jonathan M.↗

NASA NTRS2021

Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows

The unstructured, mixed-element, cell-centered, finite-volume flow solver USM3D is enhanced with new capabilities such as line generation for general unstructured grids and optimization of the iterative solver. The efficiency of the new developments is assessed in a massively parallel environment. The assessments are conducted using a baseline method and the recent hierarchical adaptive nonlinear iteration method framework. Three benchmark turbulent flows, namely, a subsonic separated flow around a three-dimensional hemisphere cylinder configuration, a transonic flow around the ONERA M6 wing, and a supersonic flow through a square duct are considered.

Mohagna J Pandya↗

NASA NTRS1994

Preconditioned conjugate gradient methods for the Navier-Stokes equations

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Ajmani, Kumud↗

NASA NTRS1994

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a multiple-instruction/multiple-data stream parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed: one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All of the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the Intel iPSC/860.

TRT-THEORETICAL↗

NASA NTRS1977

Effects of damping on mode shapes, volume 1

Displacement, velocity, and acceleration admittances were calculated for a realistic NASTRAN structural model of space shuttle for three conditions: liftoff, maximum dynamic pressure and end of solid rocket booster burn. The realistic model of the orbiter, external tank, and solid rocket motors included the representation of structural joint transmissibilities by finite stiffness and damping elements. Methods developed to incorporate structural joints and their damping characteristics into a finite element model of the space shuttle, to determine the point damping parameters required to produce realistic damping in the primary modes, and to calculate the effect of distributed damping on structural resonances through the calculation of admittances.

Gates, R. M.↗

DOE OSTI2025

Software For Advanced Large-scale Analysis Of Magnetic Confinement For Numerical Design, Engineering & Research (salamander)

As magnetic confinement fusion energy gains traction internationally to enable abundant energy production, designing components for fusion systems is a pressing challenge. During the planned lifetime of a fusion device, components evolve in extreme environments and must withstand large, repeated thermal loads and bombardment by 14 MeV neutrons, plasma ions, and neutral particles (deuterium, tritium, and helium), corrosive conditions, etc. All these physical processes take place simultaneously, interact in intricate ways, and impose important constraints that can affect performance. Experimental data is rare and costly to obtain, making design particularly challenging. Predictive computational frameworks must be an integral part of an accelerated and cost-effective design process by modeling fusion system performance in simulated environments. To better understand component degradation and operational impacts on their performance, the Software for Advanced Large-scale Analysis of MAgnetic confinement for Numerical Design, Engineering & Research (SALAMANDER) is designed as an open-source, fully integrated, multiphysics, multiscale, NQA-1 compliant framework facilitating 3D, high-fidelity fusion system modeling. To that end, SALAMANDER is a MOOSE-based framework, and therefore leverages MOOSE upstream libraries such as PETSc and libMesh to deliver sophisticated finite element, finite volume, and nonlinear solver technology for fusion energy simulations. SALAMANDER couples MOOSE physics module capabilities—such as thermal hydraulics, heat conduction, Navier-Stokes, and thermomechanics—with tritium transport via TMAP8, neutronics via Cardinal, and nascent particle-in-cell capabilities. Direct simulation Monte Carlo methods will be used to address neutral transport near the walls. By coupling all these physics in an integrated application, SALAMANDER will enable high-fidelity modeling of irradiation levels and plasma exposure conditions of plasma facing components and their impact on heat and tritium distributions, as well as the resulting mechanical constraints experienced by the plasma facing components and performance of blanket systems. Furthermore, SALAMANDER will be particularly suited for engineering studies thanks to the stochastic tool module readily available in MOOSE, allowing for extended uncertainty quantification and risk analysis studies. It is also able to use computer-aided design (CAD) meshes to model complex geometries, which is indispensable for fusion systems. SALAMANDER therefore supports design, safety, engineering, and research projects for magnetic confinement fusion systems

Simon, Pierre-Clement [Idaho National Laboratory (↗

NASA NTRS2023

A Hybrid Transfer Function Procedure for Broadband Auralization Within Small Flight Vehicle Interiors

Auralization of the sound fields within flight vehicle interiors is of interest to aircraft designers considering crew and passenger ride quality. Computer models can be used to predict the filtering effects that the fuselage structure and interior volume have on the exterior sound field in order to simulate the resulting cabin interior noise. However, this can become expensive when a wide frequency range of analysis suitable for passenger auralization is desired. This is particularly the case when using deterministic modeling methods such as finite element analysis (FEA) wherein prohibitively high levels of detail and finite element discretizations are required to resolve the wavelengths at high frequencies. On the contrary, Statistical Energy Analysis (SEA), while not capturing important modal behaviors at low frequencies, is better suited for higher frequency analyses where structural and interior dynamics exhibit high modal overlap and spatially averaged physical quantities suffice. For this reason, a hybrid procedure is considered here that utilizes FE modal solutions at lower frequencies and SEA results at higher frequencies. A transfer function dataset containing the exterior to interior vibroacoustic filtering effect is calculated accordingly and subsequently stored to be used for a variety of exterior dynamic load cases. At low frequencies, the transfer function dataset detail is related to the level of FE model refinement whereas at high frequencies it functions as an equalizer array with a level of detail corresponding to the SEA subsystem partitioning scheme. The above procedure is described herein and demonstrated on a six passenger flight vehicle with eight propulsors in a hover flight condition.

auralization↗

NASA NTRS2023

A Hybrid Transfer Function Procedure for Broadband Auralization Within Small Flight Vehicle Interiors

Auralization of the sound fields within flight vehicle interiors is of interest to aircraft designers considering crew and passenger ride quality. Computer models can be used to predict the filtering effects that the fuselage structure and interior volume have on the exterior sound field in order to simulate the resulting cabin interior noise. However, this can become expensive when a wide frequency range of analysis suitable for passenger auralization is desired. This is particularly the case when using deterministic modeling methods such as finite element analysis (FEA) wherein prohibitively high levels of detail and finite element discretizations are required to resolve the wavelengths at high frequencies. On the contrary, Statistical Energy Analysis (SEA), while not capturing important modal behaviors at low frequencies, is better suited for higher frequency analyses where structural and interior dynamics exhibit high modal overlap and spatially averaged physical quantities suffice. For this reason, a hybrid procedure is considered here that utilizes FE modal solutions at lower frequencies and SEA results at higher frequencies. A transfer function dataset containing the exterior to interior vibroacoustic filtering effect is calculated accordingly and subsequently stored to be used for a variety of exterior dynamic load cases. At low frequencies, the transfer function dataset detail is related to the level of FE model refinement whereas at high frequencies it functions as an equalizer array with a level of detail corresponding to the SEA subsystem partitioning scheme. The above procedure is described herein and demonstrated on a six passenger flight vehicle with eight propulsors in a hover flight condition.

auralization↗

NASA NTRS1980

Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics, production version (SOUSSA-P 1.1). Volume 1: Theoretical manual

Recent developments of the Green's function method and the computer program SOUSSA (Steady, Oscillatory, and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed and summarized. Applying the Green's function method to the fully unsteady (transient) potential equation yields an integro-differential-delay equation. With spatial discretization by the finite-element method, this equation is approximated by a set of differential-delay equations in time. Time solution by Laplace transform yields a matrix relating the velocity potential to the normal wash. Premultiplying and postmultiplying by the matrices relating generalized forces to the potential and the normal wash to the generalized coordinates one obtains the matrix of the generalized aerodynamic forces. The frequency and mode-shape dependence of this matrix makes the program SOUSSA useful for multiple frequency and repeated mode-shape evaluations.

Morino, L.↗

NASA NTRS1987

A linearized Euler analysis of unsteady flows in turbomachinery

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗

NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗

NASA NTRS1979

Numerical study of an explosion in a non-homogeneous medium with and without magnetic fields

A version of the two step Lax-Wendroff difference method with second order accuracy is used to seek solutions of the unsteady magnetohydrodynamic (MHD) equations for the study of an explosion in a non-homogeneous medium with and without magnetic fields. The explosion is initiated by introducing a finite amount of energy in a small volume of gas which leads to an instantaneous increase of gas temperature. Two types of magnetic field configurations (i.e. open and closed) are considered to illustrate the dependence and differences of magnetic and a non-magnetic flow motion. Numerical results show the strong dependence of induced MHD flow field on the magnetic field configuration and strength. The development and decay of the fast and slow MHD shock waves, as well as the ordinary gasdynamic shock waves, are also represented well by the present computer simulations. In conclusion, we have demonstrated that the numerical scheme we have used is a reliable one for studying 2-dimensional MHD problems in non-homogeneous medium.

Han, S. M.↗

NASA NTRS1990

Metal matrix composites microfracture: Computational simulation

Fiber/matrix fracture and fiber-matrix interface debonding in a metal matrix composite (MMC) are computationally simulated. These simulations are part of a research activity to develop computational methods for microfracture, microfracture propagation and fracture toughness of the metal matrix composites. The three-dimensional finite element model used in the simulation consists of a group of nine unidirectional fibers in three by three unit cell array of SiC/Ti15 metal matrix composite with a fiber volume ration of 0.35. This computational procedure is used to predict the fracture process and establish the hierarchy of fracture modes based on strain energy release rate. It is also used to predict stress redistribution to surrounding matrix-fibers due to initial and progressive fracture of fiber/matrix and due to debonding of fiber-matrix interface. Microfracture results for various loading cases such as longitudinal, transverse, shear and bending are presented and discussed. Step-by-step procedures are outlined to evaluate composite microfracture for a given composite system.

Mital, Subodh K.↗

NASA NTRS1990

Metal matrix composites microfracture - Computational simulation

Fiber/matrix fracture and fiber-matrix interface debonding in a metal matrix composite (MMC) are computationally simulated. These simulations are part of a research activity to develop computational methods for microfracture, microfracture propagation and fracture toughness of the metal matrix composites. The three-dimensional finite element model used in the simulation consists of a group of nine unidirectional fibers in three by three unit cell array of SiC/Ti15 metal matrix composite with a fiber volume ration of 0.35. This computational procedure is used to predict the fracture process and establish the hierarchy of fracture modes based on strain energy release rate. It is also used to predict stress redistribution to surrounding matrix-fibers due to initial and progressive fracture of fiber/matrix and due to debonding of fiber-matrix interface. Microfracture results for various loading cases such as longitudinal, transverse, shear and bending are presented and discussed. Step-by-step procedures are outlined to evaluate composite microfracture for a given composite system.

Mital, S. K.↗

NASA NTRS1992

Computational simulation of intermingled-fiber hybrid composite behavior

Three-dimensional finite-element analysis and a micromechanics based computer code ICAN (Integrated Composite Analyzer) are used to predict the composite properties and microstresses of a unidirectional graphite/epoxy primary composite with varying percentages of S-glass fibers used as hydridizing fibers at a total fiber volume of 0.54. The three-dimensional finite-element model used in the analyses consists of a group of nine fibers, all unidirectional, in a three-by-three unit cell array. There is generally good agreement between the composite properties and microstresses obtained from both methods. The results indicate that the finite-element methods and the micromechanics equations embedded in the ICAN computer code can be used to obtain the properties of intermingled fiber hybrid composites needed for the analysis/design of hybrid composite structures. However, the finite-element model should be big enough to be able to simulate the conditions assumed in the micromechanics equations.

Mital, Subodh K.↗