A matrix-free implicit unstructured multigrid finite volume method for simulating structural dynamics and fluid structure interaction

NASA Astrophysics Data System (ADS)

Lv, X.; Zhao, Y.; Huang, X. Y.; Xia, G. H.; Su, X. H.

2007-07-01

A new three-dimensional (3D) matrix-free implicit unstructured multigrid finite volume (FV) solver for structural dynamics is presented in this paper. The solver is first validated using classical 2D and 3D cantilever problems. It is shown that very accurate predictions of the fundamental natural frequencies of the problems can be obtained by the solver with fast convergence rates. This method has been integrated into our existing FV compressible solver [X. Lv, Y. Zhao, et al., An efficient parallel/unstructured-multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects, Journal of Computational Physics 215(2) (2006) 661-690] based on the immersed membrane method (IMM) [X. Lv, Y. Zhao, et al., as mentioned above]. Results for the interaction between the fluid and an immersed fixed-free cantilever are also presented to demonstrate the potential of this integrated fluid-structure interaction approach.

Development of advanced Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan

1994-01-01

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

User`s guide for UTCHEM implicit (1.0) a three dimensional chemical flood simulator. Final report, September 30, 1992--December 31, 1995

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1996-07-01

UTCHEM IMPLICIT is a three-dimensional chemical flooding simulator. The solution scheme is fully implicit. The pressure equation and the mass conservation equations are solved simultaneously for the aqueous phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used to reduce numerical dispersion effects. Saturations and phase concentrations are solved in a flash routine. The major physical phenomena modeled in the simulator are: dispersion, adsorption, aqueous-oleic-microemulsion phase behavior, interfacial tension, relative permeability, capillary trapping, compositional phase viscosity, capillary pressure, phase density, polymer properties: shear thinning viscosity, inaccessiblemore » pore volume, permeability reduction, and adsorption. The following options are available in the simulator: constant or variable time-step sizes, uniform or nonuniform grid, pressure or rate constrained wells, horizontal and vertical wells.« less

Some problems of the calculation of three-dimensional boundary layer flows on general configurations

NASA Technical Reports Server (NTRS)

Cebeci, T.; Kaups, K.; Mosinskis, G. J.; Rehn, J. A.

1973-01-01

An accurate solution of the three-dimensional boundary layer equations over general configurations such as those encountered in aircraft and space shuttle design requires a very efficient, fast, and accurate numerical method with suitable turbulence models for the Reynolds stresses. The efficiency, speed, and accuracy of a three-dimensional numerical method together with the turbulence models for the Reynolds stresses are examined. The numerical method is the implicit two-point finite difference approach (Box Method) developed by Keller and applied to the boundary layer equations by Keller and Cebeci. In addition, a study of some of the problems that may arise in the solution of these equations for three-dimensional boundary layer flows over general configurations.

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1990-01-01

A new computer code was developed for predicting the turbulent and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

Computational Fluid Dynamics: Algorithms and Supercomputers

DTIC Science & Technology

1988-03-01

1985. 1.2. Pulliam, T., and Steger, J. , Implicit Finite Difference Simulations of Three Dimensional Compressible Flow, AIAA Journal , Vol. 18, No. 2...approaches infinity, assuming N is bounded. The question as to actual performance when M is finite and N varies, is a different matter. (Note: the CYBER...PARTICLE-IN-CELL 9i% 3.b7 j.48 WEATHER FORECAST 98% 3.77 3.55 SEISMIC MIGRATION 98% 3.85 3.45 MONTE CARLO 99% 3.85 3.75 LATTICE GAUGE 100% 4.00 3.77

An efficicient data structure for three-dimensional vertex based finite volume method

NASA Astrophysics Data System (ADS)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan D.; Kirk, Benjamin S.

2010-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Two-Dimensional Finite Element Ablative Thermal Response Analysis of an Arcjet Stagnation Test

NASA Technical Reports Server (NTRS)

Dec, John A.; Laub, Bernard; Braun, Robert D.

2011-01-01

The finite element ablation and thermal response (FEAtR, hence forth called FEAR) design and analysis program simulates the one, two, or three-dimensional ablation, internal heat conduction, thermal decomposition, and pyrolysis gas flow of thermal protection system materials. As part of a code validation study, two-dimensional axisymmetric results from FEAR are compared to thermal response data obtained from an arc-jet stagnation test in this paper. The results from FEAR are also compared to the two-dimensional axisymmetric computations from the two-dimensional implicit thermal response and ablation program under the same arcjet conditions. The ablating material being used in this arcjet test is phenolic impregnated carbon ablator with an LI-2200 insulator as backup material. The test is performed at the NASA, Ames Research Center Interaction Heating Facility. Spatially distributed computational fluid dynamics solutions for the flow field around the test article are used for the surface boundary conditions.

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

An unstructured grid, three-dimensional model based on the shallow water equations

USGS Publications Warehouse

Casulli, V.; Walters, R.A.

2000-01-01

A semi-implicit finite difference model based on the three-dimensional shallow water equations is modified to use unstructured grids. There are obvious advantages in using unstructured grids in problems with a complicated geometry. In this development, the concept of unstructured orthogonal grids is introduced and applied to this model. The governing differential equations are discretized by means of a semi-implicit algorithm that is robust, stable and very efficient. The resulting model is relatively simple, conserves mass, can fit complicated boundaries and yet is sufficiently flexible to permit local mesh refinements in areas of interest. Moreover, the simulation of the flooding and drying is included in a natural and straightforward manner. These features are illustrated by a test case for studies of convergence rates and by examples of flooding on a river plain and flow in a shallow estuary. Copyright ?? 2000 John Wiley & Sons, Ltd.

Computational simulation of laser heat processing of materials

NASA Astrophysics Data System (ADS)

Shankar, Vijaya; Gnanamuthu, Daniel

1987-04-01

A computational model simulating the laser heat treatment of AISI 4140 steel plates with a CW CO2 laser beam has been developed on the basis of the three-dimensional, time-dependent heat equation (subject to the appropriate boundary conditions). The solution method is based on Newton iteration applied to a triple-approximate factorized form of the equation. The method is implicit and time-accurate; the maintenance of time-accuracy in the numerical formulation is noted to be critical for the simulation of finite length workpieces with a finite laser beam dwell time.

An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems

NASA Technical Reports Server (NTRS)

Farhat, C.; Park, K. C.; Dubois-Pelerin, Y.

1991-01-01

An unconditionally stable second order accurate implicit-implicit staggered procedure for the finite element solution of fully coupled thermoelasticity transient problems is proposed. The procedure is stabilized with a semi-algebraic augmentation technique. A comparative cost analysis reveals the superiority of the proposed computational strategy to other conventional staggered procedures. Numerical examples of one and two-dimensional thermomechanical coupled problems demonstrate the accuracy of the proposed numerical solution algorithm.

An implicit fast Fourier transform method for integration of the time dependent Schrodinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Riley, M.E.; Ritchie, A.B.

1997-12-31

One finds that the conventional exponentiated split operator procedure is subject to difficulties when solving the time-dependent Schrodinger equation for Coulombic systems. By rearranging the kinetic and potential energy terms in the temporal propagator of the finite difference equations, one can find a propagation algorithm for three dimensions that looks much like the Crank-Nicholson and alternating direction implicit methods for one- and two-space-dimensional partial differential equations. The authors report investigations of this novel implicit split operator procedure. The results look promising for a purely numerical approach to certain electron quantum mechanical problems. A charge exchange calculation is presented as anmore » example of the power of the method.« less

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

An efficient three-dimensional Poisson solver for SIMD high-performance-computing architectures

NASA Technical Reports Server (NTRS)

Cohl, H.

1994-01-01

We present an algorithm that solves the three-dimensional Poisson equation on a cylindrical grid. The technique uses a finite-difference scheme with operator splitting. This splitting maps the banded structure of the operator matrix into a two-dimensional set of tridiagonal matrices, which are then solved in parallel. Our algorithm couples FFT techniques with the well-known ADI (Alternating Direction Implicit) method for solving Elliptic PDE's, and the implementation is extremely well suited for a massively parallel environment like the SIMD architecture of the MasPar MP-1. Due to the highly recursive nature of our problem, we believe that our method is highly efficient, as it avoids excessive interprocessor communication.

Solution of Poisson equations for 3-dimensional grid generations. [computations of a flow field over a thin delta wing

NASA Technical Reports Server (NTRS)

Fujii, K.

1983-01-01

A method for generating three dimensional, finite difference grids about complicated geometries by using Poisson equations is developed. The inhomogenous terms are automatically chosen such that orthogonality and spacing restrictions at the body surface are satisfied. Spherical variables are used to avoid the axis singularity, and an alternating-direction-implicit (ADI) solution scheme is used to accelerate the computations. Computed results are presented that show the capability of the method. Since most of the results presented have been used as grids for flow-field computations, this is indicative that the method is a useful tool for generating three-dimensional grids about complicated geometries.

Three-Dimensional Flow of Nanofluid Induced by an Exponentially Stretching Sheet: An Application to Solar Energy

PubMed Central

Khan, Junaid Ahmad; Mustafa, M.; Hayat, T.; Sheikholeslami, M.; Alsaedi, A.

2015-01-01

This work deals with the three-dimensional flow of nanofluid over a bi-directional exponentially stretching sheet. The effects of Brownian motion and thermophoretic diffusion of nanoparticles are considered in the mathematical model. The temperature and nanoparticle volume fraction at the sheet are also distributed exponentially. Local similarity solutions are obtained by an implicit finite difference scheme known as Keller-box method. The results are compared with the existing studies in some limiting cases and found in good agreement. The results reveal the existence of interesting Sparrow-Gregg-type hills for temperature distribution corresponding to some range of parametric values. PMID:25785857

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan; Kirk, Benjamin S.

2011-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

The NCOREL computer program for 3D nonlinear supersonic potential flow computations

NASA Technical Reports Server (NTRS)

Siclari, M. J.

1983-01-01

An innovative computational technique (NCOREL) was established for the treatment of three dimensional supersonic flows. The method is nonlinear in that it solves the nonconservative finite difference analog of the full potential equation and can predict the formation of supercritical cross flow regions, embedded and bow shocks. The method implicitly computes a conical flow at the apex (R = 0) of a spherical coordinate system and uses a fully implicit marching technique to obtain three dimensional cross flow solutions. This implies that the radial Mach number must remain supersonic. The cross flow solutions are obtained by using type dependent transonic relaxation techniques with the type dependency linked to the character of the cross flow velocity (i.e., subsonic/supersonic). The spherical coordinate system and marching on spherical surfaces is ideally suited to the computation of wing flows at low supersonic Mach numbers due to the elimination of the subsonic axial Mach number problems that exist in other marching codes that utilize Cartesian transverse marching planes.

Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1990-01-01

In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.

Development of a three dimensional numerical water quality model for continental shelf applications

NASA Technical Reports Server (NTRS)

Spaulding, M.; Hunter, D.

1975-01-01

A model to predict the distribution of water quality parameters in three dimensions was developed. The mass transport equation was solved using a non-dimensional vertical axis and an alternating-direction-implicit finite difference technique. The reaction kinetics of the constituents were incorporated into a matrix method which permits computation of the interactions of multiple constituents. Methods for the computation of dispersion coefficients and coliform bacteria decay rates were determined. Numerical investigations of dispersive and dissipative effects showed that the three-dimensional model performs as predicted by analysis of simpler cases. The model was then applied to a two dimensional vertically averaged tidal dynamics model for the Providence River. It was also extended to a steady state application by replacing the time step with an iteration sequence. This modification was verified by comparison to analytical solutions and applied to a river confluence situation.

On the construction and application of implicit factored schemes for conservation laws. [in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Warming, R. F.; Beam, R. M.

1978-01-01

Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

A three-dimensional multiphase flow model for assesing NAPL contamination in porous and fractured media, 1. Formulation

NASA Astrophysics Data System (ADS)

Huyakorn, P. S.; Panday, S.; Wu, Y. S.

1994-06-01

A three-dimensional, three-phase numerical model is presented for stimulating the movement on non-aqueous-phase liquids (NAPL's) through porous and fractured media. The model is designed for practical application to a wide variety of contamination and remediation scenarios involving light or dense NAPL's in heterogeneous subsurface systems. The model formulation is first derived for three-phase flow of water, NAPL and air (or vapor) in porous media. The formulation is then extended to handle fractured systems using the dual-porosity and discrete-fracture modeling approaches The model accommodates a wide variety of boundary conditions, including withdrawal and injection well conditions which are treated rigorously using fully implicit schemes. The three-phase of formulation collapses to its simpler forms when air-phase dynamics are neglected, capillary effects are neglected, or two-phase-air-liquid, liquid-liquid systems with one or two active phases are considered. A Galerkin procedure with upstream weighting of fluid mobilities, storage matrix lumping, and fully implicit treatment of nonlinear coefficients and well conditions is used. A variety of nodal connectivity schemes leading to finite-difference, finite-element and hybrid spatial approximations in three dimensions are incorporated in the formulation. Selection of primary variables and evaluation of the terms of the Jacobian matrix for the Newton-Raphson linearized equations is discussed. The various nodal lattice options, and their significance to the computational time and memory requirements with regards to the block-Orthomin solution scheme are noted. Aggressive time-stepping schemes and under-relaxation formulas implemented in the code further alleviate the computational burden.

Three-dimensional multigrid algorithms for the flux-split Euler equations

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Thomas, James L.; Whitfield, David L.

1988-01-01

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.

A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong

2013-02-01

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.

A nonlinear dynamic finite element approach for simulating muscular hydrostats.

PubMed

Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A

2014-01-01

An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.

Application of adaptive gridding to magnetohydrodynamic flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schnack, D.D.; Lotatti, I.; Satyanarayana, P.

1996-12-31

The numerical simulation of the primitive, three-dimensional, time-dependent, resistive MHD equations on an unstructured, adaptive poloidal mesh using the TRIM code has been reported previously. The toroidal coordinate is approximated pseudo-spectrally with finite Fourier series and Fast-Fourier Transforms. The finite-volume algorithm preserves the magnetic field as solenoidal to round-off error, and also conserves mass, energy, and magnetic flux exactly. A semi-implicit method is used to allow for large time steps on the unstructured mesh. This is important for tokamak calculations where the relevant time scale is determined by the poloidal Alfven time. This also allows the viscosity to be treatedmore » implicitly. A conjugate-gradient method with pre-conditioning is used for matrix inversion. Applications to the growth and saturation of ideal instabilities in several toroidal fusion systems has been demonstrated. Recently we have concentrated on the details of the mesh adaption algorithm used in TRIM. We present several two-dimensional results relating to the use of grid adaptivity to track the evolution of hydrodynamic and MHD structures. Examples of plasma guns, opening switches, and supersonic flow over a magnetized sphere are presented. Issues relating to mesh adaption criteria are discussed.« less

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

A fully implicit finite element method for bidomain models of cardiac electromechanics

PubMed Central

Dal, Hüsnü; Göktepe, Serdar; Kaliske, Michael; Kuhl, Ellen

2012-01-01

We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes. PMID:23175588

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

1995-01-01

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

Nonlinear three-dimensional verification of the SPECYL and PIXIE3D magnetohydrodynamics codes for fusion plasmas

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Chacón, L.; Cappello, S.

2010-08-01

With the increasing impact of scientific discovery via advanced computation, there is presently a strong emphasis on ensuring the mathematical correctness of computational simulation tools. Such endeavor, termed verification, is now at the center of most serious code development efforts. In this study, we address a cross-benchmark nonlinear verification study between two three-dimensional magnetohydrodynamics (3D MHD) codes for fluid modeling of fusion plasmas, SPECYL [S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996)] and PIXIE3D [L. Chacón, Phys. Plasmas 15, 056103 (2008)], in their common limit of application: the simple viscoresistive cylindrical approximation. SPECYL is a serial code in cylindrical geometry that features a spectral formulation in space and a semi-implicit temporal advance, and has been used extensively to date for reversed-field pinch studies. PIXIE3D is a massively parallel code in arbitrary curvilinear geometry that features a conservative, solenoidal finite-volume discretization in space, and a fully implicit temporal advance. The present study is, in our view, a first mandatory step in assessing the potential of any numerical 3D MHD code for fluid modeling of fusion plasmas. Excellent agreement is demonstrated over a wide range of parameters for several fusion-relevant cases in both two- and three-dimensional geometries.

Nonlinear three-dimensional verification of the SPECYL and PIXIE3D magnetohydrodynamics codes for fusion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonfiglio, Daniele; Chacon, Luis; Cappello, Susanna

2010-01-01

With the increasing impact of scientific discovery via advanced computation, there is presently a strong emphasis on ensuring the mathematical correctness of computational simulation tools. Such endeavor, termed verification, is now at the center of most serious code development efforts. In this study, we address a cross-benchmark nonlinear verification study between two three-dimensional magnetohydrodynamics (3D MHD) codes for fluid modeling of fusion plasmas, SPECYL [S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996)] and PIXIE3D [L. Chacon, Phys. Plasmas 15, 056103 (2008)], in their common limit of application: the simple viscoresistive cylindrical approximation. SPECYL is a serial code inmore » cylindrical geometry that features a spectral formulation in space and a semi-implicit temporal advance, and has been used extensively to date for reversed-field pinch studies. PIXIE3D is a massively parallel code in arbitrary curvilinear geometry that features a conservative, solenoidal finite-volume discretization in space, and a fully implicit temporal advance. The present study is, in our view, a first mandatory step in assessing the potential of any numerical 3D MHD code for fluid modeling of fusion plasmas. Excellent agreement is demonstrated over a wide range of parameters for several fusion-relevant cases in both two- and three-dimensional geometries.« less

Sierra/Solid Mechanics 4.48 User's Guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Merewether, Mark Thomas; Crane, Nathan K; de Frias, Gabriel Jose

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutionsmore » of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.« less

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Halem, Milton (Technical Monitor)

2000-01-01

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

A streamwise upwind algorithm for solving the unsteady 3-D Navier-Stokes equations was extended to handle the moving grid system. It is noted that the finite volume concept is essential to extend the algorithm. The resulting algorithm is conservative for any motion of the coordinate system. Two extensions to an implicit method were considered and the implicit extension that makes the algorithm computationally efficient is implemented into Ames's aeroelasticity code, ENSAERO. The new flow solver has been validated through the solution of test problems. Test cases include three-dimensional problems with fixed and moving grids. The first test case shown is an unsteady viscous flow over an F-5 wing, while the second test considers the motion of the leading edge vortex as well as the motion of the shock wave for a clipped delta wing. The resulting algorithm has been implemented into ENSAERO. The upwind version leads to higher accuracy in both steady and unsteady computations than the previously used central-difference method does, while the increase in the computational time is small.

A New Discretization Method of Order Four for the Numerical Solution of One-Space Dimensional Second-Order Quasi-Linear Hyperbolic Equation

ERIC Educational Resources Information Center

Mohanty, R. K.; Arora, Urvashi

2002-01-01

Three level-implicit finite difference methods of order four are discussed for the numerical solution of the mildly quasi-linear second-order hyperbolic equation A(x, t, u)u[subscript xx] + 2B(x, t, u)u[subscript xt] + C(x, t, u)u[subscript tt] = f(x, t, u, u[subscript x], u[subscript t]), 0 less than x less than 1, t greater than 0 subject to…

International Conference on Numerical Ship Hydrodynamics (6th), Held in Iowa City, Iowa on 2-5 August 1993,

DTIC Science & Technology

1994-01-01

length scales mensional hydrofoil and tip vortex flow around a F circulation three dimensional hydrofoil. The simulated mean v molecular viscosity flow...Unstructured Grid for Free Surface Flow Simulations , by T. Hino, L. Martinelli, and A. Jameson 173 "A Semi-Implicit Semi-Lagrangian Finite Element Model...Haussling Solid-Fluid Juncture Boundary Layer and Wake with Waves, by J.E. Choi and F. Stern 215 Direct Numerical and Large-Eddy Simulations of Turbulent

Characteristic-based algorithms for flows in thermo-chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Walters, Robert W.; Cinnella, Pasquale; Slack, David C.; Halt, David

1990-01-01

A generalized finite-rate chemistry algorithm with Steger-Warming, Van Leer, and Roe characteristic-based flux splittings is presented in three-dimensional generalized coordinates for the Navier-Stokes equations. Attention is placed on convergence to steady-state solutions with fully coupled chemistry. Time integration schemes including explicit m-stage Runge-Kutta, implicit approximate-factorization, relaxation and LU decomposition are investigated and compared in terms of residual reduction per unit of CPU time. Practical issues such as code vectorization and memory usage on modern supercomputers are discussed.

Application of the Hughes-LIU algorithm to the 2-dimensional heat equation

NASA Technical Reports Server (NTRS)

Malkus, D. S.; Reichmann, P. I.; Haftka, R. T.

1982-01-01

An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an L-shaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the Hughes-Liu, and the fully implicit Crank-Nicholson algorithms. The Hughes-Liu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated.

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1997-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic responses of axial-flow turbo-machinery blading.The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to a far-field eigenanalysis, is also described. The linearized aerodynamic and numerical models have been implemented into a three-dimensional linearized unsteady flow code, called LINFLUX. This code has been applied to selected, benchmark, unsteady, subsonic flows to establish its accuracy and to demonstrate its current capabilities. The unsteady flows considered, have been chosen to allow convenient comparisons between the LINFLUX results and those of well-known, two-dimensional, unsteady flow codes. Detailed numerical results for a helical fan and a three-dimensional version of the 10th Standard Cascade indicate that important progress has been made towards the development of a reliable and useful, three-dimensional, prediction capability that can be used in aeroelastic and aeroacoustic design studies.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Computation of viscous blast wave flowfields

NASA Technical Reports Server (NTRS)

Atwood, Christopher A.

1991-01-01

A method to determine unsteady solutions of the Navier-Stokes equations was developed and applied. The structural finite-volume, approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the interaction of blast-waves with stationary targets. The inviscid flux is evaluated using MacCormack's modified Steger-Warming flux or Roe flux difference splittings with total variation diminishing limiters, while the viscous flux is computed using central differences. The use of implicit boundary conditions in conjunction with a telescoping in time and space method permitted solutions to this strongly unsteady class of problems. Comparisons of numerical, analytical, and experimental results were made in two and three dimensions. These comparisons revealed accurate wave speed resolution with nonoscillatory discontinuity capturing. The purpose of this effort was to address the three-dimensional, viscous blast-wave problem. Test cases were undertaken to reveal these methods' weaknesses in three regimes: (1) viscous-dominated flow; (2) complex unsteady flow; and (3) three-dimensional flow. Comparisons of these computations to analytic and experimental results provided initial validation of the resultant code. Addition details on the numerical method and on the validation can be found in the appendix. Presently, the code is capable of single zone computations with selection of any permutation of solid wall or flow-through boundaries.

Shock/vortex interaction and vortex-breakdown modes

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Kandil, H. A.; Liu, C. H.

1992-01-01

Computational simulation and study of shock/vortex interaction and vortex-breakdown modes are considered for bound (internal) and unbound (external) flow domains. The problem is formulated using the unsteady, compressible, full Navier-Stokes (NS) equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. For the bound flow domain, a supersonic swirling flow is considered in a configured circular duct and the problem is solved for quasi-axisymmetric and three-dimensional flows. For the unbound domain, a supersonic swirling flow issued from a nozzle into a uniform supersonic flow of lower Mach number is considered for quasi-axisymmetric and three-dimensional flows. The results show several modes of breakdown; e.g., no-breakdown, transient single-bubble breakdown, transient multi-bubble breakdown, periodic multi-bubble multi-frequency breakdown and helical breakdown.

Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

NASA Technical Reports Server (NTRS)

Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.

2000-01-01

A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

NASA Astrophysics Data System (ADS)

Tay, Wei Choon; Tan, Eng Leong

2014-07-01

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

HEATING 7. 1 user's manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Childs, K.W.

1991-07-01

HEATING is a FORTRAN program designed to solve steady-state and/or transient heat conduction problems in one-, two-, or three- dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heating generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- and position-dependent. The boundary conditions, which maymore » be surface-to-boundary or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General graybody radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING is variably dimensioned and utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion). The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1989-01-01

A new computer code was developed for predicting the turbulent, and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, 3-D Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

Convergence speeding up in the calculation of the viscous flow about an airfoil

NASA Technical Reports Server (NTRS)

Radespiel, R.; Rossow, C.

1988-01-01

A finite volume method to solve the three dimensional Navier-Stokes equations was developed. It is based on a cell-vertex scheme with central differences and explicit Runge-Kutta time steps. A good convergence for a stationary solution was obtained by the use of local time steps, implicit smoothing of the residues, a multigrid algorithm, and a carefully controlled artificial dissipative term. The method is illustrated by results for transonic profiles and airfoils. The method allows a routine solution of the Navier-Stokes equations.

Application of an unstructured grid flow solver to planes, trains and automobiles

NASA Technical Reports Server (NTRS)

Spragle, Gregory S.; Smith, Wayne A.; Yadlin, Yoram

1993-01-01

Rampant, an unstructured flow solver developed at Fluent Inc., is used to compute three-dimensional, viscous, turbulent, compressible flow fields within complex solution domains. Rampant is an explicit, finite-volume flow solver capable of computing flow fields using either triangular (2d) or tetrahedral (3d) unstructured grids. Local time stepping, implicit residual smoothing, and multigrid techniques are used to accelerate the convergence of the explicit scheme. The paper describes the Rampant flow solver and presents flow field solutions about a plane, train, and automobile.

Preconditioned upwind methods to solve 3-D incompressible Navier-Stokes equations for viscous flows

NASA Technical Reports Server (NTRS)

Hsu, C.-H.; Chen, Y.-M.; Liu, C. H.

1990-01-01

A computational method for calculating low-speed viscous flowfields is developed. The method uses the implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. An extensive study of optimizing the preconditioned system is carried out for two viscous flow problems. Computed results are compared with analytical solutions and experimental data.

Three-dimensional implicit lambda methods

NASA Technical Reports Server (NTRS)

Napolitano, M.; Dadone, A.

1983-01-01

This paper derives the three dimensional lambda-formulation equations for a general orthogonal curvilinear coordinate system and provides various block-explicit and block-implicit methods for solving them, numerically. Three model problems, characterized by subsonic, supersonic and transonic flow conditions, are used to assess the reliability and compare the efficiency of the proposed methods.

A new solution method for wheel/rail rolling contact.

PubMed

Yang, Jian; Song, Hua; Fu, Lihua; Wang, Meng; Li, Wei

2016-01-01

To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit-explicit order solution method is used to solve the FE model. Results show that the explicit-explicit order solution method has faster operation speed and higher efficiency than the implicit-explicit order solution method while the solution accuracy is almost the same. Hence, the explicit-explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

A cubic spline approximation for problems in fluid mechanics

NASA Technical Reports Server (NTRS)

Rubin, S. G.; Graves, R. A., Jr.

1975-01-01

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

NASA Technical Reports Server (NTRS)

1982-01-01

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

A finite-volume ELLAM for three-dimensional solute-transport modeling

USGS Publications Warehouse

Russell, T.F.; Heberton, C.I.; Konikow, Leonard F.; Hornberger, G.Z.

2003-01-01

A three-dimensional finite-volume ELLAM method has been developed, tested, and successfully implemented as part of the U.S. Geological Survey (USGS) MODFLOW-2000 ground water modeling package. It is included as a solver option for the Ground Water Transport process. The FVELLAM uses space-time finite volumes oriented along the streamlines of the flow field to solve an integral form of the solute-transport equation, thus combining local and global mass conservation with the advantages of Eulerian-Lagrangian characteristic methods. The USGS FVELLAM code simulates solute transport in flowing ground water for a single dissolved solute constituent and represents the processes of advective transport, hydrodynamic dispersion, mixing from fluid sources, retardation, and decay. Implicit time discretization of the dispersive and source/sink terms is combined with a Lagrangian treatment of advection, in which forward tracking moves mass to the new time level, distributing mass among destination cells using approximate indicator functions. This allows the use of large transport time increments (large Courant numbers) with accurate results, even for advection-dominated systems (large Peclet numbers). Four test cases, including comparisons with analytical solutions and benchmarking against other numerical codes, are presented that indicate that the FVELLAM can usually yield excellent results, even if relatively few transport time steps are used, although the quality of the results is problem-dependent.

Application of the implicit MacCormack scheme to the PNS equations

NASA Technical Reports Server (NTRS)

Lawrence, S. L.; Tannehill, J. C.; Chaussee, D. S.

1983-01-01

The two-dimensional parabolized Navier-Stokes equations are solved using MacCormack's (1981) implicit finite-difference scheme. It is shown that this method for solving the parabolized Navier-Stokes equations does not require the inversion of block tridiagonal systems of algebraic equations and allows the original explicit scheme to be employed in those regions where implicit treatment is not needed. The finite-difference algorithm is discussed and the computational results for two laminar test cases are presented. Results obtained using this method for the case of a flat plate boundary layer are compared with those obtained using the conventional Beam-Warming scheme, as well as those obtained from a boundary layer code. The computed results for a more severe test of the method, the hypersonic flow past a 15 deg compression corner, are found to compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

A geometrically exact formulation for three-dimensional numerical simulation of the umbilical cable in a deep-sea ROV system

NASA Astrophysics Data System (ADS)

Quan, Wei-cai; Zhang, Zhu-ying; Zhang, Ai-qun; Zhang, Qi-feng; Tian, Yu

2015-04-01

This paper proposes a geometrically exact formulation for three-dimensional static and dynamic analyses of the umbilical cable in a deep-sea remotely operated vehicle (ROV) system. The presented formulation takes account of the geometric nonlinearities of large displacement, effects of axial load and bending stiffness for modeling of slack cables. The resulting nonlinear second-order governing equations are discretized spatially by the finite element method and solved temporally by the generalized- α implicit time integration algorithm, which is adapted to the case of varying coefficient matrices. The ability to consider three-dimensional union action of ocean current and ship heave motion upon the umbilical cable is the key feature of this analysis. The presented formulation is firstly validated, and then three numerical examples for the umbilical cable in a deep-sea ROV system are demonstrated and discussed, including the steady configurations only under the action of depth-dependent ocean current, the dynamic responses in the case of the only ship heave motion, and in the case of the combined action of the ship heave motion and ocean current.

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1996-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic response characteristics of axial-flow turbomachinery blading. The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. In addition, a numerical model for linearized inviscid unsteady flow, which is based upon an existing nonlinear, implicit, wave-split, finite volume analysis, is described. These aerodynamic and numerical models have been implemented into an unsteady flow code, called LINFLUX. A preliminary version of the LINFLUX code is applied herein to selected, benchmark three-dimensional, subsonic, unsteady flows, to illustrate its current capabilities and to uncover existing problems and deficiencies. The numerical results indicate that good progress has been made toward developing a reliable and useful three-dimensional prediction capability. However, some problems, associated with the implementation of an unsteady displacement field and numerical errors near solid boundaries, still exist. Also, accurate far-field conditions must be incorporated into the FINFLUX analysis, so that this analysis can be applied to unsteady flows driven be external aerodynamic excitations.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Multigrid Methods for Aerodynamic Problems in Complex Geometries

NASA Technical Reports Server (NTRS)

Caughey, David A.

1995-01-01

Work has been directed at the development of efficient multigrid methods for the solution of aerodynamic problems involving complex geometries, including the development of computational methods for the solution of both inviscid and viscous transonic flow problems. The emphasis is on problems of complex, three-dimensional geometry. The methods developed are based upon finite-volume approximations to both the Euler and the Reynolds-Averaged Navier-Stokes equations. The methods are developed for use on multi-block grids using diagonalized implicit multigrid methods to achieve computational efficiency. The work is focused upon aerodynamic problems involving complex geometries, including advanced engine inlets.

A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model

USGS Publications Warehouse

McDonald, Michael G.; Harbaugh, Arlen W.; Guo, Weixing; Lu, Guoping

1988-01-01

This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.

Numerical simulation of one-dimensional heat transfer in composite bodies with phase change. M.S. Thesis, 1980 Final Report; [wing deicing pads

NASA Technical Reports Server (NTRS)

Dewitt, K. J.; Baliga, G.

1982-01-01

A numerical simulation was developed to investigate the one dimensional heat transfer occurring in a system composed of a layered aircraft blade having an ice deposit on its surface. The finite difference representation of the heat conduction equations was done using the Crank-Nicolson implicit finite difference formulation. The simulation considers uniform or time dependent heat sources, from heaters which can be either point sources or of finite thickness. For the ice water phase change, a numerical method which approximates the latent heat effect by a large heat capacity over a small temperature interval was applied. The simulation describes the temperature profiles within the various layers of the de-icer pad, as well as the movement of the ice water interface. The simulation could also be used to predict the one dimensional temperature profiles in any composite slab having different boundary conditions.

A computer program for the calculation of the flow field including boundary layer effects for mixed-compression inlets at angle of attack

NASA Technical Reports Server (NTRS)

Vadyak, J.; Hoffman, J. D.

1982-01-01

A computer program was developed which is capable of calculating the flow field in the supersonic portion of a mixed compression aircraft inlet operating at angle of attack. The supersonic core flow is computed using a second-order three dimensional method-of-characteristics algorithm. The bow shock and the internal shock train are treated discretely using a three dimensional shock fitting procedure. The boundary layer flows are computed using a second-order implicit finite difference method. The shock wave-boundary layer interaction is computed using an integral formulation. The general structure of the computer program is discussed, and a brief description of each subroutine is given. All program input parameters are defined, and a brief discussion on interpretation of the output is provided. A number of sample cases, complete with data listings, are provided.

Computations of the three-dimensional flow and heat transfer within a coolant passage of a radial turbine blade

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Roelke, R. J.; Steinthorsson, E.

1991-01-01

A numerical code is developed for computing three-dimensional, turbulent, compressible flow within coolant passages of turbine blades. The code is based on a formulation of the compressible Navier-Stokes equations in a rotating frame of reference in which the velocity dependent variable is specified with respect to the rotating frame instead of the inertial frame. The algorithm employed to obtain solutions to the governing equation is a finite-volume LU algorithm that allows convection, source, as well as diffusion terms to be treated implicitly. In this study, all convection terms are upwind differenced by using flux-vector splitting, and all diffusion terms are centrally differenced. This paper describes the formulation and algorithm employed in the code. Some computed solutions for the flow within a coolant passage of a radial turbine are also presented.

Three Dimensional Solution of Pneumatic Active Control of Forebody Vortex Asymmetry

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; SharafEl-Din, Hazem H.; Liu, C. H.

1995-01-01

Pneumatic active control of asymmetric vortical flows around a slender pointed forebody is investigated using the three dimensional solution for the compressible thin-layer Navier-Stokes equation. The computational applications cover the normal and tangential injection control of asymmetric flows around a 5 degree semi-apex angle cone at a 40 degree angle of attack, 1.4 freestream Mach number and 6 x 10(exp 6) freestream Reynolds number (based on the cone length). The effective tangential angle range of 67.5 approaches minus 67.5 degrees is used for both normal and tangential ports of injection. The effective axial length of injection is varied from 0.03 to 0.05. The computational solver uses the implicit, upwind, flux difference splitting finite volume scheme, and the grid consists of 161 x 55 x 65 points in the wrap around, normal and axial directions, respectively. The results show that tangential injection is more effective than normal injection.

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Technical Reports Server (NTRS)

Chitsomboon, Tawit

1992-01-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Astrophysics Data System (ADS)

Chitsomboon, Tawit

1992-02-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Toward high-speed 3D nonlinear soft tissue deformation simulations using Abaqus software.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2015-12-01

We aim to achieve a fast and accurate three-dimensional (3D) simulation of a porcine liver deformation under a surgical tool pressure using the commercial finite element software Abaqus. The liver geometry is obtained using magnetic resonance imaging, and a nonlinear constitutive law is employed to capture large deformations of the tissue. Effects of implicit versus explicit analysis schemes, element type, and mesh density on computation time are studied. We find that Abaqus explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. This study provides new insights and guidance on accurate and relatively fast nonlinear soft tissue simulations. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents.

Gradient-Based Aerodynamic Shape Optimization Using ADI Method for Large-Scale Problems

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Baysal, Oktay

1997-01-01

A gradient-based shape optimization methodology, that is intended for practical three-dimensional aerodynamic applications, has been developed. It is based on the quasi-analytical sensitivities. The flow analysis is rendered by a fully implicit, finite volume formulation of the Euler equations.The aerodynamic sensitivity equation is solved using the alternating-direction-implicit (ADI) algorithm for memory efficiency. A flexible wing geometry model, that is based on surface parameterization and platform schedules, is utilized. The present methodology and its components have been tested via several comparisons. Initially, the flow analysis for for a wing is compared with those obtained using an unfactored, preconditioned conjugate gradient approach (PCG), and an extensively validated CFD code. Then, the sensitivities computed with the present method have been compared with those obtained using the finite-difference and the PCG approaches. Effects of grid refinement and convergence tolerance on the analysis and shape optimization have been explored. Finally the new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4. Despite the expected increase in the computational time, the results indicate that shape optimization, which require large numbers of grid points can be resolved with a gradient-based approach.

Nonlinear 3D visco-resistive MHD modeling of fusion plasmas: a comparison between numerical codes

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Chacon, L.; Cappello, S.

2008-11-01

Fluid plasma models (and, in particular, the MHD model) are extensively used in the theoretical description of laboratory and astrophysical plasmas. We present here a successful benchmark between two nonlinear, three-dimensional, compressible visco-resistive MHD codes. One is the fully implicit, finite volume code PIXIE3D [1,2], which is characterized by many attractive features, notably the generalized curvilinear formulation (which makes the code applicable to different geometries) and the possibility to include in the computation the energy transport equation and the extended MHD version of Ohm's law. In addition, the parallel version of the code features excellent scalability properties. Results from this code, obtained in cylindrical geometry, are compared with those produced by the semi-implicit cylindrical code SpeCyl, which uses finite differences radially, and spectral formulation in the other coordinates [3]. Both single and multi-mode simulations are benchmarked, regarding both reversed field pinch (RFP) and ohmic tokamak magnetic configurations. [1] L. Chacon, Computer Physics Communications 163, 143 (2004). [2] L. Chacon, Phys. Plasmas 15, 056103 (2008). [3] S. Cappello, Plasma Phys. Control. Fusion 46, B313 (2004) & references therein.

Multigrid calculation of three-dimensional turbomachinery flows

NASA Technical Reports Server (NTRS)

Caughey, David A.

1989-01-01

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

Numerical Simulation of a Solar Domestic Hot Water System

NASA Astrophysics Data System (ADS)

Mongibello, L.; Bianco, N.; Di Somma, M.; Graditi, G.; Naso, V.

2014-11-01

An innovative transient numerical model is presented for the simulation of a solar Domestic Hot Water (DHW) system. The solar collectors have been simulated by using a zerodimensional analytical model. The temperature distributions in the heat transfer fluid and in the water inside the tank have been evaluated by one-dimensional models. The reversion elimination algorithm has been used to include the effects of natural convection among the water layers at different heights in the tank on the thermal stratification. A finite difference implicit scheme has been implemented to solve the energy conservation equation in the coil heat exchanger, and the energy conservation equation in the tank has been solved by using the finite difference Euler implicit scheme. Energy conservation equations for the solar DHW components models have been coupled by means of a home-made implicit algorithm. Results of the simulation performed using as input data the experimental values of the ambient temperature and the solar irradiance in a summer day are presented and discussed.

The assessment of nanofluid in a Von Karman flow with temperature relied viscosity

NASA Astrophysics Data System (ADS)

Tanveer, Anum; Salahuddin, T.; Khan, Mumtaz; Alshomrani, Ali Saleh; Malik, M. Y.

2018-06-01

This work endeavor to study the heat and mass transfer viscous nanofluid features in a Von Karman flow invoking the variable viscosity mechanism. Moreover, we have extended our study in view of heat generation and uniform suction effects. The flow triggering non-linear partial differential equations are inscribed in the non-dimensional form by manipulating suitable transformations. The resulting non-linear ordinary differential equations are solved numerically via implicit finite difference scheme in conjecture with the Newton's linearization scheme afterwards. The sought solutions are plotted graphically to present comparison between MATLAB routine bvp4c and implicit finite difference schemes. Impact of different parameters on the concentration/temperature/velocity profiles are highlighted. Further Nusselt number, skin friction and Sherwood number characteristics are discussed for better exposition.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1994-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques, and a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical, and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data.

A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zheng, Xiang; Yang, Chao; State Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190

2015-03-15

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracymore » (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.« less

Computational technique and performance of Transient Inundation Model for Rivers--2 Dimensional (TRIM2RD) : a depth-averaged two-dimensional flow model

USGS Publications Warehouse

Fulford, Janice M.

2003-01-01

A numerical computer model, Transient Inundation Model for Rivers -- 2 Dimensional (TrimR2D), that solves the two-dimensional depth-averaged flow equations is documented and discussed. The model uses a semi-implicit, semi-Lagrangian finite-difference method. It is a variant of the Trim model and has been used successfully in estuarine environments such as San Francisco Bay. The abilities of the model are documented for three scenarios: uniform depth flows, laboratory dam-break flows, and large-scale riverine flows. The model can start computations from a ?dry? bed and converge to accurate solutions. Inflows are expressed as source terms, which limits the use of the model to sufficiently long reaches where the flow reaches equilibrium with the channel. The data sets used by the investigation demonstrate that the model accurately propagates flood waves through long river reaches and simulates dam breaks with abrupt water-surface changes.

Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.

1986-01-01

The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

Development of a Linearized Unsteady Euler Analysis with Application to Wake/Blade-Row Interactions

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Chuang, H. Andrew

1999-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide a comprehensive and efficient unsteady aerodynamic analysis for predicting the aeroacoustic and aeroelastic responses of axial-flow turbomachinery blading. The mathematical models needed to describe nonlinear and linearized, inviscid, unsteady flows through a blade row operating within a cylindrical annular duct are presented in this report. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to far-field eigen analyses, is also described. The linearized aerodynamic and numerical models have been implemented into the three-dimensional unsteady flow code, LINFLUX. This code is applied herein to predict unsteady subsonic flows driven by wake or vortical excitations. The intent is to validate the LINFLUX analysis via numerical results for simple benchmark unsteady flows and to demonstrate this analysis via application to a realistic wake/blade-row interaction. Detailed numerical results for a three-dimensional version of the 10th Standard Cascade and a fan exit guide vane indicate that LINFLUX is becoming a reliable and useful unsteady aerodynamic prediction capability that can be applied, in the future, to assess the three-dimensional flow physics important to blade-row, aeroacoustic and aeroelastic responses.

Level set methods for detonation shock dynamics using high-order finite elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dobrev, V. A.; Grogan, F. C.; Kolev, T. V.

Level set methods are a popular approach to modeling evolving interfaces. We present a level set ad- vection solver in two and three dimensions using the discontinuous Galerkin method with high-order nite elements. During evolution, the level set function is reinitialized to a signed distance function to maintain ac- curacy. Our approach leads to stable front propagation and convergence on high-order, curved, unstructured meshes. The ability of the solver to implicitly track moving fronts lends itself to a number of applications; in particular, we highlight applications to high-explosive (HE) burn and detonation shock dynamics (DSD). We provide results for two-more » and three-dimensional benchmark problems as well as applications to DSD.« less

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

Analysis of viscous transonic flow over airfoil sections

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Wu, Jiunn-Chi; Sankar, L. N.

1987-01-01

A full Navier-Stokes solver has been used to model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to be held at the AIAA 25th Aerospace Sciences Meeting. The NACA 0012, RAE 2822 and Jones airfoils have been investigated for both attached and separated transonic flows. Predictions for pressure distributions, loads, skin friction coefficients, boundary layer displacement thickness and velocity profiles are included and compared with experimental data when possible. Overall, the results are in good agreement with experimental data.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Lesoinne, Michel

1993-01-01

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

Numerical study of supersonic combustion using a finite rate chemistry model

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.; Kumar, A.; Drummond, J. P.

1986-01-01

The governing equations of two-dimensional chemically reacting flows are presented together with a global two-step chemistry model for H2-air combustion. The explicit unsplit MacCormack finite difference algorithm is used to advance the discrete system of the governing equations in time until convergence is attained. The source terms in the species equations are evaluated implicitly to alleviate stiffness associated with fast reactions. With implicit source terms, the species equations give rise to a block-diagonal system which can be solved very efficiently on vector-processing computers. A supersonic reacting flow in an inlet-combustor configuration is calculated for the case where H2 is injected into the flow from the side walls and the strut. Results of the calculation are compared against the results obtained by using a complete reaction model.

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Explicit and implicit calculations of turbulent cavity flows with and without yaw angle

NASA Astrophysics Data System (ADS)

Yen, Guan-Wei

1989-08-01

Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.

Explicit and implicit calculations of turbulent cavity flows with and without yaw angle. M.S. Thesis

NASA Technical Reports Server (NTRS)

Yen, Guan-Wei

1989-01-01

Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.

Algorithm For Hypersonic Flow In Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Development of computational methods for heavy lift launch vehicles

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Ryan, James S.

1993-01-01

The research effort has been focused on the development of an advanced flow solver for complex viscous turbulent flows with shock waves. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. A new computer program named CENS3D has been developed for viscous turbulent flows with discontinuities. Details of the code are described in Appendix A and Appendix B. With the developments of the numerical algorithm and dissipation model, the simulation of three-dimensional viscous compressible flows has become more efficient and accurate. The results of the research are expected to yield a direct impact on the design process of future liquid fueled launch systems.

Three-Dimensional Viscous Alternating Direction Implicit Algorithm and Strategies for Shape Optimization

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Baysal, Oktay

1997-01-01

A gradient-based shape optimization based on quasi-analytical sensitivities has been extended for practical three-dimensional aerodynamic applications. The flow analysis has been rendered by a fully implicit, finite-volume formulation of the Euler and Thin-Layer Navier-Stokes (TLNS) equations. Initially, the viscous laminar flow analysis for a wing has been compared with an independent computational fluid dynamics (CFD) code which has been extensively validated. The new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4 with coarse- and fine-grid based computations performed with Euler and TLNS equations. The influence of the initial constraints on the geometry and aerodynamics of the optimized shape has been explored. Various final shapes generated for an identical initial problem formulation but with different optimization path options (coarse or fine grid, Euler or TLNS), have been aerodynamically evaluated via a common fine-grid TLNS-based analysis. The initial constraint conditions show significant bearing on the optimization results. Also, the results demonstrate that to produce an aerodynamically efficient design, it is imperative to include the viscous physics in the optimization procedure with the proper resolution. Based upon the present results, to better utilize the scarce computational resources, it is recommended that, a number of viscous coarse grid cases using either a preconditioned bi-conjugate gradient (PbCG) or an alternating-direction-implicit (ADI) method, should initially be employed to improve the optimization problem definition, the design space and initial shape. Optimized shapes should subsequently be analyzed using a high fidelity (viscous with fine-grid resolution) flow analysis to evaluate their true performance potential. Finally, a viscous fine-grid-based shape optimization should be conducted, using an ADI method, to accurately obtain the final optimized shape.

Parallel Computing of Upwelling in a Rotating Stratified Flow

NASA Astrophysics Data System (ADS)

Cui, A.; Street, R. L.

1997-11-01

A code for the three-dimensional, unsteady, incompressible, and turbulent flow has been implemented on the IBM SP2, using message passing. The effects of rotation and variable density are included. A finite volume method is used to discretize the Navier-Stokes equations in general curvilinear coordinates on a non-staggered grid. All the spatial derivatives are approximated using second-order central differences with the exception of the convection terms, which are handled with special upwind-difference schemes. The semi-implicit, second-order accurate, time-advancement scheme employs the Adams-Bashforth method for the explicit terms and Crank-Nicolson for the implicit terms. A multigrid method, with the four-color ZEBRA as smoother, is used to solve the Poisson equation for pressure, while the momentum equations are solved with an approximate factorization technique. The code was successfully validated for a variety test cases. Simulations of a laboratory model of coastal upwelling in a rotating annulus are in progress and will be presented.

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

PubMed

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Discontinuous dual-primal mixed finite elements for elliptic problems

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo

2000-01-01

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

An interacting boundary layer model for cascades

NASA Technical Reports Server (NTRS)

Davis, R. T.; Rothmayer, A. P.

1983-01-01

A laminar, incompressible interacting boundary layer model is developed for two-dimensional cascades. In the limit of large cascade spacing these equations reduce to the interacting boundary layer equations for a single body immersed in an infinite stream. A fully implicit numerical method is used to solve the governing equations, and is found to be at least as efficient as the same technique applied to the single body problem. Solutions are then presented for a cascade of finite flat plates and a cascade of finite sine-waves, with cusped leading and trailing edges.

A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; CoCoMans Team

2014-10-01

For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

NASA Technical Reports Server (NTRS)

Marx, Yves P.

1990-01-01

An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

A computational/experimental study of the flow around a body of revolution at angle of attack

NASA Technical Reports Server (NTRS)

Zilliac, Gregory G.

1986-01-01

The incompressible Navier-Stokes equations are numerically solved for steady flow around an ogive-cylinder (fineness ration 4.5) at angle of attack. The three-dimensional vortical flow is investigated with emphasis on the tip and the near wake region. The implicit, finite-difference computation is performed on the CRAY X-MP computer using the method of pseudo-compressibility. Comparisons of computational results with results of a companion towing tank experiment are presented for two symmetric leeside flow cases of moderate angles of attack. The topology of the flow is discussed and conclusions are drawn concerning the growth and stability of the primary vortices.

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

Incompressible viscous flow computations for the pump components and the artificial heart

NASA Technical Reports Server (NTRS)

Kiris, Cetin

1992-01-01

A finite difference, three dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. Here, equations are solved in steadily rotating reference frames by using the steady state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two.

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chima, Rodrick V.; Turkel, Eli; Schaffer, Steve

1987-01-01

Three explicit multigrid methods, Ni's method, Jameson's finite-volume method, and a finite-difference method based on Brandt's work, are described and compared for two model problems. All three methods use an explicit multistage Runge-Kutta scheme on the fine grid, and this scheme is also described. Convergence histories for inviscid flow over a bump in a channel for the fine-grid scheme alone show that convergence rate is proportional to Courant number and that implicit residual smoothing can significantly accelerate the scheme. Ni's method was slightly slower than the implicitly-smoothed scheme alone. Brandt's and Jameson's methods are shown to be equivalent in form but differ in their node versus cell-centered implementations. They are about 8.5 times faster than Ni's method in terms of CPU time. Results for an oblique shock/boundary layer interaction problem verify the accuracy of the finite-difference code. All methods slowed considerably on the stretched viscous grid but Brandt's method was still 2.1 times faster than Ni's method.

Three dimensional PNS solutions of hypersonic internal flows with equilibrium chemistry

NASA Technical Reports Server (NTRS)

Liou, May-Fun

1989-01-01

An implicit procedure for solving parabolized Navier-Stokes equations under the assumption of a general equation of state for a gas in chemical equilibrium is given. A general and consistent approach for the evaluation of Jacobian matrices in the implicit operator avoids the use of unnecessary auxiliary quantities and approximations, and leads to a simple expression. Applications to two- and three-dimensional flow problems show efficiency in computer time and economy in storage.

Viscous computations of cold air/air flow around scramjet nozzle afterbody

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Engelund, Walter C.

1991-01-01

The flow field in and around the nozzle afterbody section of a hypersonic vehicle was computationally simulated. The compressible, Reynolds averaged, Navier Stokes equations were solved by an implicit, finite volume, characteristic based method. The computational grids were adapted to the flow as the solutions were developing in order to improve the accuracy. The exhaust gases were assumed to be cold. The computational results were obtained for the two dimensional longitudinal plane located at the half span of the internal portion of the nozzle for over expanded and under expanded conditions. Another set of results were obtained, where the three dimensional simulations were performed for a half span nozzle. The surface pressures were successfully compared with the data obtained from the wind tunnel tests. The results help in understanding this complex flow field and, in turn, should help the design of the nozzle afterbody section.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1995-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data. This report summarizes the research that took place from August 1,1994 to January 1, 1995.

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

NASA Technical Reports Server (NTRS)

Anderson, O. L.

1984-01-01

Zonal concepts are utilized to delineate regions of application of three-dimensional boundary layer (DBL) theory. The zonal approach requires three distinct analyses. A modified version of the 3-DBL code named TABLET is used to analyze the boundary layer flow. This modified code solves the finite difference form of the compressible 3-DBL equations in a nonorthogonal surface coordinate system which includes coriolis forces produced by coordinate rotation. These equations are solved using an efficient, implicit, fully coupled finite difference procedure. The nonorthogonal surface coordinate system is calculated using a general analysis based on the transfinite mapping of Gordon which is valid for any arbitrary surface. Experimental data is used to determine the boundary layer edge conditions. The boundary layer edge conditions are determined by integrating the boundary layer edge equations, which are the Euler equations at the edge of the boundary layer, using the known experimental wall pressure distribution. Starting solutions along the inflow boundaries are estimated by solving the appropriate limiting form of the 3-DBL equations.

[Construction of platform on the three-dimensional finite element model of the dentulous mandibular body of a normal person].

PubMed

Gong, Lu-Lu; Zhu, Jing; Ding, Zu-Quan; Li, Guo-Qiang; Wang, Li-Ming; Yan, Bo-Yong

2008-04-01

To develop a method to construct a three-dimensional finite element model of the dentulous mandibular body of a normal person. A series of pictures with the interval of 0.1 mm were taken by CT scanning. After extracting the coordinates of key points of some pictures by the procedure, we used a C program to process the useful data, and constructed a platform of the three-dimensional finite element model of the dentulous mandibular body with the Ansys software for finite element analysis. The experimental results showed that the platform of the three-dimensional finite element model of the dentulous mandibular body was more accurate and applicable. The exact three-dimensional shape of model was well constructed, and each part of this model, such as one single tooth, can be deleted, which can be used to emulate various tooth-loss clinical cases. The three-dimensional finite element model is constructed with life-like shapes of dental cusps. Each part of this model can be easily removed. In conclusion, this experiment provides a good platform of biomechanical analysis on various tooth-loss clinical cases.

Construction of Three Dimensional Solutions for the Maxwell Equations

NASA Technical Reports Server (NTRS)

Yefet, A.; Turkel, E.

1998-01-01

We consider numerical solutions for the three dimensional time dependent Maxwell equations. We construct a fourth order accurate compact implicit scheme and compare it to the Yee scheme for free space in a box.

Numerical study of the flow in a three-dimensional thermally driven cavity

NASA Astrophysics Data System (ADS)

Rauwoens, Pieter; Vierendeels, Jan; Merci, Bart

2008-06-01

Solutions for the fully compressible Navier-Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied. Results are computed using a finite volume method on a structured, collocated grid. An explicit third-order discretization for the convective part and an implicit central discretization for the acoustic part and for the diffusive part are used. To stabilize the scheme an artificial dissipation term for the pressure and the temperature is introduced. The discrete equations are solved using a time-marching method with restrictions on the timestep corresponding to the explicit parts of the solver. Multigrid is used as acceleration technique.

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Slack, David C.; Whitaker, D. L.; Walters, Robert W.

1994-01-01

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Using Virtual Testing for Characterization of Composite Materials

NASA Astrophysics Data System (ADS)

Harrington, Joseph

Composite materials are finally providing uses hitherto reserved for metals in structural systems applications -- airframes and engine containment systems, wraps for repair and rehabilitation, and ballistic/blast mitigation systems. They have high strength-to-weight ratios, are durable and resistant to environmental effects, have high impact strength, and can be manufactured in a variety of shapes. Generalized constitutive models are being developed to accurately model composite systems so they can be used in implicit and explicit finite element analysis. These models require extensive characterization of the composite material as input. The particular constitutive model of interest for this research is a three-dimensional orthotropic elasto-plastic composite material model that requires a total of 12 experimental stress-strain curves, yield stresses, and Young's Modulus and Poisson's ratio in the material directions as input. Sometimes it is not possible to carry out reliable experimental tests needed to characterize the composite material. One solution is using virtual testing to fill the gaps in available experimental data. A Virtual Testing Software System (VTSS) has been developed to address the need for a less restrictive method to characterize a three-dimensional orthotropic composite material. The system takes in the material properties of the constituents and completes all 12 of the necessary characterization tests using finite element (FE) models. Verification and validation test cases demonstrate the capabilities of the VTSS.

Calculation of flow about two-dimensional bodies by means of the velocity-vorticity formulation on a staggered grid

NASA Technical Reports Server (NTRS)

Stremel, Paul M.

1991-01-01

A method for calculating the incompressible viscous flow about two-dimensional bodies, utilizing the velocity-vorticity form of the Navier-Stokes equations using a staggered-grid formulation is presented. The solution is obtained by employing an alternative-direction implicit method for the solution of the block tridiagonal matrix resulting from the finite-difference representation of the governing equations. The boundary vorticity and the conservation of mass are calculated implicitly as a part of the solution. The mass conservation is calculated to machine zero for the duration of the computation. Calculations for the flow about a circular cylinder, a 2-pct thick flat plate at 90-deg incidence, an elliptic cylinder at 45-deg incidence, and a NACA 0012, with and without a deflected flap, at - 90-deg incidence are performed and compared with the results of other numerical investigations.

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

NASA Technical Reports Server (NTRS)

Williams, S. D.; Curry, D. M.

1977-01-01

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

An implicit numerical model for multicomponent compressible two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2015-11-01

We introduce a new implicit approach to model multicomponent compressible two-phase flow in porous media with species transfer between the phases. In the implicit discretization of the species transport equation in our formulation we calculate for the first time the derivative of the molar concentration of component i in phase α (cα, i) with respect to the total molar concentration (ci) under the conditions of a constant volume V and temperature T. The species transport equation is discretized by the finite volume (FV) method. The fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides the pressure at grid-cell interfaces in addition to the pressure at the grid-cell center. The efficiency of the proposed model is demonstrated by comparing our results with three existing implicit compositional models. Our algorithm has low numerical dispersion despite the fact it is based on first-order space discretization. The proposed algorithm is very robust.

A modified Dodge algorithm for the parabolized Navier-Stokes equation and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions.

Detailed Aerodynamic Analysis of a Shrouded Tail Rotor Using an Unstructured Mesh Flow Solver

NASA Astrophysics Data System (ADS)

Lee, Hee Dong; Kwon, Oh Joon

The detailed aerodynamics of a shrouded tail rotor in hover has been numerically studied using a parallel inviscid flow solver on unstructured meshes. The numerical method is based on a cell-centered finite-volume discretization and an implicit Gauss-Seidel time integration. The calculation was made for a single blade by imposing a periodic boundary condition between adjacent rotor blades. The grid periodicity was also imposed at the periodic boundary planes to avoid numerical inaccuracy resulting from solution interpolation. The results were compared with available experimental data and those from a disk vortex theory for validation. It was found that realistic three-dimensional modeling is important for the prediction of detailed aerodynamics of shrouded rotors including the tip clearance gap flow.

Fluid-structure interaction simulations of deformable structures with non-linear thin shell elements

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Hedayat, Mohammadali; Borazjani, Iman; Scientific Computing; Biofluids Laboratory Team

2017-11-01

Large deformation of structures in a fluid is simulated using a strongly coupled partitioned fluid-structure interaction (FSI) approach which is stabilized with under-relaxation and the Aitken acceleration technique. The fluid is simulated using a recently developed implicit Newton-Krylov method with a novel analytical Jacobian. Structures are simulated using a triangular thin-shell finite element formulation, which considers only translational degrees of freedom. The thin-shell method is developed on the top of a previously implemented membrane finite element formulation. A sharp interface immersed boundary method is used to handle structures in the fluid domain. The developed FSI framework is validated against two three-dimensional experiments: (1) a flexible aquatic vegetation in the fluid and (2) a heaving flexible panel in fluid. Furthermore, the developed FSI framework is used to simulate tissue heart valves, which involve large deformations and non-linear material properties. This work was supported by American Heart Association (AHA) Grant 13SDG17220022 and the Center of Computational Research (CCR) of University at Buffalo.

Finite Element Simulation of Temperature and Strain Distribution during Friction Stir Welding of AA2024 Aluminum Alloy

NASA Astrophysics Data System (ADS)

Jain, Rahul; Pal, Surjya Kanta; Singh, Shiv Brat

2017-02-01

Friction Stir Welding (FSW) is a solid state joining process and is handy for welding aluminum alloys. Finite Element Method (FEM) is an important tool to predict state variables of the process but numerical simulation of FSW is highly complex due to non-linear contact interactions between tool and work piece and interdependency of displacement and temperature. In the present work, a three dimensional coupled thermo-mechanical method based on Lagrangian implicit method is proposed to study the thermal history, strain distribution and thermo-mechanical process in butt welding of Aluminum alloy 2024 using DEFORM-3D software. Workpiece is defined as rigid-visco plastic material and sticking condition between tool and work piece is defined. Adaptive re-meshing is used to tackle high mesh distortion. Effect of tool rotational and welding speed on plastic strain is studied and insight is given on asymmetric nature of FSW process. Temperature distribution on the workpiece and tool is predicted and maximum temperature is found in workpiece top surface.

An analysis of a charring ablator with thermal nonequilibrium, chemical kinetics, and mass transfer

NASA Technical Reports Server (NTRS)

Clark, R. K.

1973-01-01

The differential equations governing the transient response of a one-dimensional ablative thermal protection system are presented for thermal nonequilibrium between the pyrolysis gases and the char layer and with finite rate chemical reactions occurring. The system consists of three layers (the char layer, the uncharred layer, and an optical insulation layer) with concentrated heat sinks at the back surface and between the second and third layers. The equations are solved numerically by using a modified implicit finite difference scheme to obtain solutions for the thickness of the charred and uncharred layers, surface recession and pyrolysis rates, solid temperatures, porosity profiles, and profiles of pyrolysis-gas temperature, pressure, composition, and flow rate. Good agreement is obtained between numerical results and exact solutions for a number of simplified cases. The complete numerical analysis is used to obtain solutions for an ablative system subjected to a constant heating environment. Effects of thermal, chemical, and mass transfer processes are shown.

Radiative interactions in chemically reacting supersonic internal flows

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Chandrasekhar, R.

1991-01-01

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with finite-rate chemistry and radiation for hydrogen-air systems. The chemistry source terms in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed flow in a channel with a ten-degree compression ramp. Three different chemistry models are used, accounting for increasing number of reactions and participating species. Two chemistry models assure nitrogen as inert, while the third model accounts for nitrogen reactions and NO(x) formation. The tangent slab approximation is used in the radiative flux formulation. A pseudo-gray model is used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interactions vary substantially, depending on reactions involving HO2 and NO species and that this can have a significant influence on the flowfield.

Linearized Unsteady Aerodynamic Analysis of the Acoustic Response to Wake/Blade-Row Interaction

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Huff, Dennis L. (Technical Monitor)

2001-01-01

The three-dimensional, linearized Euler analysis, LINFLUX, is being developed to provide a comprehensive and efficient unsteady aerodynamic scheme for predicting the aeroacoustic and aeroelastic responses of axial-flow turbomachinery blading. LINFLUX couples a near-field, implicit, wave-split, finite-volume solution to far-field acoustic eigensolutions, to predict the aerodynamic responses of a blade row to prescribed structural and aerodynamic excitations. It is applied herein to predict the acoustic responses of a fan exit guide vane (FEGV) to rotor wake excitations. The intent is to demonstrate and assess the LINFLUX analysis via application to realistic wake/blade-row interactions. Numerical results are given for the unsteady pressure responses of the FEGV, including the modal pressure responses at inlet and exit. In addition, predictions for the modal and total acoustic power levels at the FEGV exit are compared with measurements. The present results indicate that the LINFLUX analysis should be useful in the aeroacoustic design process, and for understanding the three-dimensional flow physics relevant to blade-row noise generation and propagation.

Numerical simulation of flow through the Langley parametric scramjet engine

NASA Technical Reports Server (NTRS)

Srinivasan, Shivakumar; Kamath, Pradeep S.; Mcclinton, Charles R.

1989-01-01

The numerical simulation of a three-dimensional turbulent, reacting flow through the entire Langley parametric scramjet engine has been obtained using a piecewise elliptic approach. The last section in the combustor has been analyzed using a parabolized Navier-Stokes code. The facility nozzle flow was analyzed as a first step. The outflow conditions from the nozzle were chosen as the inflow conditions of the scramjet inlet. The nozzle and the inlet simulation were accomplished by solving the three-dimensional Navier-Stokes equations with a perfect gas assumption. The inlet solution downstream of the scramjet throat was used to provide inflow conditions for the combustor region. The first two regions of the combustor were analyzed using the MacCormack's explicit scheme. However, the source terms in the species equations were solved implicitly. The finite rate chemistry was modeled using the two-step reaction model of Rogers and Chinitz. A complete reaction model was used in the PNS code to solve the last combustor region. The numerical solutions provide an insight of the flow details in a complete hydrogen-fueled scramjet engine module.

Three dimensional modelling of earthquake rupture cycles on frictional faults

NASA Astrophysics Data System (ADS)

Simpson, Guy; May, Dave

2017-04-01

We are developing an efficient MPI-parallel numerical method to simulate earthquake sequences on preexisting faults embedding within a three dimensional viscoelastic half-space. We solve the velocity form of the elasto(visco)dynamic equations using a continuous Galerkin Finite Element Method on an unstructured pentahedral mesh, which thus permits local spatial refinement in the vicinity of the fault. Friction sliding is coupled to the viscoelastic solid via rate- and state-dependent friction laws using the split-node technique. Our coupled formulation employs a picard-type non-linear solver with a fully implicit, first order accurate time integrator that utilises an adaptive time step that efficiently evolves the system through multiple seismic cycles. The implementation leverages advanced parallel solvers, preconditioners and linear algebra from the Portable Extensible Toolkit for Scientific Computing (PETSc) library. The model can treat heterogeneous frictional properties and stress states on the fault and surrounding solid as well as non-planar fault geometries. Preliminary tests show that the model successfully reproduces dynamic rupture on a vertical strike-slip fault in a half-space governed by rate-state friction with the ageing law.

A blended continuous–discontinuous finite element method for solving the multi-fluid plasma model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sousa, E.M., E-mail: sousae@uw.edu; Shumlak, U., E-mail: shumlak@uw.edu

The multi-fluid plasma model represents electrons, multiple ion species, and multiple neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. The model spans a large range of temporal and spatial scales, which renders the model stiff and presents numerical challenges. To address the large range of timescales, a blended continuous and discontinuous Galerkin method is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutralmore » physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. The details of the Blended Finite Element Method (BFEM) are presented. The numerical method is benchmarked for accuracy and tested using two-fluid one-dimensional soliton problem and electromagnetic shock problem. The results are compared to conventional finite volume and finite element methods, and demonstrate that the BFEM is particularly effective in resolving physics in stiff problems involving realistic physical parameters, including realistic electron mass and speed of light. The benefit is illustrated by computing a three-fluid plasma application that demonstrates species separation in multi-component plasmas.« less

[Three-dimensional finite element study on the change of glossopharyngeum in patient with obstructive sleep apnea hypopnea syndrome during titrated mandible advancement].

PubMed

Yang, Suixing; Feng, Jing; Zhang, Zuo; Qu, Aili; Gong, Miao; Tang, Jie; Fan, Junheng; Li, Songqing; Zhao, Yanling

2013-04-01

To construct a three-dimensional finite element model of the upper airway and adjacent structure of an obstructive sleep apnea hypopnea syndrome (OSAHS) patient for biomechanical analysis. And to study the influence of glossopharyngeum of an OSAHS patient with three-dimensional finite element model during titrated mandible advancement. DICOM format image information of an OSAHS patient's upper airway was obtained by thin-section CT scanning and digital image processing were utilized to construct a three-dimensional finite element model by Mimics 10.0, Imageware 10.0 and Ansys software. The changes and the law of glossopharyngeum were observed by biomechanics and morphology after loading with titrated mandible advancement. A three-dimensional finite element model of the adjacent upper airway structure of OSAHS was established successfully. After loading, the transverse diameter of epiglottis tip of glossopharyngeum increased significantly, although the sagittal diameter decreased correspondingly. The principal stress was mainly distributed in anterior wall of the upper airway. The location of principal stress concentration did not change significantly with the increasing of distance. The stress of glossopharyngeum increased during titrated mandible advancement. A more precise three-dimensional finite model of upper airway and adjacent structure of an OSAHS patient is established and improved efficiency by Mimics, Imageware and Ansys software. The glossopharyngeum of finite element model of OSAHS is analyzed by titrated mandible advancement and can effectively show the relationship between mandible advancement and the glossopharyngeum.

Three-dimensional finite element analysis for high velocity impact. [of projectiles from space debris

NASA Technical Reports Server (NTRS)

Chan, S. T. K.; Lee, C. H.; Brashears, M. R.

1975-01-01

A finite element algorithm for solving unsteady, three-dimensional high velocity impact problems is presented. A computer program was developed based on the Eulerian hydroelasto-viscoplastic formulation and the utilization of the theorem of weak solutions. The equations solved consist of conservation of mass, momentum, and energy, equation of state, and appropriate constitutive equations. The solution technique is a time-dependent finite element analysis utilizing three-dimensional isoparametric elements, in conjunction with a generalized two-step time integration scheme. The developed code was demonstrated by solving one-dimensional as well as three-dimensional impact problems for both the inviscid hydrodynamic model and the hydroelasto-viscoplastic model.

NASCRIN - NUMERICAL ANALYSIS OF SCRAMJET INLET

NASA Technical Reports Server (NTRS)

Kumar, A.

1994-01-01

The NASCRIN program was developed for analyzing two-dimensional flow fields in supersonic combustion ramjet (scramjet) inlets. NASCRIN solves the two-dimensional Euler or Navier-Stokes equations in conservative form by an unsplit, explicit, two-step finite-difference method. A more recent explicit-implicit, two-step scheme has also been incorporated in the code for viscous flow analysis. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow calculations. NASCRIN can analyze both inviscid and viscous flows with no struts, one strut, or multiple struts embedded in the flow field. NASCRIN can be used in a quasi-three-dimensional sense for some scramjet inlets under certain simplifying assumptions. Although developed for supersonic internal flow, NASCRIN may be adapted to a variety of other flow problems. In particular, it should be readily adaptable to subsonic inflow with supersonic outflow, supersonic inflow with subsonic outflow, or fully subsonic flow. The NASCRIN program is available for batch execution on the CDC CYBER 203. The vectorized FORTRAN version was developed in 1983. NASCRIN has a central memory requirement of approximately 300K words for a grid size of about 3,000 points.

Multigrid for hypersonic viscous two- and three-dimensional flows

NASA Technical Reports Server (NTRS)

Turkel, E.; Swanson, R. C.; Vatsa, V. N.; White, J. A.

1991-01-01

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that removes the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional flow over a blunt biconic.

H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

NASA Technical Reports Server (NTRS)

Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.

1993-01-01

The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

An efficient finite element method for simulation of droplet spreading on a topologically rough surface

NASA Astrophysics Data System (ADS)

Luo, Li; Wang, Xiao-Ping; Cai, Xiao-Chuan

2017-11-01

We study numerically the dynamics of a three-dimensional droplet spreading on a rough solid surface using a phase-field model consisting of the coupled Cahn-Hilliard and Navier-Stokes equations with a generalized Navier boundary condition (GNBC). An efficient finite element method on unstructured meshes is introduced to cope with the complex geometry of the solid surfaces. We extend the GNBC to surfaces with complex geometry by including its weak form along different normal and tangential directions in the finite element formulation. The semi-implicit time discretization scheme results in a decoupled system for the phase function, the velocity, and the pressure. In addition, a mass compensation algorithm is introduced to preserve the mass of the droplet. To efficiently solve the decoupled systems, we present a highly parallel solution strategy based on domain decomposition techniques. We validate the newly developed solution method through extensive numerical experiments, particularly for those phenomena that can not be achieved by two-dimensional simulations. On a surface with circular posts, we study how wettability of the rough surface depends on the geometry of the posts. The contact line motion for a droplet spreading over some periodic rough surfaces are also efficiently computed. Moreover, we study the spreading process of an impacting droplet on a microstructured surface, a qualitative agreement is achieved between the numerical and experimental results. The parallel performance suggests that the proposed solution algorithm is scalable with over 4,000 processors cores with tens of millions of unknowns.

Cross-ply laminates with holes in compression - Straight free-edge stresses determined by two- to three-dimensional global/local finite element analysis

NASA Technical Reports Server (NTRS)

Thompson, Danniella Muheim; Griffin, O. Hayden, Jr.; Vidussoni, Marco A.

1990-01-01

A practical example of applying two- to three-dimensional (2- to 3-D) global/local finite element analysis to laminated composites is presented. Cross-ply graphite/epoxy laminates of 0.1-in. (0.254-cm) thickness with central circular holes ranging from 1 to 6 in. (2.54 to 15.2 cm) in diameter, subjected to in-plane compression were analyzed. Guidelines for full three-dimensional finite element analysis and two- to three-dimensional global/local analysis of interlaminar stresses at straight free edges of laminated composites are included. The larger holes were found to reduce substantially the interlaminar stresses at the straight free-edge in proximity to the hole. Three-dimensional stress results were obtained for thin laminates which require prohibitive computer resources for full three-dimensional analyses of comparative accuracy.

Effects of Turbulence Model on Prediction of Hot-Gas Lateral Jet Interaction in a Supersonic Crossflow

DTIC Science & Technology

2015-07-01

performance computing time from the US Department of Defense (DOD) High Performance Computing Modernization program at the US Army Research Laboratory...Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time ...dimensional, compressible, Reynolds-averaged Navier-Stokes (RANS) equations are solved using a finite volume method. A point-implicit time - integration

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Dwoyer, D. M.

1983-01-01

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

On numerical model of time-dependent processes in three-dimensional porous heat-releasing objects

NASA Astrophysics Data System (ADS)

Lutsenko, Nickolay A.

2016-10-01

The gas flows in the gravity field through porous objects with heat-releasing sources are investigated when the self-regulation of the flow rate of the gas passing through the porous object takes place. Such objects can appear after various natural or man-made disasters (like the exploded unit of the Chernobyl NPP). The mathematical model and the original numerical method, based on a combination of explicit and implicit finite difference schemes, are developed for investigating the time-dependent processes in 3D porous energy-releasing objects. The advantage of the numerical model is its ability to describe unsteady processes under both natural convection and forced filtration. The gas cooling of 3D porous objects with different distribution of heat sources is studied using computational experiment.

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

NASA Technical Reports Server (NTRS)

Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)

1994-01-01

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

Finite difference model for aquifer simulation in two dimensions with results of numerical experiments

USGS Publications Warehouse

Trescott, Peter C.; Pinder, George Francis; Larson, S.P.

1976-01-01

The model will simulate ground-water flow in an artesian aquifer, a water-table aquifer, or a combined artesian and water-table aquifer. The aquifer may be heterogeneous and anisotropic and have irregular boundaries. The source term in the flow equation may include well discharge, constant recharge, leakage from confining beds in which the effects of storage are considered, and evapotranspiration as a linear function of depth to water. The theoretical development includes presentation of the appropriate flow equations and derivation of the finite-difference approximations (written for a variable grid). The documentation emphasizes the numerical techniques that can be used for solving the simultaneous equations and describes the results of numerical experiments using these techniques. Of the three numerical techniques available in the model, the strongly implicit procedure, in general, requires less computer time and has fewer numerical difficulties than do the iterative alternating direction implicit procedure and line successive overrelaxation (which includes a two-dimensional correction procedure to accelerate convergence). The documentation includes a flow chart, program listing, an example simulation, and sections on designing an aquifer model and requirements for data input. It illustrates how model results can be presented on the line printer and pen plotters with a program that utilizes the graphical display software available from the Geological Survey Computer Center Division. In addition the model includes options for reading input data from a disk and writing intermediate results on a disk.

Two-dimensional HID light source radiative transfer using discrete ordinates method

NASA Astrophysics Data System (ADS)

Ghrib, Basma; Bouaoun, Mohamed; Elloumi, Hatem

2016-08-01

This paper shows the implementation of the Discrete Ordinates Method for handling radiation problems in High Intensity Discharge (HID) lamps. Therefore, we start with presenting this rigorous method for treatment of radiation transfer in a two-dimensional, axisymmetric HID lamp. Furthermore, the finite volume method is used for the spatial discretization of the Radiative Transfer Equation. The atom and electron densities were calculated using temperature profiles established by a 2D semi-implicit finite-element scheme for the solution of conservation equations relative to energy, momentum, and mass. Spectral intensities as a function of position and direction are first calculated, and then axial and radial radiative fluxes are evaluated as well as the net emission coefficient. The results are given for a HID mercury lamp on a line-by-line basis. A particular attention is paid on the 253.7 nm resonance and 546.1 nm green lines.

DOE Office of Scientific and Technical Information (OSTI.GOV)

McHugh, P.R.; Ramshaw, J.D.

MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equationmore » voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs.« less

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems, task 1: Ducted propfan analysis

NASA Technical Reports Server (NTRS)

Hall, Edward J.; Delaney, Robert A.; Bettner, James L.

1990-01-01

The time-dependent three-dimensional Euler equations of gas dynamics were solved numerically to study the steady compressible transonic flow about ducted propfan propulsion systems. Aerodynamic calculations were based on a four-stage Runge-Kutta time-marching finite volume solution technique with added numerical dissipation. An implicit residual smoothing operator was used to aid convergence. Two calculation grids were employed in this study. The first grid utilized an H-type mesh network with a branch cut opening to represent the axisymmetric cowl. The second grid utilized a multiple-block mesh system with a C-type grid about the cowl. The individual blocks were numerically coupled in the Euler solver. Grid systems were generated by a combined algebraic/elliptic algortihm developed specifically for ducted propfans. Numerical calculations were initially performed for unducted propfans to verify the accuracy of the three-dimensional Euler formulation. The Euler analyses were then applied for the calculation of ducted propfan flows, and predicted results were compared with experimental data for two cases. The three-dimensional Euler analyses displayed exceptional accuracy, although certain parameters were observed to be very sensitive to geometric deflections. Both solution schemes were found to be very robust and demonstrated nearly equal efficiency and accuracy, although it was observed that the multi-block C-grid formulation provided somewhat better resolution of the cowl leading edge region.

A parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.

PubMed

Gong, Chunye; Bao, Weimin; Tang, Guojian; Jiang, Yuewen; Liu, Jie

2014-01-01

It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(2)). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.

An Interactive Preprocessor Program with Graphics for a Three-Dimensional Finite Element Code.

ERIC Educational Resources Information Center

Hamilton, Claude Hayden, III

The development and capabilities of an interactive preprocessor program with graphics for an existing three-dimensional finite element code is presented. This preprocessor program, EDGAP3D, is designed to be used in conjunction with the Texas Three Dimensional Grain Analysis Program (TXCAP3D). The code presented in this research is capable of the…

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

Numerical analysis of the three-dimensional swirling flow in centrifugal compressor volutes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayder, E.; Van den Braembussche, R.

1994-07-01

The improvement of centrifugal compressor performance and the control of the radial forces acting on the impeller due to the circumferential variation of the static pressure caused by the volute require a good understanding of the flow mechanisms and an accurate prediction of the flow pattern inside the volute. A three-dimensional volute calculation method has been developed for this purpose. The volute is discretized by means of hexahedral elements. A cell vertex finite volume approach is used in combination with a time-marching procedure. The numerical procedure makes use of a central space discretization and a four-step Runge-Kutta time-stepping scheme. Themore » artificial dissipation used in the solver is based on the fourth-order differences of the conservative variables. Implicit residual smoothing improves the convergence rate. The loss model implemented in the code accounts for the losses due to internal shear and friction losses on the walls. A comparison of the calculated and measured results inside a volute with elliptical cross section reveals that the modified Euler solver accurately predicts the velocity and pressure distribution inside and upstream of the volute.« less

The Coupling of Finite Element and Integral Equation Representations for Efficient Three-Dimensional Modeling of Electromagnetic Scattering and Radiation

NASA Technical Reports Server (NTRS)

Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz

1996-01-01

Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giunta, G.; Belouettar, S.

In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigationsmore » show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.« less

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

NASA Technical Reports Server (NTRS)

Barth, T. J.; Steger, J. L.

1985-01-01

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Prediction and control of slender-wing rock

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Salman, Ahmed A.

1992-01-01

The unsteady Euler equations and the Euler equations of rigid-body dynamics, both written in the moving frame of reference, are sequentially solved to simulate the limit-cycle rock motion of slender delta wings. The governing equations of the fluid flow and the dynamics of the present multidisciplinary problem are solved using an implicit, approximately-factored, central-difference-like, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. For the control of wing-rock motion, leading-edge flaps are forced to oscillate anti-symmetrically at prescribed frequency and amplitude, which are tuned in order to suppress the rock motion. Since the computational grid deforms due to the leading-edge flaps motion, the grid is dynamically deformed using the Navier-displacement equations. Computational applications cover locally-conical and three-dimensional solutions for the wing-rock simulation and its control.

A three-dimensional method-of-characteristics solute-transport model (MOC3D)

USGS Publications Warehouse

Konikow, Leonard F.; Goode, D.J.; Hornberger, G.Z.

1996-01-01

This report presents a model, MOC3D, that simulates three-dimensional solute transport in flowing ground water. The model computes changes in concentration of a single dissolved chemical constituent over time that are caused by advective transport, hydrodynamic dispersion (including both mechanical dispersion and diffusion), mixing (or dilution) from fluid sources, and mathematically simple chemical reactions (including linear sorption, which is represented by a retardation factor, and decay). The transport model is integrated with MODFLOW, a three-dimensional ground-water flow model that uses implicit finite-difference methods to solve the transient flow equation. MOC3D uses the method of characteristics to solve the transport equation on the basis of the hydraulic gradients computed with MODFLOW for a given time step. This implementation of the method of characteristics uses particle tracking to represent advective transport and explicit finite-difference methods to calculate the effects of other processes. However, the explicit procedure has several stability criteria that may limit the size of time increments for solving the transport equation; these are automatically determined by the program. For improved efficiency, the user can apply MOC3D to a subgrid of the primary MODFLOW grid that is used to solve the flow equation. However, the transport subgrid must have uniform grid spacing along rows and columns. The report includes a description of the theoretical basis of the model, a detailed description of input requirements and output options, and the results of model testing and evaluation. The model was evaluated for several problems for which exact analytical solutions are available and by benchmarking against other numerical codes for selected complex problems for which no exact solutions are available. These test results indicate that the model is very accurate for a wide range of conditions and yields minimal numerical dispersion for advection-dominated problems. Mass-balance errors are generally less than 10 percent, and tend to decrease and stabilize with time.

Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

NASA Technical Reports Server (NTRS)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

NASA Technical Reports Server (NTRS)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

Comparison of Implicit Collocation Methods for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)

2001-01-01

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.

Unmitigated numerical solution to the diffraction term in the parabolic nonlinear ultrasound wave equation.

PubMed

Hasani, Mojtaba H; Gharibzadeh, Shahriar; Farjami, Yaghoub; Tavakkoli, Jahan

2013-09-01

Various numerical algorithms have been developed to solve the Khokhlov-Kuznetsov-Zabolotskaya (KZK) parabolic nonlinear wave equation. In this work, a generalized time-domain numerical algorithm is proposed to solve the diffraction term of the KZK equation. This algorithm solves the transverse Laplacian operator of the KZK equation in three-dimensional (3D) Cartesian coordinates using a finite-difference method based on the five-point implicit backward finite difference and the five-point Crank-Nicolson finite difference discretization techniques. This leads to a more uniform discretization of the Laplacian operator which in turn results in fewer calculation gridding nodes without compromising accuracy in the diffraction term. In addition, a new empirical algorithm based on the LU decomposition technique is proposed to solve the system of linear equations obtained from this discretization. The proposed empirical algorithm improves the calculation speed and memory usage, while the order of computational complexity remains linear in calculation of the diffraction term in the KZK equation. For evaluating the accuracy of the proposed algorithm, two previously published algorithms are used as comparison references: the conventional 2D Texas code and its generalization for 3D geometries. The results show that the accuracy/efficiency performance of the proposed algorithm is comparable with the established time-domain methods.

Multigrid finite element method in stress analysis of three-dimensional elastic bodies of heterogeneous structure

NASA Astrophysics Data System (ADS)

Matveev, A. D.

2016-11-01

To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.

TRUST84. Sat-Unsat Flow in Deformable Media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narasimhan, T.N.

1984-11-01

TRUST84 solves for transient and steady-state flow in variably saturated deformable media in one, two, or three dimensions. It can handle porous media, fractured media, or fractured-porous media. Boundary conditions may be an arbitrary function of time. Sources or sinks may be a function of time or of potential. The theoretical model considers a general three-dimensional field of flow in conjunction with a one-dimensional vertical deformation field. The governing equation expresses the conservation of fluid mass in an elemental volume that has a constant volume of solids. Deformation of the porous medium may be nonelastic. Permeability and the compressibility coefficientsmore » may be nonlinearly related to effective stress. Relationships between permeability and saturation with pore water pressure in the unsaturated zone may be characterized by hysteresis. The relation between pore pressure change and effective stress change may be a function of saturation. The basic calculational model of the conductive heat transfer code TRUMP is applied in TRUST84 to the flow of fluids in porous media. The model combines an integrated finite difference algorithm for numerically solving the governing equation with a mixed explicit-implicit iterative scheme in which the explicit changes in potential are first computed for all elements in the system, after which implicit corrections are made only for those elements for which the stable time-step is less than the time-step being used. Time-step sizes are automatically controlled to optimize the number of iterations, to control maximum change to potential during a time-step, and to obtain desired output information. Time derivatives, estimated on the basis of system behavior during the two previous time-steps, are used to start the iteration process and to evaluate nonlinear coefficients. Both heterogeneity and anisotropy can be handled.« less

A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers

NASA Astrophysics Data System (ADS)

Tavelli, Maurizio; Dumbser, Michael

2017-07-01

We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved meshes. The method is pressure-based and semi-implicit and is able to deal with all Mach number flows. The new DG scheme extends the seminal ideas outlined in [1], where a second order semi-implicit finite volume method for the solution of the compressible Navier-Stokes equations with a general equation of state was introduced on staggered Cartesian grids. Regarding the high order extension we follow [2], where a staggered space-time DG scheme for the incompressible Navier-Stokes equations was presented. In our scheme, the discrete pressure is defined on the primal grid, while the discrete velocity field and the density are defined on a face-based staggered dual grid. Then, the mass conservation equation, as well as the nonlinear convective terms in the momentum equation and the transport of kinetic energy in the energy equation are discretized explicitly, while the pressure terms appearing in the momentum and energy equation are discretized implicitly. Formal substitution of the discrete momentum equation into the total energy conservation equation yields a linear system for only one unknown, namely the scalar pressure. Here the equation of state is assumed linear with respect to the pressure. The enthalpy and the kinetic energy are taken explicitly and are then updated using a simple Picard procedure. Thanks to the use of a staggered grid, the final pressure system is a very sparse block five-point system for three dimensional problems and it is a block four-point system in the two dimensional case. Furthermore, for high order in space and piecewise constant polynomials in time, the system is observed to be symmetric and positive definite. This allows to use fast linear solvers such as the conjugate gradient (CG) method. In addition, all the volume and surface integrals needed by the scheme depend only on the geometry and the polynomial degree of the basis and test functions and can therefore be precomputed and stored in a preprocessing stage. This leads to significant savings in terms of computational effort for the time evolution part. In this way also the extension to a fully curved isoparametric approach becomes natural and affects only the preprocessing step. The viscous terms and the heat flux are also discretized making use of the staggered grid by defining the viscous stress tensor and the heat flux vector on the dual grid, which corresponds to the use of a lifting operator, but on the dual grid. The time step of our new numerical method is limited by a CFL condition based only on the fluid velocity and not on the sound speed. This makes the method particularly interesting for low Mach number flows. Finally, a very simple combination of artificial viscosity and the a posteriori MOOD technique allows to deal with shock waves and thus permits also to simulate high Mach number flows. We show computational results for a large set of two and three-dimensional benchmark problems, including both low and high Mach number flows and using polynomial approximation degrees up to p = 4.

Numerical simulation of weakly ionized hypersonic flow over reentry capsules

NASA Astrophysics Data System (ADS)

Scalabrin, Leonardo C.

The mathematical and numerical formulation employed in the development of a new multi-dimensional Computational Fluid Dynamics (CFD) code for the simulation of weakly ionized hypersonic flows in thermo-chemical non-equilibrium over reentry configurations is presented. The flow is modeled using the Navier-Stokes equations modified to include finite-rate chemistry and relaxation rates to compute the energy transfer between different energy modes. The set of equations is solved numerically by discretizing the flowfield using unstructured grids made of any mixture of quadrilaterals and triangles in two-dimensions or hexahedra, tetrahedra, prisms and pyramids in three-dimensions. The partial differential equations are integrated on such grids using the finite volume approach. The fluxes across grid faces are calculated using a modified form of the Steger-Warming Flux Vector Splitting scheme that has low numerical dissipation inside boundary layers. The higher order extension of inviscid fluxes in structured grids is generalized in this work to be used in unstructured grids. Steady state solutions are obtained by integrating the solution over time implicitly. The resulting sparse linear system is solved by using a point implicit or by a line implicit method in which a tridiagonal matrix is assembled by using lines of cells that are formed starting at the wall. An algorithm that assembles these lines using completely general unstructured grids is developed. The code is parallelized to allow simulation of computationally demanding problems. The numerical code is successfully employed in the simulation of several hypersonic entry flows over space capsules as part of its validation process. Important quantities for the aerothermodynamics design of capsules such as aerodynamic coefficients and heat transfer rates are compared to available experimental and flight test data and other numerical results yielding very good agreement. A sensitivity analysis of predicted radiative heating of a space capsule to several thermo-chemical non-equilibrium models is also performed.

[Establishment and validation of normal human L1-L5 lumbar three-dimensional finite element model].

PubMed

Zhu, Zhenqi; Liu, Chenjun; Wang, Jiefu; Wang, Kaifeng; Huang, Zhixin; Wang, Weida; Liu, Haiying

2014-10-14

To create and validate a L1-L5 lumbar three-dimensional finite element model. The L1-L5 lumbar spines of a male healthy volunteer were scanned with computed tomography (CT). And a L1-L5 lumbar three-dimensional finite element model was created with the aid of software packages of Mimics, Geomagic and Ansys. Then border conditions were set, unit type was determined, finite element mesh was divided and a model was established for loading and calculating. Average model stiffness under the conditions of flexion, extension, lateral bending and axial rotation was calculated and compared with the outcomes of former articles for validation. A normal human L1-L5 lumbar three-dimensional finite element model was established to include 459 340 elements and 661 938 nodes. After constraining the inferior endplate of L5 vertebral body, 500 kg × m × s⁻² compressive loading was imposed averagely on the superior endplate of L1 vertebral body. Then 10 kg × m² × s⁻² moment simulating flexion, extension, lateral bending and axial rotation were imposed on the superior endplate of L1 vertebral body. Eventually the average stiffness of all directions was calculated and it was similar to the outcomes of former articles. The L1-L5 lumbar three-dimensional finite element model is validated so that it may used with biomechanical simulation and analysis of normal or surgical models.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Tidal, Residual, Intertidal Mudflat (TRIM) Model and its Applications to San Francisco Bay, California

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.; Gartner, J.W.

1993-01-01

A numerical model using a semi-implicit finite-difference method for solving the two-dimensional shallow-water equations is presented. The gradient of the water surface elevation in the momentum equations and the velocity divergence in the continuity equation are finite-differenced implicitly, the remaining terms are finite-differenced explicitly. The convective terms are treated using an Eulerian-Lagrangian method. The combination of the semi-implicit finite-difference solution for the gravity wave propagation, and the Eulerian-Lagrangian treatment of the convective terms renders the numerical model unconditionally stable. When the baroclinic forcing is included, a salt transport equation is coupled to the momentum equations, and the numerical method is subject to a weak stability condition. The method of solution and the properties of the numerical model are given. This numerical model is particularly suitable for applications to coastal plain estuaries and tidal embayments in which tidal currents are dominant, and tidally generated residual currents are important. The model is applied to San Francisco Bay, California where extensive historical tides and current-meter data are available. The model calibration is considered by comparing time-series of the field data and of the model results. Alternatively, and perhaps more meaningfully, the model is calibrated by comparing the harmonic constants of tides and tidal currents derived from field data with those derived from the model. The model is further verified by comparing the model results with an independent data set representing the wet season. The strengths and the weaknesses of the model are assessed based on the results of model calibration and verification. Using the model results, the properties of tides and tidal currents in San Francisco Bay are characterized and discussed. Furthermore, using the numerical model, estimates of San Francisco Bay's volume, surface area, mean water depth, tidal prisms, and tidal excursions at spring and neap tides are computed. Additional applications of the model reveal, qualitatively the spatial distribution of residual variables. ?? 1993 Academic Press. All rights reserved.

Three Dimensional Compressible Turbulent Flow Computations for a Diffusing S-Duct With/Without Vortex Generators

NASA Technical Reports Server (NTRS)

Cho, Soo-Yong; Greber, Isaac

1994-01-01

Numerical investigations on a diffusing S-duct with/without vortex generators and a straight duct with vortex generators are presented. The investigation consists of solving the full three-dimensional unsteady compressible mass averaged Navier-Stokes equations. An implicit finite volume lower-upper time marching code (RPLUS3D) has been employed and modified. A three-dimensional Baldwin-Lomax turbulence model has been modified in conjunction with the flow physics. A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vortical structure for modeling the shed vortex is used as a source term in the computation domain. The injected vortex paths in the straight duct are compared with the analysis by two kinds of prediction models. The flow structure by the vortex generators are investigated along the duct. Computed results of the flow in a circular diffusing S-duct provide an understanding of the flow structure within a typical engine inlet system. These are compared with the experimental wall static-pressure, static- and total-pressure field, and secondary velocity profiles. Additionally, boundary layer thickness, skin friction values, and velocity profiles in wall coordinates are presented. In order to investigate the effect of vortex generators, various vortex strengths are examined in this study. The total-pressure recovery and distortion coefficients are obtained at the exit of the S-duct. The numerical results clearly depict the interaction between the low velocity flow by the flow separation and the injected vortices.

Development of an energy storage tank model

NASA Astrophysics Data System (ADS)

Buckley, Robert Christopher

A linearized, one-dimensional finite difference model employing an implicit finite difference method for energy storage tanks is developed, programmed with MATLAB, and demonstrated for different applications. A set of nodal energy equations is developed by considering the energy interactions on a small control volume. The general method of solving these equations is described as are other features of the simulation program. Two modeling applications are presented: the first using a hot water storage tank with a solar collector and an absorption chiller to cool a building in the summer, the second using a molten salt storage system with a solar collector and steam power plant to generate electricity. Recommendations for further study as well as all of the source code generated in the project are also provided.

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

NASA Technical Reports Server (NTRS)

Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

2011-01-01

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Godfrey, Andrew G.; Walters, Robert W.; Van Leer, Bram

1993-01-01

The preconditioning procedure for generalized finite-rate chemistry and the proper preconditioning for the one-dimensional Navier-Stokes equations are presented. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from the incompressible to the hypersonic. Specific benefits are realized at low and transonic flow speeds. The extended preconditioning matrix accounts for thermal and chemical non-equilibrium and its implementation is explained for both explicit and implicit time marching. The effect of higher-order spatial accuracy and various flux splittings is investigated. Numerical analysis reveals the possible theoretical improvements from using proconditioning at all Mach numbers. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number regions.

A finite area scheme for shallow granular flows on three-dimensional surfaces

NASA Astrophysics Data System (ADS)

Rauter, Matthias

2017-04-01

Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.

Heating 7.2 user`s manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Heating 7. 2 user's manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

A three-dimensional finite-volume Eulerian-Lagrangian Localized Adjoint Method (ELLAM) for solute-transport modeling

USGS Publications Warehouse

Heberton, C.I.; Russell, T.F.; Konikow, Leonard F.; Hornberger, G.Z.

2000-01-01

This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.

Advances in three-dimensional field analysis and evaluation of performance parameters of electrical machines

NASA Astrophysics Data System (ADS)

Sivasubramaniam, Kiruba

This thesis makes advances in three dimensional finite element analysis of electrical machines and the quantification of their parameters and performance. The principal objectives of the thesis are: (1)the development of a stable and accurate method of nonlinear three-dimensional field computation and application to electrical machinery and devices; and (2)improvement in the accuracy of determination of performance parameters, particularly forces and torque computed from finite elements. Contributions are made in two general areas: a more efficient formulation for three dimensional finite element analysis which saves time and improves accuracy, and new post-processing techniques to calculate flux density values from a given finite element solution. A novel three-dimensional magnetostatic solution based on a modified scalar potential method is implemented. This method has significant advantages over the traditional total scalar, reduced scalar or vector potential methods. The new method is applied to a 3D geometry of an iron core inductor and a permanent magnet motor. The results obtained are compared with those obtained from traditional methods, in terms of accuracy and speed of computation. A technique which has been observed to improve force computation in two dimensional analysis using a local solution of Laplace's equation in the airgap of machines is investigated and a similar method is implemented in the three dimensional analysis of electromagnetic devices. A new integral formulation to improve force calculation from a smoother flux-density profile is also explored and implemented. Comparisons are made and conclusions drawn as to how much improvement is obtained and at what cost. This thesis also demonstrates the use of finite element analysis to analyze torque ripples due to rotor eccentricity in permanent magnet BLDC motors. A new method for analyzing torque harmonics based on data obtained from a time stepping finite element analysis of the machine is explored and implemented.

Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers

NASA Technical Reports Server (NTRS)

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Three-dimensional compact explicit-finite difference time domain scheme with density variation

NASA Astrophysics Data System (ADS)

Tsuchiya, Takao; Maruta, Naoki

2018-07-01

In this paper, the density variation is implemented in the three-dimensional compact-explicit finite-difference time-domain (CE-FDTD) method. The formulation is first developed based on the continuity equation and the equation of motion, which include the density. Some numerical demonstrations are performed for the three-dimensional sound wave propagation in a two density layered medium. The numerical results are compared with the theoretical results to verify the proposed formulation.

Unsteady solute-transport simulation in streamflow using a finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

This report documents a rather simple, general purpose, one-dimensional, one-parameter, mass-transport model for field use. The model assumes a well-mixed conservative solute that may be coming from an unsteady source and is moving in unsteady streamflow. The quantity of solute being transported is in the units of concentration. Results are reported as such. An implicit finite-difference technique is used to solve the mass transport equation. It consists of creating a tridiagonal matrix and using the Thomas algorithm to solve the matrix for the unknown concentrations at the new time step. The computer program pesented is designed to compute the concentration of a water-quality constituent at any point and at any preselected time in a one-dimensional stream. The model is driven by the inflowing concentration of solute at the upstream boundary and is influenced by the solute entering the stream from tributaries and lateral ground-water inflow and from a source or sink. (Woodard-USGS)

An Integrated Magnetic Circuit Model and Finite Element Model Approach to Magnetic Bearing Design

NASA Technical Reports Server (NTRS)

Provenza, Andrew J.; Kenny, Andrew; Palazzolo, Alan B.

2003-01-01

A code for designing magnetic bearings is described. The code generates curves from magnetic circuit equations relating important bearing performance parameters. Bearing parameters selected from the curves by a designer to meet the requirements of a particular application are input directly by the code into a three-dimensional finite element analysis preprocessor. This means that a three-dimensional computer model of the bearing being developed is immediately available for viewing. The finite element model solution can be used to show areas of magnetic saturation and make more accurate predictions of the bearing load capacity, current stiffness, position stiffness, and inductance than the magnetic circuit equations did at the start of the design process. In summary, the code combines one-dimensional and three-dimensional modeling methods for designing magnetic bearings.

Ablation, Thermal Response, and Chemistry Program for Analysis of Thermal Protection Systems

NASA Technical Reports Server (NTRS)

Milos, Frank S.; Chen, Yih-Kanq

2010-01-01

In previous work, the authors documented the Multicomponent Ablation Thermochemistry (MAT) and Fully Implicit Ablation and Thermal response (FIAT) programs. In this work, key features from MAT and FIAT were combined to create the new Fully Implicit Ablation, Thermal response, and Chemistry (FIATC) program. FIATC is fully compatible with FIAT (version 2.5) but has expanded capabilities to compute the multispecies surface chemistry and ablation rate as part of the surface energy balance. This new methodology eliminates B' tables, provides blown species fractions as a function of time, and enables calculations that would otherwise be impractical (e.g. 4+ dimensional tables) such as pyrolysis and ablation with kinetic rates or unequal diffusion coefficients. Equations and solution procedures are presented, then representative calculations of equilibrium and finite-rate ablation in flight and ground-test environments are discussed.

Least-squares finite element solutions for three-dimensional backward-facing step flow

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Hou, Lin-Jun; Lin, Tsung-Liang

1993-01-01

Comprehensive numerical solutions of the steady state incompressible viscous flow over a three-dimensional backward-facing step up to Re equals 800 are presented. The results are obtained by the least-squares finite element method (LSFEM) which is based on the velocity-pressure-vorticity formulation. The computed model is of the same size as that of Armaly's experiment. Three-dimensional phenomena are observed even at low Reynolds number. The calculated values of the primary reattachment length are in good agreement with experimental results.

Simulation of wave propagation in three-dimensional random media

NASA Astrophysics Data System (ADS)

Coles, Wm. A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1995-04-01

Quantitative error analyses for the simulation of wave propagation in three-dimensional random media, when narrow angular scattering is assumed, are presented for plane-wave and spherical-wave geometry. This includes the errors that result from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive indices of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared with the spatial spectra of

Accurate color synthesis of three-dimensional objects in an image

NASA Astrophysics Data System (ADS)

Xin, John H.; Shen, Hui-Liang

2004-05-01

Our study deals with color synthesis of a three-dimensional object in an image; i.e., given a single image, a target color can be accurately mapped onto the object such that the color appearance of the synthesized object closely resembles that of the actual one. As it is almost impossible to acquire the complete geometric description of the surfaces of an object in an image, this study attempted to recover the implicit description of geometry for the color synthesis. The description was obtained from either a series of spectral reflectances or the RGB signals at different surface positions on the basis of the dichromatic reflection model. The experimental results showed that this implicit image-based representation is related to the object geometry and is sufficient for accurate color synthesis of three-dimensional objects in an image. The method established is applicable to the color synthesis of both rigid and deformable objects and should contribute to color fidelity in virtual design, manufacturing, and retailing.

On a model of three-dimensional bursting and its parallel implementation

NASA Astrophysics Data System (ADS)

Tabik, S.; Romero, L. F.; Garzón, E. M.; Ramos, J. I.

2008-04-01

A mathematical model for the simulation of three-dimensional bursting phenomena and its parallel implementation are presented. The model consists of four nonlinearly coupled partial differential equations that include fast and slow variables, and exhibits bursting in the absence of diffusion. The differential equations have been discretized by means of a second-order accurate in both space and time, linearly-implicit finite difference method in equally-spaced grids. The resulting system of linear algebraic equations at each time level has been solved by means of the Preconditioned Conjugate Gradient (PCG) method. Three different parallel implementations of the proposed mathematical model have been developed; two of these implementations, i.e., the MPI and the PETSc codes, are based on a message passing paradigm, while the third one, i.e., the OpenMP code, is based on a shared space address paradigm. These three implementations are evaluated on two current high performance parallel architectures, i.e., a dual-processor cluster and a Shared Distributed Memory (SDM) system. A novel representation of the results that emphasizes the most relevant factors that affect the performance of the paralled implementations, is proposed. The comparative analysis of the computational results shows that the MPI and the OpenMP implementations are about twice more efficient than the PETSc code on the SDM system. It is also shown that, for the conditions reported here, the nonlinear dynamics of the three-dimensional bursting phenomena exhibits three stages characterized by asynchronous, synchronous and then asynchronous oscillations, before a quiescent state is reached. It is also shown that the fast system reaches steady state in much less time than the slow variables.

Creating physically-based three-dimensional microstructures: Bridging phase-field and crystal plasticity models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lim, Hojun; Owen, Steven J.; Abdeljawad, Fadi F.

In order to better incorporate microstructures in continuum scale models, we use a novel finite element (FE) meshing technique to generate three-dimensional polycrystalline aggregates from a phase field grain growth model of grain microstructures. The proposed meshing technique creates hexahedral FE meshes that capture smooth interfaces between adjacent grains. Three dimensional realizations of grain microstructures from the phase field model are used in crystal plasticity-finite element (CP-FE) simulations of polycrystalline a -iron. We show that the interface conformal meshes significantly reduce artificial stress localizations in voxelated meshes that exhibit the so-called "wedding cake" interfaces. This framework provides a direct linkmore » between two mesoscale models - phase field and crystal plasticity - and for the first time allows mechanics simulations of polycrystalline materials using three-dimensional hexahedral finite element meshes with realistic topological features.« less

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight. [atmospheric general circulation experiment, convection in a float zone, and the Bridgman-Stockbarger crystal growing system

NASA Technical Reports Server (NTRS)

Roberts, G. O.; Fowlis, W. W.; Miller, T. L.

1984-01-01

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Low-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional ODE systems

NASA Astrophysics Data System (ADS)

Cavaglieri, Daniele; Bewley, Thomas

2015-04-01

Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storage RK schemes are especially effective for time-marching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop and characterize eight new low-storage implicit/explicit RK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep.

Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

NASA Technical Reports Server (NTRS)

Whitaker, David L.

1993-01-01

A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.

Thermal Modelling Analysis of Spiral Wound Supercapacitor under Constant-Current Cycling

PubMed Central

Wang, Kai; Li, Liwei; Yin, Huaixian; Zhang, Tiezhu; Wan, Wubo

2015-01-01

A three-dimensional modelling approach is used to study the effects of operating and ambient conditions on the thermal behaviour of the spiral wound supercapacitor. The transient temperature distribution during cycling is obtained by using the finite element method with an implicit predictor-multicorrector algorithm. At the constant current of 2A, the results show that the maximum temperature appears in core area. After 5 cycles, the maximum temperature is 34.5°C, while in steady state, it’s up to 42.5°C. This paper further studies the relationship between the maximum temperature and charge-discharge current. The maximum temperature will be more than 60°C after 5 cycles at the current of 4A, and cooling measurements should be taken at that time. It can provide thoughts on inner temperature field distribution and structure design of the spiral wound supercapacitor in working process. PMID:26444687

Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous Flows

NASA Technical Reports Server (NTRS)

Frink, Neal T.

1996-01-01

A method Is presented for solving turbulent flow problems on three-dimensional unstructured grids. Spatial discretization Is accomplished by a cell-centered finite-volume formulation using an accurate lin- ear reconstruction scheme and upwind flux differencing. Time is advanced by an implicit backward- Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy In predictions of skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer, and for the ONERA M6 wing under a high Reynolds number, transonic, separated flow condition.

Effects of bleed-hole geometry and plenum pressure on three-dimensional shock-wave/boundary-layer/bleed interactions

NASA Technical Reports Server (NTRS)

Chyu, Wei J.; Rimlinger, Mark J.; Shih, Tom I.-P.

1993-01-01

A numerical study was performed to investigate 3D shock-wave/boundary-layer interactions on a flat plate with bleed through one or more circular holes that vent into a plenum. This study was focused on how bleed-hole geometry and pressure ratio across bleed holes affect the bleed rate and the physics of the flow in the vicinity of the holes. The aspects of the bleed-hole geometry investigated include angle of bleed hole and the number of bleed holes. The plenum/freestream pressure ratios investigated range from 0.3 to 1.7. This study is based on the ensemble-averaged, 'full compressible' Navier-Stokes (N-S) equations closed by the Baldwin-Lomax algebraic turbulence model. Solutions to the ensemble-averaged N-S equations were obtained by an implicit finite-volume method using the partially-split, two-factored algorithm of Steger on an overlapping Chimera grid.

Large eddy simulation of incompressible turbulent channel flow

NASA Technical Reports Server (NTRS)

Moin, P.; Reynolds, W. C.; Ferziger, J. H.

1978-01-01

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous Flows

NASA Technical Reports Server (NTRS)

Frink, Neal T.

1996-01-01

A method is presented for solving turbulent flow problems on three-dimensional unstructured grids. Spatial discretization is accomplished by a cell-centered finite-volume formulation using an accurate linear reconstruction scheme and upwind flux differencing. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy in predictions of skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer, and for the ONERA M6 wing under a high Reynolds number, transonic, separated flow condition.

Incompressible viscous flow computations for the pump components and the artificial heart

NASA Technical Reports Server (NTRS)

Kiris, Cetin

1992-01-01

A finite-difference, three-dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. In this work, the equations are solved in steadily rotating reference frames by using the steady-state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two. Included in the appendix is a paper on incompressible viscous flow through artificial heart devices with moving boundaries. Time-accurate calculations, such as impeller and diffusor interaction, will be reported in future work.

[Three dimensional finite element model of a modified posterior cervical single open-door laminoplasty].

PubMed

Wang, Q; Yang, Y; Fei, Q; Li, D; Li, J J; Meng, H; Su, N; Fan, Z H; Wang, B Q

2017-06-06

Objective: To build a three-dimensional finite element models of a modified posterior cervical single open-door laminoplasty with short-segmental lateral mass screws fusion. Methods: The C(2)-C(7) segmental data were obtained from computed tomography (CT) scans of a male patient with cervical spondylotic myelopathy and spinal stenosis.Three-dimensional finite element models of a modified cervical single open-door laminoplasty (before and after surgery) were constructed by the combination of software package MIMICS, Geomagic and ABAQUS.The models were composed of bony vertebrae, articulating facets, intervertebral disc and associated ligaments.The loads of moments 1.5Nm at different directions (flexion, extension, lateral bending and axial rotation)were applied at preoperative model to calculate intersegmental ranges of motion.The results were compared with the previous studies to verify the validation of the models. Results: Three-dimensional finite element models of the modified cervical single open- door laminoplasty had 102258 elements (preoperative model) and 161 892 elements (postoperative model) respectively, including C(2-7) six bony vertebraes, C(2-3)-C(6-7) five intervertebral disc, main ligaments and lateral mass screws.The intersegmental responses at the preoperative model under the loads of moments 1.5 Nm at different directions were similar to the previous published data. Conclusion: Three-dimensional finite element models of the modified cervical single open- door laminoplasty were successfully established and had a good biological fidelity, which can be used for further study.

3-d finite element model development for biomechanics: a software demonstration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hollerbach, K.; Hollister, A.M.; Ashby, E.

1997-03-01

Finite element analysis is becoming an increasingly important part of biomechanics and orthopedic research, as computational resources become more powerful, and data handling algorithms become more sophisticated. Until recently, tools with sufficient power did not exist or were not accessible to adequately model complicated, three-dimensional, nonlinear biomechanical systems. In the past, finite element analyses in biomechanics have often been limited to two-dimensional approaches, linear analyses, or simulations of single tissue types. Today, we have the resources to model fully three-dimensional, nonlinear, multi-tissue, and even multi-joint systems. The authors will present the process of developing these kinds of finite element models,more » using human hand and knee examples, and will demonstrate their software tools.« less

Electromagnetic density of modes for a finite-size three-dimensional structure.

PubMed

D'Aguanno, Giuseppe; Mattiucci, Nadia; Centini, Marco; Scalora, Michael; Bloemer, Mark J

2004-05-01

The concept of the density of modes has been lacking a precise mathematical definition for a finite-size structure. With the explosive growth in the fabrication of photonic crystals and nanostructures, which are inherently finite in size, a workable definition is imperative. We give a simple and physically intuitive definition of the electromagnetic density of modes based on the Green's function for a generic three-dimensional open cavity filled with a linear, isotropic, dielectric material.

[Construction and validation of a three-dimensional finite element model of cranio-maxillary complex with sutures in unilateral cleft lip and palate patient].

PubMed

Wu, Zhi-fang; Lei, Yong-hua; Li, Wen-jie; Liao, Sheng-hui; Zhao, Zi-jin

2013-02-01

To explore an effective method to construct and validate a finite element model of the unilateral cleft lip and palate(UCLP) craniomaxillary complex with sutures, which could be applied in further three-dimensional finite element analysis (FEA). One male patient aged 9 with left complete lip and palate cleft was selected and CT scan was taken at 0.75mm intervals on the skull. The CT data was saved in Dicom format, which was, afterwards, imported into Software Mimics 10.0 to generate a three-dimensional anatomic model. Then Software Geomagic Studio 12.0 was used to match, smoothen and transfer the anatomic model into a CAD model with NURBS patches. Then, 12 circum-maxillary sutures were integrated into the CAD model by Solidworks (2011 version). Finally meshing by E-feature Biomedical Modeler was done and a three-dimensional finite element model with sutures was obtained. A maxillary protraction force (500 g per side, 20° downward and forward from the occlusal plane) was applied. Displacement and stress distribution of some important craniofacial structures were measured and compared with the results of related researches in the literature. A three-dimensional finite element model of UCLP craniomaxillary complex with 12 sutures was established from the CT scan data. This simulation model consisted of 206 753 individual elements with 260 662 nodes, which was a more precise simulation and a better representation of human craniomaxillary complex than the formerly available FEA models. By comparison, this model was proved to be valid. It is an effective way to establish the three-dimensional finite element model of UCLP cranio-maxillary complex with sutures from CT images with the help of the following softwares: Mimics 10.0, Geomagic Studio 12.0, Solidworks and E-feature Biomedical Modeler.

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

A variable resolution nonhydrostatic global atmospheric semi-implicit semi-Lagrangian model

NASA Astrophysics Data System (ADS)

Pouliot, George Antoine

2000-10-01

The objective of this project is to develop a variable-resolution finite difference adiabatic global nonhydrostatic semi-implicit semi-Lagrangian (SISL) model based on the fully compressible nonhydrostatic atmospheric equations. To achieve this goal, a three-dimensional variable resolution dynamical core was developed and tested. The main characteristics of the dynamical core can be summarized as follows: Spherical coordinates were used in a global domain. A hydrostatic/nonhydrostatic switch was incorporated into the dynamical equations to use the fully compressible atmospheric equations. A generalized horizontal variable resolution grid was developed and incorporated into the model. For a variable resolution grid, in contrast to a uniform resolution grid, the order of accuracy of finite difference approximations is formally lost but remains close to the order of accuracy associated with the uniform resolution grid provided the grid stretching is not too significant. The SISL numerical scheme was implemented for the fully compressible set of equations. In addition, the generalized minimum residual (GMRES) method with restart and preconditioner was used to solve the three-dimensional elliptic equation derived from the discretized system of equations. The three-dimensional momentum equation was integrated in vector-form to incorporate the metric terms in the calculations of the trajectories. Using global re-analysis data for a specific test case, the model was compared to similar SISL models previously developed. Reasonable agreement between the model and the other independently developed models was obtained. The Held-Suarez test for dynamical cores was used for a long integration and the model was successfully integrated for up to 1200 days. Idealized topography was used to test the variable resolution component of the model. Nonhydrostatic effects were simulated at grid spacings of 400 meters with idealized topography and uniform flow. Using a high-resolution topographic data set and the variable resolution grid, sets of experiments with increasing resolution were performed over specific regions of interest. Using realistic initial conditions derived from re-analysis fields, nonhydrostatic effects were significant for grid spacings on the order of 0.1 degrees with orographic forcing. If the model code was adapted for use in a message passing interface (MPI) on a parallel supercomputer today, it was estimated that a global grid spacing of 0.1 degrees would be achievable for a global model. In this case, nonhydrostatic effects would be significant for most areas. A variable resolution grid in a global model provides a unified and flexible approach to many climate and numerical weather prediction problems. The ability to configure the model from very fine to very coarse resolutions allows for the simulation of atmospheric phenomena at different scales using the same code. We have developed a dynamical core illustrating the feasibility of using a variable resolution in a global model.

A Numerical Model for Predicting Shoreline Changes.

DTIC Science & Technology

1980-07-01

minimal shorelines for finite - difference scheme of time lAt (B) . . . 27 11 Transport function Q(ao) = cos ao sin za o for selected values of z . 28 12...generate the preceding examples was based on the use of implicit finite differences . Such schemes, whether implicit or ex- plicit (or both), are...10(A) shows an initially straight shoreline. In any finite - difference scheme, after one time increment At, the shoreline is bounded below by the solid

Advanced numerical methods for three dimensional two-phase flow calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toumi, I.; Caruge, D.

1997-07-01

This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses anmore » extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.« less

Two-level schemes for the advection equation

NASA Astrophysics Data System (ADS)

Vabishchevich, Petr N.

2018-06-01

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

3-D thermal analysis using finite difference technique with finite element model for improved design of components of rocket engine turbomachines for Space Shuttle Main Engine SSME

NASA Technical Reports Server (NTRS)

Sohn, Kiho D.; Ip, Shek-Se P.

1988-01-01

Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.; Collins, Jeffery D.

1991-01-01

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.

The effectiveness of element downsizing on a three-dimensional finite element model of bone trabeculae in implant biomechanics.

PubMed

Sato, Y; Wadamoto, M; Tsuga, K; Teixeira, E R

1999-04-01

More validity of finite element analysis in implant biomechanics requires element downsizing. However, excess downsizing needs computer memory and calculation time. To investigate the effectiveness of element downsizing on the construction of a three-dimensional finite element bone trabeculae model, with different element sizes (600, 300, 150 and 75 microm) models were constructed and stress induced by vertical 10 N loading was analysed. The difference in von Mises stress values between the models with 600 and 300 microm element sizes was larger than that between 300 and 150 microm. On the other hand, no clear difference of stress values was detected among the models with 300, 150 and 75 microm element sizes. Downsizing of elements from 600 to 300 microm is suggested to be effective in the construction of a three-dimensional finite element bone trabeculae model for possible saving of computer memory and calculation time in the laboratory.

Further analytical study of hybrid rocket combustion

NASA Technical Reports Server (NTRS)

Hung, W. S. Y.; Chen, C. S.; Haviland, J. K.

1972-01-01

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

Numerical simulation of two-dimensional heat transfer in composite bodies with application to de-icing of aircraft components. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Chao, D. F. K.

1983-01-01

Transient, numerical simulations of the de-icing of composite aircraft components by electrothermal heating were performed for a two dimensional rectangular geometry. The implicit Crank-Nicolson formulation was used to insure stability of the finite-difference heat conduction equations and the phase change in the ice layer was simulated using the Enthalpy method. The Gauss-Seidel point iterative method was used to solve the system of difference equations. Numerical solutions illustrating de-icer performance for various composite aircraft structures and environmental conditions are presented. Comparisons are made with previous studies. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Symmetry restoring bifurcations and quasiperiodic chaos induced by a new intermittency in a vibro-impact system.

PubMed

Yue, Yuan; Miao, Pengcheng; Xie, Jianhua; Celso, Grebogi

2016-11-01

Quasiperiodic chaos (QC), which is a combination of quasiperiodic sets and a chaotic set, is uncovered in the six dimensional Poincaré map of a symmetric three-degree of freedom vibro-impact system. Accompanied by symmetry restoring bifurcation, this QC is the consequence of a novel intermittency that occurs between two conjugate quasiperiodic sets and a chaotic set. The six dimensional Poincaré map P is the 2-fold composition of another virtual implicit map Q, yielding the symmetry of the system. Map Q can capture two conjugate attractors, which is at the core of the dynamics of the vibro-impact system. Three types of symmetry restoring bifurcations are analyzed in detail. First, if two conjugate chaotic attractors join together, the chaos-chaos intermittency induced by attractor-merging crisis takes place. Second, if two conjugate quasiperiodic sets are suddenly embedded in a chaotic one, QC is induced by a new intermittency between the three attractors. Third, if two conjugate quasiperiodic attractors connect with each other directly, they merge to form a single symmetric quasiperiodic one. For the second case, the new intermittency is caused by the collision of two conjugate quasiperiodic attractors with an unstable symmetric limit set. As the iteration number is increased, the largest finite-time Lyapunov exponent of the QC does not converge to a constant, but fluctuates in the positive region.

Calculation methods for compressible turbulent boundary layers, 1976

NASA Technical Reports Server (NTRS)

Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.

1977-01-01

Equations and closure methods for compressible turbulent boundary layers are discussed. Flow phenomena peculiar to calculation of these boundary layers were considered, along with calculations of three dimensional compressible turbulent boundary layers. Procedures for ascertaining nonsimilar two and three dimensional compressible turbulent boundary layers were appended, including finite difference, finite element, and mass-weighted residual methods.

The development of an explicit thermochemical nonequilibrium algorithm and its application to compute three dimensional AFE flowfields

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

This study presents a three-dimensional explicit, finite-difference, shock-capturing numerical algorithm applied to viscous hypersonic flows in thermochemical nonequilibrium. The algorithm employs a two-temperature physical model. Equations governing the finite-rate chemical reactions are fully-coupled to the gas dynamic equations using a novel coupling technique. The new coupling method maintains stability in the explicit, finite-rate formulation while allowing relatively large global time steps. The code uses flux-vector accuracy. Comparisons with experimental data and other numerical computations verify the accuracy of the present method. The code is used to compute the three-dimensional flowfield over the Aeroassist Flight Experiment (AFE) vehicle at one of its trajectory points.

NASTRAN analysis for the Airmass Sunburst model 'C' Ultralight Aircraft

NASA Technical Reports Server (NTRS)

Verbestel, John; Smith, Howard W.

1993-01-01

The purpose of this project was to create a three dimensional NASTRAN model of the Airmass Sunburst Ultralight comparable to one made for finite element analysis. A two dimensional sample problem will be calculated by hand and by NASTRAN to make sure that NASTRAN finds similar results. A three dimensional model, similar to the one analyzed by the finite element program, will be run on NASTRAN. A comparison will be done between the NASTRAN results and the finite element program results. This study will deal mainly with the aerodynamic loads on the wing and surrounding support structure at an attack angle of 10 degrees.

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

NASA Astrophysics Data System (ADS)

Lonsdale, R. D.; Webster, R.

This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

Applications of an exponential finite difference technique

DOE Office of Scientific and Technical Information (OSTI.GOV)

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques

NASA Astrophysics Data System (ADS)

Van Londersele, Arne; De Zutter, Daniël; Vande Ginste, Dries

2017-08-01

This work focuses on efficient full-wave solutions of multiscale electromagnetic problems in the time domain. Three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the Finite-Difference Time-Domain (FDTD) method on a nonuniform, staggered, tensor product grid: Newmark, Crank-Nicolson (CN) and Alternating-Direction-Implicit (ADI) implicitization. All of them are applied in preferable directions, alike Hybrid Implicit-Explicit (HIE) methods, as to limit the rank of the sparse linear systems. Both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous, possibly lossy, isotropic media. Numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed, relaxed limit. Apart from the theoretical contributions, new accomplishments such as the development of the leapfrog Alternating-Direction-Hybrid-Implicit-Explicit (ADHIE) FDTD method and a less stringent Courant-like time step limit for the conventional, fully explicit FDTD method on a nonuniform grid, have immediate practical applications.

TOPAZ2D heat transfer code users manual and thermal property data base

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shapiro, A.B.; Edwards, A.L.

1990-05-01

TOPAZ2D is a two dimensional implicit finite element computer code for heat transfer analysis. This user's manual provides information on the structure of a TOPAZ2D input file. Also included is a material thermal property data base. This manual is supplemented with The TOPAZ2D Theoretical Manual and the TOPAZ2D Verification Manual. TOPAZ2D has been implemented on the CRAY, SUN, and VAX computers. TOPAZ2D can be used to solve for the steady state or transient temperature field on two dimensional planar or axisymmetric geometries. Material properties may be temperature dependent and either isotropic or orthotropic. A variety of time and temperature dependentmore » boundary conditions can be specified including temperature, flux, convection, and radiation. Time or temperature dependent internal heat generation can be defined locally be element or globally by material. TOPAZ2D can solve problems of diffuse and specular band radiation in an enclosure coupled with conduction in material surrounding the enclosure. Additional features include thermally controlled reactive chemical mixtures, thermal contact resistance across an interface, bulk fluid flow, phase change, and energy balances. Thermal stresses can be calculated using the solid mechanics code NIKE2D which reads the temperature state data calculated by TOPAZ2D. A three dimensional version of the code, TOPAZ3D is available. The material thermal property data base, Chapter 4, included in this manual was originally published in 1969 by Art Edwards for use with his TRUMP finite difference heat transfer code. The format of the data has been altered to be compatible with TOPAZ2D. Bob Bailey is responsible for adding the high explosive thermal property data.« less

Three-dimensional supersonic flow around double compression ramp with finite span

NASA Astrophysics Data System (ADS)

Lee, H. S.; Lee, J. H.; Park, G.; Park, S. H.; Byun, Y. H.

2017-01-01

Three-dimensional flows of Mach number 3 around a double-compression ramp with finite span have been investigated numerically. Shadowgraph visualisation images obtained in a supersonic wind tunnel are used for comparison. A three-dimensional Reynolds-averaged Navier-Stokes solver was used to obtain steady numerical solutions. Two-dimensional numerical results are also compared. Four different cases were studied: two different second ramp angles of 30° and 45° in configurations with and without sidewalls, respectively. Results showed that there is a leakage of mass and momentum fluxes heading outwards in the spanwise direction for three-dimensional cases without sidewalls. The leakage changed the flow characteristics of the shock-induced boundary layer and resulted in the discrepancy between the experimental data and two-dimensional numerical results. It is found that suppressing the flow leakage by attaching the sidewalls enhances the two-dimensionality of the experimental data for the double-compression ramp flow.

Three-dimensional finite element modelling of muscle forces during mastication.

PubMed

Röhrle, Oliver; Pullan, Andrew J

2007-01-01

This paper presents a three-dimensional finite element model of human mastication. Specifically, an anatomically realistic model of the masseter muscles and associated bones is used to investigate the dynamics of chewing. A motion capture system is used to track the jaw motion of a subject chewing standard foods. The three-dimensional nonlinear deformation of the masseter muscles are calculated via the finite element method, using the jaw motion data as boundary conditions. Motion-driven muscle activation patterns and a transversely isotropic material law, defined in a muscle-fibre coordinate system, are used in the calculations. Time-force relationships are presented and analysed with respect to different tasks during mastication, e.g. opening, closing, and biting, and are also compared to a more traditional one-dimensional model. The results strongly suggest that, due to the complex arrangement of muscle force directions, modelling skeletal muscles as conventional one-dimensional lines of action might introduce a significant source of error.

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, Roy C., Jr.; Turkel, Eli; Rossow, C.-C.

2007-01-01

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

2-D to 3-D global/local finite element analysis of cross-ply composite laminates

NASA Technical Reports Server (NTRS)

Thompson, D. Muheim; Griffin, O. Hayden, Jr.

1990-01-01

An example of two-dimensional to three-dimensional global/local finite element analysis of a laminated composite plate with a hole is presented. The 'zoom' technique of global/local analysis is used, where displacements of the global/local interface from the two-dimensional global model are applied to the edges of the three-dimensional local model. Three different hole diameters, one, three, and six inches, are considered in order to compare the effect of hole size on the three-dimensional stress state around the hole. In addition, three different stacking sequences are analyzed for the six inch hole case in order to study the effect of stacking sequence. The existence of a 'critical' hole size, where the interlaminar stresses are maximum, is indicated. Dispersion of plies at the same angle, as opposed to clustering, is found to reduce the magnitude of some interlaminar stress components and increase others.

Comparison of 2D Finite Element Modeling Assumptions with Results From 3D Analysis for Composite Skin-Stiffener Debonding

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Paris, Isbelle L.; OBrien, T. Kevin; Minguet, Pierre J.

2004-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized plane strain type approaches were performed. The computed skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Influence of 2D Finite Element Modeling Assumptions on Debonding Prediction for Composite Skin-stiffener Specimens Subjected to Tension and Bending

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Minguet, Pierre J.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane strain elements as well as three different generalized plane strain type approaches were performed. The computed deflections, skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with lamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Fast Implicit Methods For Elliptic Moving Interface Problems

DTIC Science & Technology

2015-12-11

analyzed, and tested for the Fourier transform of piecewise polynomials given on d-dimensional simplices in D-dimensional Euclidean space. These transforms...evaluation, and one to three orders of magnitude slower than the classical uniform Fast Fourier Transform. Second, bilinear quadratures ---which...a fast algorithm was derived, analyzed, and tested for the Fourier transform of pi ecewise polynomials given on d-dimensional simplices in D

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Three-Dimensional Finite Element Ablative Thermal Response and Thermostructural Design of Thermal Protection Systems

NASA Technical Reports Server (NTRS)

Dec, John A.; Braun, Robert D.

2011-01-01

A finite element ablation and thermal response program is presented for simulation of three-dimensional transient thermostructural analysis. The three-dimensional governing differential equations and finite element formulation are summarized. A novel probabilistic design methodology for thermal protection systems is presented. The design methodology is an eight step process beginning with a parameter sensitivity study and is followed by a deterministic analysis whereby an optimum design can determined. The design process concludes with a Monte Carlo simulation where the probabilities of exceeding design specifications are estimated. The design methodology is demonstrated by applying the methodology to the carbon phenolic compression pads of the Crew Exploration Vehicle. The maximum allowed values of bondline temperature and tensile stress are used as the design specifications in this study.

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Hsieh, Kwang-Chung; Shuen, Jian-Shun; Mcbride, Bonnie J.

1988-01-01

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Godfrey, Andrew G.

1993-01-01

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

User's guide for NASCRIN: A vectorized code for calculating two-dimensional supersonic internal flow fields

NASA Technical Reports Server (NTRS)

Kumar, A.

1984-01-01

A computer program NASCRIN has been developed for analyzing two-dimensional flow fields in high-speed inlets. It solves the two-dimensional Euler or Navier-Stokes equations in conservation form by an explicit, two-step finite-difference method. An explicit-implicit method can also be used at the user's discretion for viscous flow calculations. For turbulent flow, an algebraic, two-layer eddy-viscosity model is used. The code is operational on the CDC CYBER 203 computer system and is highly vectorized to take full advantage of the vector-processing capability of the system. It is highly user oriented and is structured in such a way that for most supersonic flow problems, the user has to make only a few changes. Although the code is primarily written for supersonic internal flow, it can be used with suitable changes in the boundary conditions for a variety of other problems.

Two-Dimensional Mathematical Modeling of the Pack Carburizing Process

NASA Astrophysics Data System (ADS)

Sarkar, S.; Gupta, G. S.

2008-10-01

Pack carburization is the oldest method among the case-hardening treatments, and sufficient attempts have not been made to understand this process in terms of heat and mass transfer, effect of alloying elements, dimensions of the sample, etc. Thus, a two-dimensional mathematical model in cylindrical coordinate is developed for simulating the pack carburization process for chromium-bearing steel in this study. Heat and mass balance equations are solved simultaneously, where the surface temperature of the sample varies with time, but the carbon potential at the surface during the process remains constant. The fully implicit finite volume technique is used to solve the governing equations. Good agreement has been found between the predicted and published data. The effect of temperature, carburizing time, dimensions of the sample, etc. on the pack carburizing process shows some interesting results. It is found that the two-dimensional model gives better insight into understanding the carburizing process.

A Three-Dimensional Finite-Element Model for Simulating Water Flow in Variably Saturated Porous Media

NASA Astrophysics Data System (ADS)

Huyakorn, Peter S.; Springer, Everett P.; Guvanasen, Varut; Wadsworth, Terry D.

1986-12-01

A three-dimensional finite-element model for simulating water flow in variably saturated porous media is presented. The model formulation is general and capable of accommodating complex boundary conditions associated with seepage faces and infiltration or evaporation on the soil surface. Included in this formulation is an improved Picard algorithm designed to cope with severely nonlinear soil moisture relations. The algorithm is formulated for both rectangular and triangular prism elements. The element matrices are evaluated using an "influence coefficient" technique that avoids costly numerical integration. Spatial discretization of a three-dimensional region is performed using a vertical slicing approach designed to accommodate complex geometry with irregular boundaries, layering, and/or lateral discontinuities. Matrix solution is achieved using a slice successive overrelaxation scheme that permits a fairly large number of nodal unknowns (on the order of several thousand) to be handled efficiently on small minicomputers. Six examples are presented to verify and demonstrate the utility of the proposed finite-element model. The first four examples concern one- and two-dimensional flow problems used as sample problems to benchmark the code. The remaining examples concern three-dimensional problems. These problems are used to illustrate the performance of the proposed algorithm in three-dimensional situations involving seepage faces and anisotropic soil media.

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Cannizzaro, Frank; Melson, N. D.

1991-01-01

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

Investigation of deformation of elements of three-dimensional reinforced concrete structures located in the soil, interacting with each other through rubber gaskets

NASA Astrophysics Data System (ADS)

Berezhnoi, D. V.; Balafendieva, I. S.; Sachenkov, A. A.; Sekaeva, L. R.

2017-06-01

In work the technique of calculation of elements of three-dimensional reinforced concrete substructures located in a soil, interacting with each other through rubber linings is realized. To describe the interaction of deformable structures with the ground, special “semi-infinite” finite elements are used. A technique has been implemented that allows one to describe the contact interaction of three-dimensional structures by means of a special contact finite element with specific properties. The obtained numerical results are compared with the experimental data, their good agreement is noted.

Stress-intensity factor equations for cracks in three-dimensional finite bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Raju, I. S.

1981-01-01

Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

An Implicit LU/AF FDTD Method

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

There has been some recent work to develop two and three-dimensional alternating direction implicit (ADI) FDTD schemes. These ADI schemes are based upon the original ADI concept developed by Peaceman and Rachford and Douglas and Gunn, which is a popular solution method in Computational Fluid Dynamics (CFD). These ADI schemes work well and they require solution of a tridiagonal system of equations. A new approach proposed in this paper applies a LU/AF approximate factorization technique from CFD to Maxwell s equations in flux conservative form for one space dimension. The result is a scheme that will retain its unconditional stability in three space dimensions, but does not require the solution of tridiagonal systems. The theory for this new algorithm is outlined in a one-dimensional context for clarity. An extension to two and threedimensional cases is discussed. Results of Fourier analysis are discussed for both stability and dispersion/damping properties of the algorithm. Results are presented for a one-dimensional model problem, and the explicit FDTD algorithm is chosen as a convenient reference for comparison.

Construction and validation of a three-dimensional finite element model of degenerative scoliosis.

PubMed

Zheng, Jie; Yang, Yonghong; Lou, Shuliang; Zhang, Dongsheng; Liao, Shenghui

2015-12-24

With the aging of the population, degenerative scoliosis (DS) incidence rate is increasing. In recent years, increasing research on this topic has been carried out, yet biomechanical research on the subject is seldom seen and in vitro biomechanical model of DS nearly cannot be available. The objective of this study was to develop and validate a complete three-dimensional finite element model of DS in order to build the digital platform for further biomechanical study. A 55-year-old female DS patient (Suer Pan, ID number was P141986) was selected for this study. This study was performed in accordance with the ethical standards of Declaration of Helsinki and its amendments and was approved by the local ethics committee (117 hospital of PLA ethics committee). Spiral computed tomography (CT) scanning was conducted on the patient's lumbar spine from the T12 to S1. CT images were then imported into a finite element modeling system. A three-dimensional solid model was then formed from segmentation of the CT scan. The three-dimensional model of each vertebra was then meshed, and material properties were assigned to each element according to the pathological characteristics of DS. Loads and boundary conditions were then applied in such a manner as to simulate in vitro biomechanical experiments conducted on lumbar segments. The results of the model were then compared with experimental results in order to validate the model. An integral three-dimensional finite element model of DS was built successfully, consisting of 113,682 solid elements, 686 cable elements, 33,329 shell elements, 4968 target elements, 4968 contact elements, totaling 157,635 elements, and 197,374 nodes. The model accurately described the physical features of DS and was geometrically similar to the object of study. The results of analysis with the finite element model agreed closely with in vitro experiments, validating the accuracy of the model. The three-dimensional finite element model of DS built in this study is clear, reliable, and effective for further biomechanical simulation study of DS.

[Analysis of a three-dimensional finite element model of atlas and axis complex fracture].

PubMed

Tang, X M; Liu, C; Huang, K; Zhu, G T; Sun, H L; Dai, J; Tian, J W

2018-05-22

Objective: To explored the clinical application of the three-dimensional finite element model of atlantoaxial complex fracture. Methods: A three-dimensional finite element model of cervical spine (FEM/intact) was established by software of Abaqus6.12.On the basis of this model, a three-dimensional finite element model of four types of atlantoaxial complex fracture was established: C(1) fracture (Jefferson)+ C(2) fracture (type Ⅱfracture), Jefferson+ C(2) fracture(type Ⅲfracture), Jefferson+ C(2) fracture(Hangman), Jefferson+ stable C(2) fracture (FEM/fracture). The range of motion under flexion, extension, lateral bending and axial rotation were measured and compared with the model of cervical spine. Results: The three-dimensional finite element model of four types of atlantoaxial complex fracture had the same similarity and profile.The range of motion (ROM) of different segments had different changes.Compared with those in the normal model, the ROM of C(0/1) and C(1/2) in C(1) combined Ⅱ odontoid fracture model in flexion/extension, lateral bending and rotation increased by 57.45%, 29.34%, 48.09% and 95.49%, 88.52%, 36.71%, respectively.The ROM of C(0/1) and C(1/2) in C(1) combined Ⅲodontoid fracture model in flexion/extension, lateral bending and rotation increased by 47.01%, 27.30%, 45.31% and 90.38%, 27.30%, 30.0%.The ROM of C(0/1) and C(1/2) in C(1) combined Hangman fracture model in flexion/extension, lateral bending and rotation increased by 32.68%, 79.34%, 77.62% and 60.53%, 81.20%, 21.48%, respectively.The ROM of C(0/1) and C(1/2) in C(1) combined axis fracture model in flexion/extension, lateral bending and rotation increased by 15.00%, 29.30%, 8.47% and 37.87%, 75.57%, 8.30%, respectively. Conclusions: The three-dimensional finite element model can be used to simulate the biomechanics of atlantoaxial complex fracture.The ROM of atlantoaxial complex fracture is larger than nomal model, which indicates that surgical treatment should be performed.

Extending the Implicit Association Test (IAT): Assessing Consumer Attitudes Based on Multi-Dimensional Implicit Associations

PubMed Central

Gattol, Valentin; Sääksjärvi, Maria; Carbon, Claus-Christian

2011-01-01

Background The authors present a procedural extension of the popular Implicit Association Test (IAT; [1]) that allows for indirect measurement of attitudes on multiple dimensions (e.g., safe–unsafe; young–old; innovative–conventional, etc.) rather than on a single evaluative dimension only (e.g., good–bad). Methodology/Principal Findings In two within-subjects studies, attitudes toward three automobile brands were measured on six attribute dimensions. Emphasis was placed on evaluating the methodological appropriateness of the new procedure, providing strong evidence for its reliability, validity, and sensitivity. Conclusions/Significance This new procedure yields detailed information on the multifaceted nature of brand associations that can add up to a more abstract overall attitude. Just as the IAT, its multi-dimensional extension/application (dubbed md-IAT) is suited for reliably measuring attitudes consumers may not be consciously aware of, able to express, or willing to share with the researcher [2], [3]. PMID:21246037

Analytical and computational studies on the vacuum performance of a chevron ejector

NASA Astrophysics Data System (ADS)

Kong, F. S.; Jin, Y. Z.; Kim, H. D.

2016-11-01

The effects of chevrons on the performance of a supersonic vacuum ejector-diffuser system are investigated numerically and evaluated theoretically in this work. A three-dimensional geometrical domain is numerically solved using a fully implicit finite volume scheme based on the unsteady Reynolds stress model. A one-dimensional mathematical model provides a useful tool to reveal the steady flow physics inside the vacuum ejector-diffuser system. The effects of the chevron nozzle on the generation of recirculation regions and Reynolds stress behaviors are studied and compared with those of a conventional convergent nozzle. The present performance parameters obtained from the simulated results and the mathematical results are validated with existing experimental data and show good agreement. Primary results show that the duration of the transient period and the secondary chamber pressure at a dynamic equilibrium state depend strongly on the primary jet conditions, such as inlet pressure and primary nozzle shape. Complicated oscillatory flow, generated by the unsteady movement of recirculation, finally settles into a dynamic equilibrium state. As a vortex generator, the chevron demonstrated its strong entrainment capacity to accelerate the starting transient flows to a certain extent and reduce the dynamic equilibrium pressure of the secondary chamber significantly.

Real gas flow fields about three dimensional configurations

NASA Technical Reports Server (NTRS)

Balakrishnan, A.; Lombard, C. K.; Davy, W. C.

1983-01-01

Real gas, inviscid supersonic flow fields over a three-dimensional configuration are determined using a factored implicit algorithm. Air in chemical equilibrium is considered and its local thermodynamic properties are computed by an equilibrium composition method. Numerical solutions are presented for both real and ideal gases at three different Mach numbers and at two different altitudes. Selected results are illustrated by contour plots and are also tabulated for future reference. Results obtained compare well with existing tabulated numerical solutions and hence validate the solution technique.

[Stress analysis of the mandible by 3D FEA in normal human being under three loading conditions].

PubMed

Sun, Jian; Zhang, Fu-qiang; Wang, Dong-wei; Yu, Jia; Wang, Cheng-tao

2004-02-01

The condition and character of stress distribution in the mandibular in normal human being during centric, protrusive, laterotrusive occlusion were analysed. The three-dimensional finite element model of the mandibular was developed by helica CT scanning and CAD/CAM software, and three-dimensional finite element stress analysis was done by ANSYS software. Three-dimensional finite element model of the mandibular was generated. Under these three occlusal conditions, the stress of various regions in the mandible were distributed unequally, and the stress feature was different;while the stress of corresponding region in bilateral mandibular was in symmetric distribution. The stress value of condyle neck, the posterior surface of coronoid process and mandibular angle were high. The material properties of mandible were closely correlated to the value of stress. Stress distribution were similar according to the three different loading patterns, but had different effects on TMJ joint. The concentrated areas of stress were in the condyle neck, the posterior surface of coronoid process and mandibular angle.

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

Scalable Implementation of Finite Elements by NASA _ Implicit (ScIFEi)

NASA Technical Reports Server (NTRS)

Warner, James E.; Bomarito, Geoffrey F.; Heber, Gerd; Hochhalter, Jacob D.

2016-01-01

Scalable Implementation of Finite Elements by NASA (ScIFEN) is a parallel finite element analysis code written in C++. ScIFEN is designed to provide scalable solutions to computational mechanics problems. It supports a variety of finite element types, nonlinear material models, and boundary conditions. This report provides an overview of ScIFEi (\\Sci-Fi"), the implicit solid mechanics driver within ScIFEN. A description of ScIFEi's capabilities is provided, including an overview of the tools and features that accompany the software as well as a description of the input and output le formats. Results from several problems are included, demonstrating the efficiency and scalability of ScIFEi by comparing to finite element analysis using a commercial code.

Modeling the curing process of thick-section autoclave cured composites

NASA Technical Reports Server (NTRS)

Loos, A. C.; Dara, P. H.

1985-01-01

Temperature gradients are significant during cure of large area, thick-section composites. Such temperature gradients result in nonuniformly cured parts with high void contents, poor ply compaction, and variations in the fiber/resin distribution. A model was developed to determine the temperature distribution in thick-section autoclave cured composites. Using the model, long with temperature measurements obtained from the thick-section composites, the effects of various processing parameters on the thermal response of the composites were examined. A one-dimensional heat transfer model was constructed for the composite-tool assembly. The governing differential equations and associated boundary conditions describing one-dimensional unsteady heat-conduction in the composite, tool plate, and pressure plate are given. Solution of the thermal model was obtained using an implicit finite difference technique.

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

NASA Technical Reports Server (NTRS)

Slack, David C.; Walters, Robert W.; Lohner, R.

1990-01-01

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Effect of absorption on nonlinear propagation of short ultrasound pulses generated by rectangular transducers

NASA Astrophysics Data System (ADS)

Khokhlova, Vera A.; Ponomaryov, Anatoly E.; Averkiou, Michalakis A.; Crum, Lawrence A.

2002-11-01

A numerical solution of the KZK-type parabolic nonlinear evolution equation is presented for finite-amplitude sound beams radiated by rectangular sources. The initial acoustic waveform is a short tone burst, similar to those used in diagnostic ultrasound. The generation of higher harmonic components and their spatial structure are investigated for media similar to tissue with various frequency dependent absorption properties. Nonlinear propagation in a thermoviscous fluid with a quadratic frequency law of absorption is compared to that in tissue with a nearly linear frequency law of absorption. The algorithm is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906-917 (1995)] to model circular sources. The algorithm is generalized for two-dimensional sources without axial symmetry. The diffraction integral is adapted in the time-domain for two dimensions with the implicit backward finite difference (IBFD) scheme in the nearfield and with the alternate direction implicit (ADI) method at longer distances. Arbitrary frequency dependence of absorption is included in this model and solved in the frequency-domain using the FFT technique. The results of simulation may be used to better understand the nonlinear beam structure for tissue harmonic imaging in modern medical diagnostic scanners. [Work supported by CRDF and RFBR.

Unsteady streamflow simulation using a linear implicit finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

A computer program for simulating one-dimensional subcritical, gradually varied, unsteady flow in a stream has been developed and documented. Given upstream and downstream boundary conditions and channel geometry data, roughness coefficients, stage, and discharge can be calculated anywhere within the reach as a function of time. The program uses a linear implicit finite-difference technique that discritizes the partial differential equations. Then it arranges the coefficients of the continuity and momentum equations into a pentadiagonal matrix for solution. Because it is a reasonable compromise between computational accuracy, speed and ease of use,the technique is one of the most commonly used. The upstream boundary condition is a depth hydrograph. However, options also allow the boundary condition to be discharge or water-surface elevation. The downstream boundary condition is a depth which may be constant, self-setting, or unsteady. The reach may be divided into uneven increments and the cross sections may be nonprismatic and may vary from one to the other. Tributary and lateral inflow may enter the reach. The digital model will simulate such common problems as (1) flood waves, (2) releases from dams, and (3) channels where storage is a consideration. It may also supply the needed flow information for mass-transport simulation. (Woodard-USGS)

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

Application of laser ranging and VLBI data to a study of plate tectonic driving forces. [finite element method

NASA Technical Reports Server (NTRS)

Solomon, S. C.

1980-01-01

The measurability of changes in plate driving or resistive forces associated with plate boundary earthquakes by laser rangefinding or VLBI is considered with emphasis on those aspects of plate forces that can be characterized by such measurements. Topics covered include: (1) analytic solutions for two dimensional stress diffusion in a plate following earthquake faulting on a finite fault; (2) two dimensional finite-element solutions for the global state of stress at the Earth's surface for possible plate driving forces; and (3) finite-element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting.

Comparison of RCS prediction techniques, computations and measurements

NASA Astrophysics Data System (ADS)

Brand, M. G. E.; Vanewijk, L. J.; Klinker, F.; Schippers, H.

1992-07-01

Three calculation methods to predict radar cross sections (RCS) of three dimensional objects are evaluated by computing the radar cross sections of a generic wing inlet configuration. The following methods are applied: a three dimensional high frequency method, a three dimensional boundary element method, and a two dimensional finite difference time domain method. The results of the computations are compared with the data of measurements.

Finite state modeling of aeroelastic systems

NASA Technical Reports Server (NTRS)

Vepa, R.

1977-01-01

A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

Simulation of wave propagation in three-dimensional random media

NASA Technical Reports Server (NTRS)

Coles, William A.; Filice, J. P.; Frehlich, R. G.; Yadlowsky, M.

1993-01-01

Quantitative error analysis for simulation of wave propagation in three dimensional random media assuming narrow angular scattering are presented for the plane wave and spherical wave geometry. This includes the errors resulting from finite grid size, finite simulation dimensions, and the separation of the two-dimensional screens along the propagation direction. Simple error scalings are determined for power-law spectra of the random refractive index of the media. The effects of a finite inner scale are also considered. The spatial spectra of the intensity errors are calculated and compared to the spatial spectra of intensity. The numerical requirements for a simulation of given accuracy are determined for realizations of the field. The numerical requirements for accurate estimation of higher moments of the field are less stringent.

SUTRA (Saturated-Unsaturated Transport). A Finite-Element Simulation Model for Saturated-Unsaturated, Fluid-Density-Dependent Ground-Water Flow with Energy Transport or Chemically-Reactive Single-Species Solute Transport.

DTIC Science & Technology

1984-12-30

as three dimensional, when the assumption is made that all SUTRA parameters and coefficients have a constant value in the third space direction. A...finite element. The type of element employed by SUTRA for two-dimensional simulation is a quadrilateral which has a finite thickness in the third ... space dimension. This type of a quad- rilateral element and a typical two-dimensional mesh is shown in Figure 3.1. - All twelve edges of the two

Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. II - Shell and three-dimensional simulations

NASA Technical Reports Server (NTRS)

Kennedy, Ronald; Padovan, Joe

1987-01-01

In a three-part series of papers, a generalized finite element solution strategy is developed to handle traveling load problems in rolling, moving and rotating structure. The main thrust of this section consists of the development of three-dimensional and shell type moving elements. In conjunction with this work, a compatible three-dimensional contact strategy is also developed. Based on these modeling capabilities, extensive analytical and experimental benchmarking is presented. Such testing includes traveling loads in rotating structure as well as low- and high-speed rolling contact involving standing wave-type response behavior. These point to the excellent modeling capabilities of moving element strategies.

MOFAT: A TWO-DIMENSIONAL FINITE ELEMENT PROGRAM FOR MULTIPHASE FLOW AND MULTICOMPONENT TRANSPORT - PROGRAM DOCUMENTATION AND USER'S GUIDE

EPA Science Inventory

This manual describes a two-dimensional, finite element model for coupled multiphase flow and multicomponent transport in planar or radially symmetric vertical sections. low and transport of three fluid phases, including water, nonaqueous phase liquid (NAPL), and gas are consider...

Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Bigelow, C. A.; Shivakumar, K. N.

1993-01-01

Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonic and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor alpha(sub g) was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of alpha(sub g) were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness.

a Speculative Study on Negative-Dimensional Potential and Wave Problems by Implicit Calculus Modeling Approach

NASA Astrophysics Data System (ADS)

Chen, Wen; Wang, Fajie

Based on the implicit calculus equation modeling approach, this paper proposes a speculative concept of the potential and wave operators on negative dimensionality. Unlike the standard partial differential equation (PDE) modeling, the implicit calculus modeling approach does not require the explicit expression of the PDE governing equation. Instead the fundamental solution of physical problem is used to implicitly define the differential operator and to implement simulation in conjunction with the appropriate boundary conditions. In this study, we conjecture an extension of the fundamental solution of the standard Laplace and Helmholtz equations to negative dimensionality. And then by using the singular boundary method, a recent boundary discretization technique, we investigate the potential and wave problems using the fundamental solution on negative dimensionality. Numerical experiments reveal that the physics behaviors on negative dimensionality may differ on positive dimensionality. This speculative study might open an unexplored territory in research.

Implicit finite difference methods on composite grids

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne

1987-01-01

Techniques for eliminating time lags in the implicit finite-difference solution of partial differential equations are investigated analytically, with a focus on transient fluid dynamics problems on overlapping multicomponent grids. The fundamental principles of the approach are explained, and the method is shown to be applicable to both rectangular and curvilinear grids. Numerical results for sample problems are compared with exact solutions in graphs, and good agreement is demonstrated.

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm

DOE PAGES

Chen, G.; Chacón, L.

2015-08-11

For decades, the Vlasov–Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. We explore a fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space–time-centered, employing particle sub-cycling and orbit-averaging. This algorithm conserves total energy, local charge,more » canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. Finally, we demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D–3V.« less

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

NASA Technical Reports Server (NTRS)

Harris, J. E.; Blanchard, D. K.

1982-01-01

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van der Holst, B.; Toth, G.; Sokolov, I. V.

We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1)more » an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.« less

A computationally fast, reduced model for simulating landslide dynamics and tsunamis generated by landslides in natural terrains

NASA Astrophysics Data System (ADS)

Mohammed, F.

2016-12-01

Landslide hazards such as fast-moving debris flows, slow-moving landslides, and other mass flows cause numerous fatalities, injuries, and damage. Landslide occurrences in fjords, bays, and lakes can additionally generate tsunamis with locally extremely high wave heights and runups. Two-dimensional depth-averaged models can successfully simulate the entire lifecycle of the three-dimensional landslide dynamics and tsunami propagation efficiently and accurately with the appropriate assumptions. Landslide rheology is defined using viscous fluids, visco-plastic fluids, and granular material to account for the possible landslide source materials. Saturated and unsaturated rheologies are further included to simulate debris flow, debris avalanches, mudflows, and rockslides respectively. The models are obtained by reducing the fully three-dimensional Navier-Stokes equations with the internal rheological definition of the landslide material, the water body, and appropriate scaling assumptions to obtain the depth-averaged two-dimensional models. The landslide and tsunami models are coupled to include the interaction between the landslide and the water body for tsunami generation. The reduced models are solved numerically with a fast semi-implicit finite-volume, shock-capturing based algorithm. The well-balanced, positivity preserving algorithm accurately accounts for wet-dry interface transition for the landslide runout, landslide-water body interface, and the tsunami wave flooding on land. The models are implemented as a General-Purpose computing on Graphics Processing Unit-based (GPGPU) suite of models, either coupled or run independently within the suite. The GPGPU implementation provides up to 1000 times speedup over a CPU-based serial computation. This enables simulations of multiple scenarios of hazard realizations that provides a basis for a probabilistic hazard assessment. The models have been successfully validated against experiments, past studies, and field data for landslides and tsunamis.

Three-dimensional simulation of vortex breakdown

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Salas, M. D.

1990-01-01

The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state.

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

On the performance of explicit and implicit algorithms for transient thermal analysis

NASA Astrophysics Data System (ADS)

Adelman, H. M.; Haftka, R. T.

1980-09-01

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit and implicit algorithms are discussed. A promising set of implicit algorithms, known as the GEAR package is described. Four test problems, used for evaluating and comparing various algorithms, have been selected and finite element models of the configurations are discribed. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system and a model of the space shuttle orbiter wing. Calculations were carried out using the SPAR finite element program, the MITAS lumped parameter program and a special purpose finite element program incorporating the GEAR algorithms. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff. Careful attention to modeling detail such as avoiding thin or short high-conducting elements can sometimes reduce the stiffness to the extent that explicit methods become advantageous.

Computation of the transonic perturbation flow fields around two- and three-dimensional oscillating wings

NASA Technical Reports Server (NTRS)

Weatherill, W. H.; Ehlers, F. E.; Sebastian, J. D.

1975-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about an harmonically oscillating wing are presented along with a discussion of the development of a pilot program for three-dimensional flow. In addition, some two- and three-dimensional examples are presented.

An alternative view of continuous forest inventories

Treesearch

Francis A. Roesch

2008-01-01

A generalized three-dimensional concept of continuous forest inventories applicable to all common forest sample designs is presented and discussed. The concept recognizes the forest through time as a three-dimensional population, two dimensions in land area and the third in time. The sample is selected from a finite three-dimensional partitioning of the population. The...

Fourier-Legendre spectral methods for incompressible channel flow

NASA Technical Reports Server (NTRS)

Zang, T. A.; Hussaini, M. Y.

1984-01-01

An iterative collocation technique is described for modeling implicit viscosity in three-dimensional incompressible wall bounded shear flow. The viscosity can vary temporally and in the vertical direction. Channel flow is modeled with a Fourier-Legendre approximation and the mean streamwise advection is treated implicitly. Explicit terms are handled with an Adams-Bashforth method to increase the allowable time-step for calculation of the implicit terms. The algorithm is applied to low amplitude unstable waves in a plane Poiseuille flow at an Re of 7500. Comparisons are made between results using the Legendre method and with Chebyshev polynomials. Comparable accuracy is obtained for the perturbation kinetic energy predicted using both discretizations.

An implicit higher-order spatially accurate scheme for solving time dependent flows on unstructured meshes

NASA Astrophysics Data System (ADS)

Tomaro, Robert F.

1998-07-01

The present research is aimed at developing a higher-order, spatially accurate scheme for both steady and unsteady flow simulations using unstructured meshes. The resulting scheme must work on a variety of general problems to ensure the creation of a flexible, reliable and accurate aerodynamic analysis tool. To calculate the flow around complex configurations, unstructured grids and the associated flow solvers have been developed. Efficient simulations require the minimum use of computer memory and computational times. Unstructured flow solvers typically require more computer memory than a structured flow solver due to the indirect addressing of the cells. The approach taken in the present research was to modify an existing three-dimensional unstructured flow solver to first decrease the computational time required for a solution and then to increase the spatial accuracy. The terms required to simulate flow involving non-stationary grids were also implemented. First, an implicit solution algorithm was implemented to replace the existing explicit procedure. Several test cases, including internal and external, inviscid and viscous, two-dimensional, three-dimensional and axi-symmetric problems, were simulated for comparison between the explicit and implicit solution procedures. The increased efficiency and robustness of modified code due to the implicit algorithm was demonstrated. Two unsteady test cases, a plunging airfoil and a wing undergoing bending and torsion, were simulated using the implicit algorithm modified to include the terms required for a moving and/or deforming grid. Secondly, a higher than second-order spatially accurate scheme was developed and implemented into the baseline code. Third- and fourth-order spatially accurate schemes were implemented and tested. The original dissipation was modified to include higher-order terms and modified near shock waves to limit pre- and post-shock oscillations. The unsteady cases were repeated using the higher-order spatially accurate code. The new solutions were compared with those obtained using the second-order spatially accurate scheme. Finally, the increased efficiency of using an implicit solution algorithm in a production Computational Fluid Dynamics flow solver was demonstrated for steady and unsteady flows. A third- and fourth-order spatially accurate scheme has been implemented creating a basis for a state-of-the-art aerodynamic analysis tool.

Evaluation of the parameters affecting bone temperature during drilling using a three-dimensional dynamic elastoplastic finite element model.

PubMed

Chen, Yung-Chuan; Tu, Yuan-Kun; Zhuang, Jun-Yan; Tsai, Yi-Jung; Yen, Cheng-Yo; Hsiao, Chih-Kun

2017-11-01

A three-dimensional dynamic elastoplastic finite element model was constructed and experimentally validated and was used to investigate the parameters which influence bone temperature during drilling, including the drill speed, feeding force, drill bit diameter, and bone density. Results showed the proposed three-dimensional dynamic elastoplastic finite element model can effectively simulate the temperature elevation during bone drilling. The bone temperature rise decreased with an increase in feeding force and drill speed, however, increased with the diameter of drill bit or bone density. The temperature distribution is significantly affected by the drilling duration; a lower drilling speed reduced the exposure duration, decreases the region of the thermally affected zone. The constructed model could be applied for analyzing the influence parameters during bone drilling to reduce the risk of thermal necrosis. It may provide important information for the design of drill bits and surgical drilling powers.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

[Analysis of the movement of long axis and the distribution of principal stress in abutment tooth retained by conical telescope].

PubMed

Lin, Ying-he; Man, Yi; Qu, Yi-li; Guan, Dong-hua; Lu, Xuan; Wei, Na

2006-01-01

To study the movement of long axis and the distribution of principal stress in the abutment teeth in removable partial denture which is retained by use of conical telescope. An ideal three dimensional finite element model was constructed by using SCT image reconstruction technique, self-programming and ANSYS software. The static loads were applied. The displacement of the long axis and the distribution of the principal stress in the abutment teeth was analyzed. There is no statistic difference of displacenat and stress distribution among different three-dimensional finite element models. Generally, the abutment teeth move along the long axis itself. Similar stress distribution was observed in each three-dimensional finite element model. The maximal principal compressive stress was observed at the distal cervix of the second premolar. The abutment teeth can be well protected by use of conical telescope.

Three dimensional finite element methods: Their role in the design of DC accelerator systems

NASA Astrophysics Data System (ADS)

Podaru, Nicolae C.; Gottdang, A.; Mous, D. J. W.

2013-04-01

High Voltage Engineering has designed, built and tested a 2 MV dual irradiation system that will be applied for radiation damage studies and ion beam material modification. The system consists of two independent accelerators which support simultaneous proton and electron irradiation (energy range 100 keV - 2 MeV) of target sizes of up to 300 × 300 mm2. Three dimensional finite element methods were used in the design of various parts of the system. The electrostatic solver was used to quantify essential parameters of the solid-state power supply generating the DC high voltage. The magnetostatic solver and ray tracing were used to optimize the electron/ion beam transport. Close agreement between design and measurements of the accelerator characteristics as well as beam performance indicate the usefulness of three dimensional finite element methods during accelerator system design.

Solidification of a binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.

1982-01-01

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

On the effects of grid ill-conditioning in three dimensional finite element vector potential magnetostatic field computations

NASA Technical Reports Server (NTRS)

Wang, R.; Demerdash, N. A.

1990-01-01

The effects of finite element grid geometries and associated ill-conditioning were studied in single medium and multi-media (air-iron) three dimensional magnetostatic field computation problems. The sensitivities of these 3D field computations to finite element grid geometries were investigated. It was found that in single medium applications the unconstrained magnetic vector potential curl-curl formulation in conjunction with first order finite elements produce global results which are almost totally insensitive to grid geometries. However, it was found that in multi-media (air-iron) applications first order finite element results are sensitive to grid geometries and consequent elemental shape ill-conditioning. These sensitivities were almost totally eliminated by means of the use of second order finite elements in the field computation algorithms. Practical examples are given in this paper to demonstrate these aspects mentioned above.

Unsteady Performance of Finite-Span Pitching Propulsors in Mixtures of Side-by-Side and In-Line Arrangements

NASA Astrophysics Data System (ADS)

Kurt, Melike; Moored, Keith

2016-11-01

Birds, insects, and fish propel themselves by flapping their wings or oscillating their fins in unsteady motions. Many of these animals fly or swim in groups or collectives, typically described as flocks, swarms and schools. The three-dimensional steady flow interactions and the two dimensional unsteady flow interactions that occur in collectives are well characterized. However, the interactions that occur among three-dimensional unsteady propulsors remain relatively unexplored. The aim of the current study is to measure the forces acting on and the energetics of two finite-span pitching wings. The wings are arranged in mixtures of canonical in-line and side-by-side configurations while the phase delay between the pitching wings is varied. The thrust force, fluid-mediated interaction force between the wings and the propulsive efficiency are quantified. The three-dimensional interaction mechanisms are compared and contrasted with previously examined two-dimensional mechanisms. Stereoscopic particle image velocimetry is employed to characterize the three-dimensional flow structures along the span of the pitching wings.

Implicitly causality enforced solution of multidimensional transient photon transport equation.

PubMed

Handapangoda, Chintha C; Premaratne, Malin

2009-12-21

A novel method for solving the multidimensional transient photon transport equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. Owing to the intrinsic causal nature of Laguerre functions, our technique automatically always preserve the causality constrains of the transient signal. This expansion of the radiance using a Laguerre basis transforms the transient photon transport equation to the steady state version. The resulting equations are solved using the discrete ordinates method, using a finite volume approach. Therefore, our method enables one to handle general anisotropic, inhomogeneous media using a single formulation but with an added degree of flexibility owing to the ability to invoke higher-order approximations of discrete ordinate quadrature sets. Therefore, compared with existing strategies, this method offers the advantage of representing the intensity with a high accuracy thus minimizing numerical dispersion and false propagation errors. The application of the method to one, two and three dimensional geometries is provided.

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.

1984-01-01

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

A Spectral Element Discretisation on Unstructured Triangle / Tetrahedral Meshes for Elastodynamics

NASA Astrophysics Data System (ADS)

May, Dave A.; Gabriel, Alice-A.

2017-04-01

The spectral element method (SEM) defined over quadrilateral and hexahedral element geometries has proven to be a fast, accurate and scalable approach to study wave propagation phenomena. In the context of regional scale seismology and or simulations incorporating finite earthquake sources, the geometric restrictions associated with hexahedral elements can limit the applicability of the classical quad./hex. SEM. Here we describe a continuous Galerkin spectral element discretisation defined over unstructured meshes composed of triangles (2D), or tetrahedra (3D). The method uses a stable, nodal basis constructed from PKD polynomials and thus retains the spectral accuracy and low dispersive properties of the classical SEM, in addition to the geometric versatility provided by unstructured simplex meshes. For the particular basis and quadrature rule we have adopted, the discretisation results in a mass matrix which is not diagonal, thereby mandating linear solvers be utilised. To that end, we have developed efficient solvers and preconditioners which are robust with respect to the polynomial order (p), and possess high arithmetic intensity. Furthermore, we also consider using implicit time integrators, together with a p-multigrid preconditioner to circumvent the CFL condition. Implicit time integrators become particularly relevant when considering solving problems on poor quality meshes, or meshes containing elements with a widely varying range of length scales - both of which frequently arise when meshing non-trivial geometries. We demonstrate the applicability of the new method by examining a number of two- and three-dimensional wave propagation scenarios. These scenarios serve to characterise the accuracy and cost of the new method. Lastly, we will assess the potential benefits of using implicit time integrators for regional scale wave propagation simulations.

Three-dimensional analysis of tubular permanent magnet machines

NASA Astrophysics Data System (ADS)

Chai, J.; Wang, J.; Howe, D.

2006-04-01

This paper presents results from a three-dimensional finite element analysis of a tubular permanent magnet machine, and quantifies the influence of the laminated modules from which the stator core is assembled on the flux linkage and thrust force capability as well as on the self- and mutual inductances. The three-dimensional finite element (FE) model accounts for the nonlinear, anisotropic magnetization characteristic of the laminated stator structure, and for the voids which exist between the laminated modules. Predicted results are compared with those deduced from an axisymmetric FE model. It is shown that the emf and thrust force deduced from the three-dimensional model are significantly lower than those which are predicted from an axisymmetric field analysis, primarily as a consequence of the teeth and yoke being more highly saturated due to the presence of the voids in the laminated stator core.

Optimal implicit 2-D finite differences to model wave propagation in poroelastic media

NASA Astrophysics Data System (ADS)

Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.

2016-08-01

Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10 kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P and slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High-order explicit FD can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here, we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.

Adaptation of multidimensional group particle tracking and particle wall-boundary condition model to the FDNS code

NASA Technical Reports Server (NTRS)

Chen, Y. S.; Farmer, R. C.

1992-01-01

A particulate two-phase flow CFD model was developed based on the FDNS code which is a pressure based predictor plus multi-corrector Navier-Stokes flow solver. Turbulence models with compressibility correction and the wall function models were employed as submodels. A finite-rate chemistry model was used for reacting flow simulation. For particulate two-phase flow simulations, a Eulerian-Lagrangian solution method using an efficient implicit particle trajectory integration scheme was developed in this study. Effects of particle-gas reaction and particle size change to agglomeration or fragmentation were not considered in this investigation. At the onset of the present study, a two-dimensional version of FDNS which had been modified to treat Lagrangian tracking of particles (FDNS-2DEL) had already been written and was operational. The FDNS-2DEL code was too slow for practical use, mainly because it had not been written in a form amenable to vectorization on the Cray, nor was the full three-dimensional form of FDNS utilized. The specific objective of this study was to reorder to calculations into long single arrays for automatic vectorization on the Cray and to implement the full three-dimensional version of FDNS to produce the FDNS-3DEL code. Since the FDNS-2DEL code was slow, a very limited number of test cases had been run with it. This study was also intended to increase the number of cases simulated to verify and improve, as necessary, the particle tracking methodology coded in FDNS.

From Laser Scanning to Finite Element Analysis of Complex Buildings by Using a Semi-Automatic Procedure.

PubMed

Castellazzi, Giovanni; D'Altri, Antonio Maria; Bitelli, Gabriele; Selvaggi, Ilenia; Lambertini, Alessandro

2015-07-28

In this paper, a new semi-automatic procedure to transform three-dimensional point clouds of complex objects to three-dimensional finite element models is presented and validated. The procedure conceives of the point cloud as a stacking of point sections. The complexity of the clouds is arbitrary, since the procedure is designed for terrestrial laser scanner surveys applied to buildings with irregular geometry, such as historical buildings. The procedure aims at solving the problems connected to the generation of finite element models of these complex structures by constructing a fine discretized geometry with a reduced amount of time and ready to be used with structural analysis. If the starting clouds represent the inner and outer surfaces of the structure, the resulting finite element model will accurately capture the whole three-dimensional structure, producing a complex solid made by voxel elements. A comparison analysis with a CAD-based model is carried out on a historical building damaged by a seismic event. The results indicate that the proposed procedure is effective and obtains comparable models in a shorter time, with an increased level of automation.

[Study on the effect of vertebrae semi-dislocation on the stress distribution in facet joint and interuertebral disc of patients with cervical syndrome based on the three dimensional finite element model].

PubMed

Zhang, Ming-cai; Lü, Si-zhe; Cheng, Ying-wu; Gu, Li-xu; Zhan, Hong-sheng; Shi, Yin-yu; Wang, Xiang; Huang, Shi-rong

2011-02-01

To study the effect of vertebrae semi-dislocation on the stress distribution in facet joint and interuertebral disc of patients with cervical syndrome using three dimensional finite element model. A patient with cervical spondylosis was randomly chosen, who was male, 28 years old, and diagnosed as cervical vertebra semidislocation by dynamic and static palpation and X-ray, and scanned from C(1) to C(7) by 0.75 mm slice thickness of CT. Based on the CT data, the software was used to construct the three dimensional finite element model of cervical vertebra semidislocation (C(4)-C(6)). Based on the model,virtual manipulation was used to correct the vertebra semidislocation by the software, and the stress distribution was analyzed. The result of finite element analysis showed that the stress distribution of C(5-6) facet joint and intervertebral disc changed after virtual manipulation. The vertebra semidislocation leads to the abnormal stress distribution of facet joint and intervertebral disc.

Time-Accurate Numerical Simulations of Synthetic Jet Quiescent Air

NASA Technical Reports Server (NTRS)

Rupesh, K-A. B.; Ravi, B. R.; Mittal, R.; Raju, R.; Gallas, Q.; Cattafesta, L.

2007-01-01

The unsteady evolution of three-dimensional synthetic jet into quiescent air is studied by time-accurate numerical simulations using a second-order accurate mixed explicit-implicit fractional step scheme on Cartesian grids. Both two-dimensional and three-dimensional calculations of synthetic jet are carried out at a Reynolds number (based on average velocity during the discharge phase of the cycle V(sub j), and jet width d) of 750 and Stokes number of 17.02. The results obtained are assessed against PIV and hotwire measurements provided for the NASA LaRC workshop on CFD validation of synthetic jets.

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

NASA Technical Reports Server (NTRS)

Woodard, Paul R.; Yang, Henry T. Y.; Batina, John T.

1992-01-01

Quality assessment procedures are described for two-dimensional and three-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate the accuracy of an implicit upwind Euler solution algorithm.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.

1990-01-01

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

A computer program for two-dimensional and axisymmetric nonreacting perfect gas and equilibrium chemically reacting laminar, transitional and-or turbulent boundary layer flows

NASA Technical Reports Server (NTRS)

Miner, E. W.; Anderson, E. C.; Lewis, C. H.

1971-01-01

A computer program is described in detail for laminar, transitional, and/or turbulent boundary-layer flows of non-reacting (perfect gas) and reacting gas mixtures in chemical equilibrium. An implicit finite difference scheme was developed for both two dimensional and axisymmetric flows over bodies, and in rocket nozzles and hypervelocity wind tunnel nozzles. The program, program subroutines, variables, and input and output data are described. Also included is the output from a sample calculation of fully developed turbulent, perfect gas flow over a flat plate. Input data coding forms and a FORTRAN source listing of the program are included. A method is discussed for obtaining thermodynamic and transport property data which are required to perform boundary-layer calculations for reacting gases in chemical equilibrium.

Rigorous joining of advanced reduced-dimensional beam models to three-dimensional finite element models

NASA Astrophysics Data System (ADS)

Song, Huimin

In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and the generalized Timoshenko beam are discussed in this chapter. VABS is also used to obtain the beam constitutive properties and warping functions for stress recovery. Several 3D-beam joint examples are presented to show the convergence and accuracy of the analysis. Accuracy is accessed by comparing the joint results with the full 3D analysis. The fourth chapter provides conclusions from present studies and recommendations for future work.

CELFE/NASTRAN Code for the Analysis of Structures Subjected to High Velocity Impact

NASA Technical Reports Server (NTRS)

Chamis, C. C.

1978-01-01

CELFE (Coupled Eulerian Lagrangian Finite Element)/NASTRAN Code three-dimensional finite element code has the capability for analyzing of structures subjected to high velocity impact. The local response is predicted by CELFE and, for large problems, the far-field impact response is predicted by NASTRAN. The coupling of the CELFE code with NASTRAN (CELFE/NASTRAN code) and the application of the code to selected three-dimensional high velocity impact problems are described.

[Three-dimensional finite element analysis on cell culture membrane under mechanical load].

PubMed

Guo, Xin; Fan, Yubo; Song, Jinlin; Chen, Junkai

2002-01-01

A three-dimensional finite element model of the cell culture membrane was developed in the culture device under tension state made by us. The magnitude of tension and the displacement distribution in the membrane made of silicon rubber under different hydrostatic load were obtained by use of FEM analysis. A comparative study was made between the numerical and the experimental results. These results can serve as guides to the related cellular mechanical research.

Three-Dimensional Temperature Field Simulation for the Rotor of an Asynchronous Motor

ERIC Educational Resources Information Center

Wang, Yanwu; Fan, Chunli; Yang, Li; Sun, Fengrui

2010-01-01

A three-dimensional heat transfer model is built according to the rotor structure of an asynchronous motor, and three-dimensional temperature fields of the rotor under different working conditions, such as the unloaded, rated loaded and that with broken rotor bars, are studied based on the finite element numerical method and experiments. The…

Study on prestressed concrete reactor vessel structures. II-5: Crack analysis by three dimensional finite elements method of 1/20 multicavity type PCRV subjected to internal pressure

NASA Technical Reports Server (NTRS)

1978-01-01

A three-dimensional finite elements analysis is reported of the nonlinear behavior of PCRV subjected to internal pressure by comparing calculated results with test results. As the first stage, an analysis considering the nonlinearity of cracking in concrete was attempted. As a result, it is found possible to make an analysis up to three times the design pressure (50 kg/sqcm), and calculated results agree well with test results.

Analyse et caracterisation d'interactions fluide-structure instationnaires en grands deplacements

NASA Astrophysics Data System (ADS)

Cori, Jean-Francois

Flapping wings for flying and oscillating fins for swimming stand out as the most complex yet efficient propulsion methods found in nature. Understanding the phenomena involved is a great challenge generating significant interests, especially in the growing field of Micro Air Vehicles. The thrust and lift are induced by oscillating foils thanks to a complex phenomenon of unsteady fluid-structure interaction (FSI). The aim of the dissertation is to develop an efficient CFD framework for simulating the FSI process involved in the propulsion or the power extraction of an oscillating flexible airfoil in a viscous incompressible flow. The numerical method relies on direct implicit monolithic formulation using high-order implicit time integrators. We use an Arbitrary Lagrangian Eulerian (ALE) formulation of the equations designed to satisfy the Geometric Conservation Law (GCL) and to guarantee that the high order temporal accuracy of the time integrators observed on fixed meshes is preserved on ALE deforming meshes. Hyperelastic structural Saint-Venant Kirchhoff model, viscous incompressible Navier-Stokes equations for the flow, Newton's law for the point mass and equilibrium equations at the interface form one large monolithic system. The fully implicit FSI approach uses coincidents nodes on the fluid-structure interface, so that loads, velocities and displacements are evaluated at the same location and at the same time. The problem is solved in an implicit manner using a Newton-Raphson pseudo-solid finite element approach. High-order implicit Runge-Kutta time integrators are implemented (up to 5th order) to improve the accuracy and reduce the computational cost. In this context of stiff interaction problems, the highly stable fully implicit one-step approach is an original alternative to traditional multistep or explicit one-step finite element approaches. The methodology has been verified with three different test-cases. Thorough time-step refinement studies for a rigid oscillating airfoil on deforming meshes, for flow induced vibrations of a flexible strip and for a self-propulsed flapping airfoil indicate that the stability of the proposed approach is always observed even with large time steps, spurious oscillations on the structure are avoided without any damping and the high order accuracy of the IRK schemes is maintained. We have applied our powerful FSI framework on three interesting applications, with a detailed dimensional analysis to obtain their characteristic parameters. Firstly, we have studied the vibrational characteristics of a well-documented fluid-structure interaction case : a flexible strip fixed behind a rigid square cylinder. Our results compare favorably with previous works. The accuracy of the IRK time integrators (even for the pressure field of incompressible flow), their unconditional stability and their non-dissipative nature produced results revealing new, never previously reported, higher frequency structural forces weakly coupled with the fluid. Secondly, we have explored the propulsive and power extraction characteristics of rigid and flexible flapping airfoils. For the power extraction, we found an excellent agreement with literature results. A parametric study indicates the optimal motion parameters to get high propulsive efficiencies. An optimal flexibility seems to improve power extraction efficiency. Finally, a survey on flapping propulsion has given initial results for a self-propulsed airfoil and has opened a new way of studying propulsive efficiency. (Abstract shortened by UMI.)

AutoCAD-To-GIFTS Translator Program

NASA Technical Reports Server (NTRS)

Jones, Andrew

1989-01-01

AutoCAD-to-GIFTS translator program, ACTOG, developed to facilitate quick generation of small finite-element models using CASA/GIFTS finite-element modeling program. Reads geometric data of drawing from Data Exchange File (DXF) used in AutoCAD and other PC-based drafting programs. Geometric entities recognized by ACTOG include points, lines, arcs, solids, three-dimensional lines, and three-dimensional faces. From this information, ACTOG creates GIFTS SRC file, which then reads into GIFTS preprocessor BULKM or modified and reads into EDITM to create finite-element model. SRC file used as is or edited for any number of uses. Written in Microsoft Quick-Basic (Version 2.0).

3DHYDROGEOCHEM: A 3-DIMENSIONAL MODEL OF DENSITY-DEPENDENT SUBSURFACE FLOW AND THERMAL MULTISPECIES-MULTICOMPONENT HYDROGEOCHEMICAL TRANSPORT

EPA Science Inventory

This report presents a three-dimensional finite-element numerical model designed to simulate chemical transport in subsurface systems with temperature effect taken into account. The three-dimensional model is developed to provide (1) a tool of application, with which one is able...

Aerodynamics of Engine-Airframe Interaction

NASA Technical Reports Server (NTRS)

Caughey, D. A.

1986-01-01

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

Numerical solutions of 2-D multi-stage rotor/stator unsteady flow interactions

NASA Astrophysics Data System (ADS)

Yang, R.-J.; Lin, S.-J.

1991-01-01

The Rai method of single-stage rotor/stator flow interaction is extended to handle multistage configurations. In this study, a two-dimensional Navier-Stokes multi-zone approach was used to investigate unsteady flow interactions within two multistage axial turbines. The governing equations are solved by an iterative, factored, implicit finite-difference, upwind algorithm. Numerical accuracy is checked by investigating the effect of time step size, the effect of subiteration in the Newton-Raphson technique, and the effect of full viscous versus thin-layer approximation. Computer results compared well with experimental data. Unsteady flow interactions, wake cutting, and the associated evolution of vortical entities are discussed.

Numerical solution of the hypersonic viscous-shock-layer equations for laminar, transitional, and turbulent flows of a perfect gas over blunt axially symmetric bodies

NASA Technical Reports Server (NTRS)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous shock layer equations applicable to hypersonic laminar, transitional, and turbulent flows of a perfect gas over two-dimensional plane or axially symmetric blunt bodies are presented. The equations are solved by means of an implicit finite difference scheme, and the results are compared with a turbulent boundary layer analysis. The agreement between the two solution procedures is satisfactory for the region of flow where streamline swallowing effects are negligible. For the downstream regions, where streamline swallowing effects are present, the expected differences in the two solution procedures are evident.

Convergence Acceleration for Multistage Time-Stepping Schemes

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, Eli L.; Rossow, C-C; Vasta, V. N.

2006-01-01

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

Algorithm development for Maxwell's equations for computational electromagnetism

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.

1990-01-01

A new algorithm has been developed for solving Maxwell's equations for the electromagnetic field. It solves the equations in the time domain with central, finite differences. The time advancement is performed implicitly, using an alternating direction implicit procedure. The space discretization is performed with finite volumes, using curvilinear coordinates with electromagnetic components along those directions. Sample calculations are presented of scattering from a metal pin, a square and a circle to demonstrate the capabilities of the new algorithm.

Three dimensional finite-element analysis of finite-thickness fracture specimens

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1977-01-01

The stress-intensity factors for most of the commonly used fracture specimens (center-crack tension, single and double edge-crack tension, and compact), those that have a through-the-thickness crack, were calculated using a three dimensional finite-element elastic stress analysis. Three-dimensional singularity elements were used around the crack front. The stress intensity factors along the crack front were evaluated by using a force method, developed herein, that requires no prior assumption of either plane stress or plane strain. The calculated stress-intensity factors from the present analysis were compared with those from the literature whenever possible and were generally found to be in good agreement. The stress-intensity factors at the midplane for all specimens analyzed were within 3 percent of the two dimensional plane strain values. The stress intensity factors at the specimen surfaces were considerably lower than at the midplanes. For the center-crack tension specimens with large thickness to crack-length ratios, the stress-intensity factor reached a maximum near the surface of the specimen. In all other specimens considered the maximum stress intensity occurred at the midplane.

Three-dimensional modeling of flexible pavements : executive summary, August 2001.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Three dimensional modeling of flexible pavements : final report, March 2002.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Development and verification of global/local analysis techniques for laminated composites

NASA Technical Reports Server (NTRS)

Thompson, Danniella Muheim; Griffin, O. Hayden, Jr.

1991-01-01

A two-dimensional to three-dimensional global/local finite element approach was developed, verified, and applied to a laminated composite plate of finite width and length containing a central circular hole. The resulting stress fields for axial compression loads were examined for several symmetric stacking sequences and hole sizes. Verification was based on comparison of the displacements and the stress fields with those accepted trends from previous free edge investigations and a complete three-dimensional finite element solution of the plate. The laminates in the compression study included symmetric cross-ply, angle-ply and quasi-isotropic stacking sequences. The entire plate was selected as the global model and analyzed with two-dimensional finite elements. Displacements along a region identified as the global/local interface were applied in a kinematically consistent fashion to independent three-dimensional local models. Local areas of interest in the plate included a portion of the straight free edge near the hole, and the immediate area around the hole. Interlaminar stress results obtained from the global/local analyses compares well with previously reported trends, and some new conclusions about interlaminar stress fields in plates with different laminate orientations and hole sizes are presented for compressive loading. The effectiveness of the global/local procedure in reducing the computational effort required to solve these problems is clearly demonstrated through examination of the computer time required to formulate and solve the linear, static system of equations which result for the global and local analyses to those required for a complete three-dimensional formulation for a cross-ply laminate. Specific processors used during the analyses are described in general terms. The application of this global/local technique is not limited software system, and was developed and described in as general a manner as possible.

BOPACE 3-D (the Boeing Plastic Analysis Capability for 3-dimensional Solids Using Isoparametric Finite Elements)

NASA Technical Reports Server (NTRS)

Vos, R. G.; Straayer, J. W.

1975-01-01

The BOPACE 3-D is a finite element computer program, which provides a general family of three-dimensional isoparametric solid elements, and includes a new algorithm for improving the efficiency of the elastic-plastic-creep solution procedure. Theoretical, user, and programmer oriented sections are presented to describe the program.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

1973-01-01

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

Three dimensional flow computations in a turbine scroll

NASA Technical Reports Server (NTRS)

Hamed, A.; Ghantous, C. A.

1982-01-01

The compressible three dimensional inviscid flow in the scroll and vaneless nozzle of radial inflow turbines is analyzed. A FORTRAN computer program for the numerical solution of this complex flow field using the finite element method is presented. The program input consists of the mass flow rate and stagnation conditions at the scroll inlet and of the finite element discretization parameters and nodal coordinates. The output includes the pressure, Mach number and velocity magnitude and direction at all the nodal points.

Elasto-Plastic 3D Finite Element Contact Analysis of a Hole Containing a Circular Insert in a Fatigue Test Coupon

DTIC Science & Technology

2015-08-01

primarily concerned with the results of a three-dimensional elasto– plastic finite element contact analysis of a typical aluminium fatigue test coupon...determine the nonlinear three-dimensional elasto–plastic contact stress distributions around a circular hole in an aluminium plate that is fitted...Australian Air Force (RAAF) airframes. An aluminium -alloy fatigue test coupon (see Figure 1) has been designed and applied in support of the validation of

User's manual for three dimensional FDTD version A code for scattering from frequency-independent dielectric materials

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.

1991-01-01

The Finite Difference Time Domain Electromagnetic Scattering Code Version A is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). This manual provides a description of the code and corresponding results for the default scattering problem. In addition to the description, the operation, resource requirements, version A code capabilities, a description of each subroutine, a brief discussion of the radar cross section computations, and a discussion of the scattering results.

Simulation of Hypervelocity Impact on Aluminum-Nextel-Kevlar Orbital Debris Shields

NASA Technical Reports Server (NTRS)

Fahrenthold, Eric P.

2000-01-01

An improved hybrid particle-finite element method has been developed for hypervelocity impact simulation. The method combines the general contact-impact capabilities of particle codes with the true Lagrangian kinematics of large strain finite element formulations. Unlike some alternative schemes which couple Lagrangian finite element models with smooth particle hydrodynamics, the present formulation makes no use of slidelines or penalty forces. The method has been implemented in a parallel, three dimensional computer code. Simulations of three dimensional orbital debris impact problems using this parallel hybrid particle-finite element code, show good agreement with experiment and good speedup in parallel computation. The simulations included single and multi-plate shields as well as aluminum and composite shielding materials. at an impact velocity of eleven kilometers per second.

Construction of a three-dimensional finite element model of maxillary first molar and it's supporting structures

PubMed Central

Begum, M. Sameena; Dinesh, M. R.; Tan, Kenneth F. H.; Jairaj, Vani; Md Khalid, K.; Singh, Varun Pratap

2015-01-01

The finite element method (FEM) is a powerful computational tool for solving stress-strain problems; its ability to handle material inhomogeneity and complex shapes makes the FEM, the most suitable method for the analysis of internal stress levels in the tooth, periodontium, and alveolar bone. This article intends to explain the steps involved in the generation of a three-dimensional finite element model of tooth, periodontal ligament (PDL) and alveolar bone, as the procedure of modeling is most important because the result is based on the nature of the modeling systems. Finite element analysis offers a means of determining strain-stress levels in the tooth, ligament, and bone structures for a broad range of orthodontic loading scenarios without producing tissue damage. PMID:26538895

Thermal History and Mantle Dynamics of Venus

NASA Technical Reports Server (NTRS)

Hsui, Albert T.

1997-01-01

One objective of this research proposal is to develop a 3-D thermal history model for Venus. The basis of our study is a finite-element computer model to simulate thermal convection of fluids with highly temperature- and pressure-dependent viscosities in a three-dimensional spherical shell. A three-dimensional model for thermal history studies is necessary for the following reasons. To study planetary thermal evolution, one needs to consider global heat budgets of a planet throughout its evolution history. Hence, three-dimensional models are necessary. This is in contrasts to studies of some local phenomena or local structures where models of lower dimensions may be sufficient. There are different approaches to treat three-dimensional thermal convection problems. Each approach has its own advantages and disadvantages. Therefore, the choice of the various approaches is subjective and dependent on the problem addressed. In our case, we are interested in the effects of viscosities that are highly temperature dependent and that their magnitudes within the computing domain can vary over many orders of magnitude. In order to resolve the rapid change of viscosities, small grid spacings are often necessary. To optimize the amount of computing, variable grids become desirable. Thus, the finite-element numerical approach is chosen for its ability to place grid elements of different sizes over the complete computational domain. For this research proposal, we did not start from scratch and develop the finite element codes from the beginning. Instead, we adopted a finite-element model developed by Baumgardner, a collaborator of this research proposal, for three-dimensional thermal convection with constant viscosity. Over the duration supported by this research proposal, a significant amount of advancements have been accomplished.

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

NASA Technical Reports Server (NTRS)

Li, Yong; Moorthi, S.; Bates, J. Ray; Suarez, Max J.

1994-01-01

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Inter- and Intra-Dimensional Dependencies in Implicit Phonotactic Learning

ERIC Educational Resources Information Center

Moreton, Elliott

2012-01-01

Is phonological learning subject to the same inductive biases as learning in other domains? Previous studies of non-linguistic learning found that intra-dimensional dependencies (between two instances of the same feature) were learned more easily than inter-dimensional ones. This study compares implicit learning of intra- and inter-dimensional…

A coupled sharp-interface immersed boundary-finite-element method for flow-structure interaction with application to human phonation.

PubMed

Zheng, X; Xue, Q; Mittal, R; Beilamowicz, S

2010-11-01

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

Reconstruction of three-dimensional porous media using generative adversarial neural networks

NASA Astrophysics Data System (ADS)

Mosser, Lukas; Dubrule, Olivier; Blunt, Martin J.

2017-10-01

To evaluate the variability of multiphase flow properties of porous media at the pore scale, it is necessary to acquire a number of representative samples of the void-solid structure. While modern x-ray computer tomography has made it possible to extract three-dimensional images of the pore space, assessment of the variability in the inherent material properties is often experimentally not feasible. We present a method to reconstruct the solid-void structure of porous media by applying a generative neural network that allows an implicit description of the probability distribution represented by three-dimensional image data sets. We show, by using an adversarial learning approach for neural networks, that this method of unsupervised learning is able to generate representative samples of porous media that honor their statistics. We successfully compare measures of pore morphology, such as the Euler characteristic, two-point statistics, and directional single-phase permeability of synthetic realizations with the calculated properties of a bead pack, Berea sandstone, and Ketton limestone. Results show that generative adversarial networks can be used to reconstruct high-resolution three-dimensional images of porous media at different scales that are representative of the morphology of the images used to train the neural network. The fully convolutional nature of the trained neural network allows the generation of large samples while maintaining computational efficiency. Compared to classical stochastic methods of image reconstruction, the implicit representation of the learned data distribution can be stored and reused to generate multiple realizations of the pore structure very rapidly.

Finite Element in Angle Unit Sphere Meshing for Charged Particle Transport.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ortega, Mario Ivan; Drumm, Clifton R.

Finite element in angle formulations of the charged particle transport equation require the discretization of the unit sphere. In Sceptre, a three-dimensional surface mesh of a sphere is transformed into a two-dimensional mesh. Projection of a sphere onto a two-dimensional surface is well studied with map makers spending the last few centuries attempting to create maps that preserve proportion and area. Using these techniques, various meshing schemes for the unit sphere were investigated.

Theoretical and experimental study on multimode optical fiber grating

NASA Astrophysics Data System (ADS)

Yunming, Wang; Jingcao, Dai; Mingde, Zhang; Xiaohan, Sun

2005-06-01

The characteristics of multimode optical fiber Bragg grating (MMFBG) are studied theoretically and experimentally. For the first time the analysis of MMFBG based on a novel quasi-three-dimensional (Q-3D) finite-difference time-domain beam propagation method (Q-FDTD-BPM) is described through separating the angle component of vector field solution from the cylindrical coordinate so that several discrete two-dimensional (2D) equations are obtained, which simplify the 3D equations. And then these equations are developed using an alternating-direction implicit method and generalized Douglas scheme, which achieves higher accuracy than the regular FD scheme. All of the 2D solutions for the field intensities are also added with different power coefficients for different angle mode order numbers to obtain 3D field distributions in MMFBG. The presented method has been demonstrated as suitable simulation tool for analyzing MMFBG. In addition, based on the hydrogen-loaded and phase mask techniques, a series of Bragg grating have been written into the silicon multimode optical fiber loaded hydrogen for a month, and the spectrums for that have been measured, which obtain good results approximate to the results in the experiment. Group delay/differentiate group delay spectrums are obtained using Agilent 81910A Photonic All-Parameter Analyzer.

Highly Parallel Alternating Directions Algorithm for Time Dependent Problems

NASA Astrophysics Data System (ADS)

Ganzha, M.; Georgiev, K.; Lirkov, I.; Margenov, S.; Paprzycki, M.

2011-11-01

In our work, we consider the time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, written in terms of velocity and pressure. For this problem, a parallel algorithm based on a novel direction splitting approach is developed. Here, the pressure equation is derived from a perturbed form of the continuity equation, in which the incompressibility constraint is penalized in a negative norm induced by the direction splitting. The scheme used in the algorithm is composed of two parts: (i) velocity prediction, and (ii) pressure correction. This is a Crank-Nicolson-type two-stage time integration scheme for two and three dimensional parabolic problems in which the second-order derivative, with respect to each space variable, is treated implicitly while the other variable is made explicit at each time sub-step. In order to achieve a good parallel performance the solution of the Poison problem for the pressure correction is replaced by solving a sequence of one-dimensional second order elliptic boundary value problems in each spatial direction. The parallel code is implemented using the standard MPI functions and tested on two modern parallel computer systems. The performed numerical tests demonstrate good level of parallel efficiency and scalability of the studied direction-splitting-based algorithm.

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

Steger, J. L.; Caradonna, F. X.

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

An Implicit Finite Difference Solution to the Viscous Radiating Shock Layer with Strong Blowing. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Garrett, L. B.

1971-01-01

An implicit finite difference scheme is developed for the fully coupled solution of the viscous radiating stagnation line equations, including strong blowing. Solutions are presented for both air injection and carbon phenolic ablation products injection into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized.

Stress concentration investigations using NASTRAN

NASA Technical Reports Server (NTRS)

Gillcrist, M. C.; Parnell, L. A.

1986-01-01

Parametic investigations are performed using several two dimensional finite element formulations to determine their suitability for use in predicting extremum stresses in marine propellers. Comparisons are made of two NASTRAN elements (CTRIM6 and CTRAIA2) wherein elasticity properties have been modified to yield plane strain results. The accuracy of the elements is investigated by comparing finite element stress predictions with experimentally determined stresses in two classical cases: (1) tension in a flat plate with a circular hole; and (2) a filleted flat bar subjected to in-plane bending. The CTRIA2 element is found to provide good results. The displacement field from a three dimensional finite element model of a representative marine propeller is used as the boundary condition for the two dimensional plane strain investigations of stresses in the propeller blade and fillet. Stress predictions from the three dimensional analysis are compared with those from the two dimensional models. The validity of the plane strain modifications to the NASTRAN element is checked by comparing the modified CTRIA2 element stress predictions with those of the ABAQUS plane strain element, CPE4.

A finite element approach for solution of the 3D Euler equations

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.; Dechaumphai, P.

1986-01-01

Prediction of thermal deformations and stresses has prime importance in the design of the next generation of high speed flight vehicles. Aerothermal load computations for complex three-dimensional shapes necessitate development of procedures to solve the full Navier-Stokes equations. This paper details the development of a three-dimensional inviscid flow approach which can be extended for three-dimensional viscous flows. A finite element formulation, based on a Taylor series expansion in time, is employed to solve the compressible Euler equations. Model generation and results display are done using a commercially available program, PATRAN, and vectorizing strategies are incorporated to ensure computational efficiency. Sample problems are presented to demonstrate the validity of the approach for analyzing high speed compressible flows.

Posttest analysis of a 1:6-scale reinforced concrete reactor containment building

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weatherby, J.R.

In an experiment conducted at Sandia National Laboratories, 1:6-scale model of a reinforced concrete light water reactor containment building was pressurized with nitrogen gas to more than three times its design pressure. The pressurization produced one large tear and several smaller tears in the steel liner plate that functioned as the primary pneumatic seal for the structure. The data collected from the overpressurization test have been used to evaluate and further refine methods of structural analysis that can be used to predict the performance of containment buildings under conditions produced by a severe accident. This report describes posttest finite elementmore » analyses of the 1:6-scale model tests and compares pretest predictions of the structural response to the experimental results. Strain and displacements calculated in axisymmetric finite element analyses of the 1:6-scale model are compared to strains and displacement measured in the experiment. Detailed analyses of the liner plate are also described in the report. The region of the liner surrounding the large tear was analyzed using two different two-dimensional finite elements model. The results from these analyzed indicate that the primary mechanisms that initiated the tear can be captured in a two- dimensional finite element model. Furthermore, the analyses show that studs used to anchor the liner to the concrete wall, played an important role in initiating the liner tear. Three-dimensional finite element analyses of liner plates loaded by studs are also presented. Results from the three-dimensional analyses are compared to results from two-dimensional analyses of the same problems. 12 refs., 56 figs., 1 tab.« less

Three-dimensional elastic-plastic finite-element analysis of fatigue crack propagation

NASA Technical Reports Server (NTRS)

Goglia, G. L.; Chermahini, R. G.

1985-01-01

Fatigue cracks are a major problem in designing structures subjected to cyclic loading. Cracks frequently occur in structures such as aircraft and spacecraft. The inspection intervals of many aircraft structures are based on crack-propagation lives. Therefore, improved prediction of propagation lives under flight-load conditions (variable-amplitude loading) are needed to provide more realistic design criteria for these structures. The main thrust was to develop a three-dimensional, nonlinear, elastic-plastic, finite element program capable of extending a crack and changing boundary conditions for the model under consideration. The finite-element model is composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material is assumed to be elastic-perfectly plastic. The cycle stress-strain curve for the material is shown Zienkiewicz's initial-stress method, von Mises's yield criterion, and Drucker's normality condition under small-strain assumptions are used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading.

Trading spaces: building three-dimensional nets from two-dimensional tilings

PubMed Central

Castle, Toen; Evans, Myfanwy E.; Hyde, Stephen T.; Ramsden, Stuart; Robins, Vanessa

2012-01-01

We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic (S2), Euclidean (E2) and hyperbolic (H2) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions. PMID:24098839

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

NASA Astrophysics Data System (ADS)

Yi, Dake; Wang, TzuChiang

2018-06-01

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J( z), the stress intensity factor K( z) and the tri-axial stress constraint level T z ( z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J( z) and T z ( z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.

Accurate solutions for transonic viscous flow over finite wings

NASA Technical Reports Server (NTRS)

Vatsa, V. N.

1986-01-01

An explicit multistage Runge-Kutta type time-stepping scheme is used for solving the three-dimensional, compressible, thin-layer Navier-Stokes equations. A finite-volume formulation is employed to facilitate treatment of complex grid topologies encountered in three-dimensional calculations. Convergence to steady state is expedited through usage of acceleration techniques. Further numerical efficiency is achieved through vectorization of the computer code. The accuracy of the overall scheme is evaluated by comparing the computed solutions with the experimental data for a finite wing under different test conditions in the transonic regime. A grid refinement study ir conducted to estimate the grid requirements for adequate resolution of salient features of such flows.

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

From Laser Scanning to Finite Element Analysis of Complex Buildings by Using a Semi-Automatic Procedure

PubMed Central

Castellazzi, Giovanni; D’Altri, Antonio Maria; Bitelli, Gabriele; Selvaggi, Ilenia; Lambertini, Alessandro

2015-01-01

In this paper, a new semi-automatic procedure to transform three-dimensional point clouds of complex objects to three-dimensional finite element models is presented and validated. The procedure conceives of the point cloud as a stacking of point sections. The complexity of the clouds is arbitrary, since the procedure is designed for terrestrial laser scanner surveys applied to buildings with irregular geometry, such as historical buildings. The procedure aims at solving the problems connected to the generation of finite element models of these complex structures by constructing a fine discretized geometry with a reduced amount of time and ready to be used with structural analysis. If the starting clouds represent the inner and outer surfaces of the structure, the resulting finite element model will accurately capture the whole three-dimensional structure, producing a complex solid made by voxel elements. A comparison analysis with a CAD-based model is carried out on a historical building damaged by a seismic event. The results indicate that the proposed procedure is effective and obtains comparable models in a shorter time, with an increased level of automation. PMID:26225978

Three dimensional finite temperature SU(3) gauge theory near the phase transition

NASA Astrophysics Data System (ADS)

Bialas, P.; Daniel, L.; Morel, A.; Petersson, B.

2013-06-01

We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent ν has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu-Goto string model in spite of the different critical behaviour.

The time course of explicit and implicit categorization.

PubMed

Smith, J David; Zakrzewski, Alexandria C; Herberger, Eric R; Boomer, Joseph; Roeder, Jessica L; Ashby, F Gregory; Church, Barbara A

2015-10-01

Contemporary theory in cognitive neuroscience distinguishes, among the processes and utilities that serve categorization, explicit and implicit systems of category learning that learn, respectively, category rules by active hypothesis testing or adaptive behaviors by association and reinforcement. Little is known about the time course of categorization within these systems. Accordingly, the present experiments contrasted tasks that fostered explicit categorization (because they had a one-dimensional, rule-based solution) or implicit categorization (because they had a two-dimensional, information-integration solution). In Experiment 1, participants learned categories under unspeeded or speeded conditions. In Experiment 2, they applied previously trained category knowledge under unspeeded or speeded conditions. Speeded conditions selectively impaired implicit category learning and implicit mature categorization. These results illuminate the processing dynamics of explicit/implicit categorization.

Computational modeling of chemo-electro-mechanical coupling: A novel implicit monolithic finite element approach

PubMed Central

Wong, J.; Göktepe, S.; Kuhl, E.

2014-01-01

Summary Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, while the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of four days on a standard desktop computer. PMID:23798328

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

A grid-doubling finite-element technique for calculating dynamic three-dimensional spontaneous rupture on an earthquake fault

USGS Publications Warehouse

Barall, Michael

2009-01-01

We present a new finite-element technique for calculating dynamic 3-D spontaneous rupture on an earthquake fault, which can reduce the required computational resources by a factor of six or more, without loss of accuracy. The grid-doubling technique employs small cells in a thin layer surrounding the fault. The remainder of the modelling volume is filled with larger cells, typically two or four times as large as the small cells. In the resulting non-conforming mesh, an interpolation method is used to join the thin layer of smaller cells to the volume of larger cells. Grid-doubling is effective because spontaneous rupture calculations typically require higher spatial resolution on and near the fault than elsewhere in the model volume. The technique can be applied to non-planar faults by morphing, or smoothly distorting, the entire mesh to produce the desired 3-D fault geometry. Using our FaultMod finite-element software, we have tested grid-doubling with both slip-weakening and rate-and-state friction laws, by running the SCEC/USGS 3-D dynamic rupture benchmark problems. We have also applied it to a model of the Hayward fault, Northern California, which uses realistic fault geometry and rock properties. FaultMod implements fault slip using common nodes, which represent motion common to both sides of the fault, and differential nodes, which represent motion of one side of the fault relative to the other side. We describe how to modify the traction-at-split-nodes method to work with common and differential nodes, using an implicit time stepping algorithm.

A computational procedure for the dynamics of flexible beams within multibody systems. Ph.D. Thesis Final Technical Report

NASA Technical Reports Server (NTRS)

Downer, Janice Diane

1990-01-01

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Convergence of an hp-Adaptive Finite Element Strategy in Two and Three Space-Dimensions

NASA Astrophysics Data System (ADS)

Bürg, Markus; Dörfler, Willy

2010-09-01

We show convergence of an automatic hp-adaptive refinement strategy for the finite element method on the elliptic boundary value problem. The strategy is a generalization of a refinement strategy proposed for one-dimensional situations to problems in two and three space-dimensions.

A three-dimensional parabolic equation model of sound propagation using higher-order operator splitting and Padé approximants.

PubMed

Lin, Ying-Tsong; Collis, Jon M; Duda, Timothy F

2012-11-01

An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. The method is tested for accuracy against an image solution in an idealized wedge problem. Computational efficiency improvements resulting from the ADI discretization are also discussed.

An application of a two-equation model of turbulence to three-dimensional chemically reacting flows

NASA Technical Reports Server (NTRS)

Lee, J.

1994-01-01

A numerical study of three dimensional chemically reacting and non-reacting flowfields is conducted using a two-equation model of turbulence. A generalized flow solver using an implicit Lower-Upper (LU) diagonal decomposition numerical technique and finite-rate chemistry has been coupled with a low-Reynolds number two-equation model of turbulence. This flow solver is then used to study chemically reacting turbulent supersonic flows inside combustors with synergetic fuel injectors. The reacting and non-reacting turbulent combustor solutions obtained are compared with zero-equation turbulence model solutions and with available experimental data. The hydrogen-air chemistry is modeled using a nine-species/eighteen reaction model. A low-Reynolds number k-epsilon model was used to model the effect of turbulence because, in general, the low-Reynolds number k-epsilon models are easier to implement numerically and are far more general than algebraic models. However, low-Reynolds number k-epsilon models require a much finer near-wall grid resolution than high-Reynolds number models to resolve accurately the near-wall physics. This is especially true in complex flowfields, where the stiff nature of the near-wall turbulence must be resolved. Therefore, the limitations imposed by the near-wall characteristics and compressible model corrections need to be evaluated further. The gradient-diffusion hypothesis is used to model the effects of turbulence on the mass diffusion process. The influence of this low-Reynolds number turbulence model on the reacting flowfield predictions was studied parametrically.

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

NASA Astrophysics Data System (ADS)

Zhu, Lianhua; Yang, Xiaofan; Guo, Zhaoli

2017-12-01

Rarefied gas flow in a three-dimensional enclosure induced by nonuniform temperature distribution is numerically investigated. The enclosure has a square channel-like geometry with alternatively heated closed ends and lateral walls with a linear temperature distribution. A recently proposed implicit discrete velocity method with a memory reduction technique is used to numerically simulate the problem based on the nonlinear Shakhov kinetic equation. The Knudsen number dependencies of the vortices pattern, slip velocity at the planar walls and edges, and heat transfer are investigated. The influences of the temperature ratio imposed at the ends of the enclosure and the geometric aspect ratio are also evaluated. The overall flow pattern shows similarities with those observed in two-dimensional configurations in literature. However, features due to the three-dimensionality are observed with vortices that are not identified in previous studies on similar two-dimensional enclosures at high Knudsen and small aspect ratios.

3DHYDROGEOCHEM: A 3-DIMENSIONAL MODEL OF DENSITY-DEPENDENT SUBSURFACE FLOW AND THERMAL MULTISPECIES-MULTICOMPONENT HYDROGEOCHEMICAL TRANSPORT (EPA/600/SR-98/159)

EPA Science Inventory

This report presents a three-dimensional finite-element numerical model designed to simulate chemical transport in subsurface systems with temperature effect taken into account. The three-dimensional model is developed to provide (1) a tool of application, with which one is able ...

Direct numerical simulation of the laminar-turbulent transition at hypersonic flow speeds on a supercomputer

NASA Astrophysics Data System (ADS)

Egorov, I. V.; Novikov, A. V.; Fedorov, A. V.

2017-08-01

A method for direct numerical simulation of three-dimensional unsteady disturbances leading to a laminar-turbulent transition at hypersonic flow speeds is proposed. The simulation relies on solving the full three-dimensional unsteady Navier-Stokes equations. The computational technique is intended for multiprocessor supercomputers and is based on a fully implicit monotone approximation scheme and the Newton-Raphson method for solving systems of nonlinear difference equations. This approach is used to study the development of three-dimensional unstable disturbances in a flat-plate and compression-corner boundary layers in early laminar-turbulent transition stages at the free-stream Mach number M = 5.37. The three-dimensional disturbance field is visualized in order to reveal and discuss features of the instability development at the linear and nonlinear stages. The distribution of the skin friction coefficient is used to detect laminar and transient flow regimes and determine the onset of the laminar-turbulent transition.

A diagonal algorithm for the method of pseudocompressibility. [for steady-state solution to incompressible Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Rogers, S. E.; Kwak, D.; Chang, J. L. C.

1986-01-01

The method of pseudocompressibility has been shown to be an efficient method for obtaining a steady-state solution to the incompressible Navier-Stokes equations. Recent improvements to this method include the use of a diagonal scheme for the inversion of the equations at each iteration. The necessary transformations have been derived for the pseudocompressibility equations in generalized coordinates. The diagonal algorithm reduces the computing time necessary to obtain a steady-state solution by a factor of nearly three. Implicit viscous terms are maintained in the equations, and it has become possible to use fourth-order implicit dissipation. The steady-state solution is unchanged by the approximations resulting from the diagonalization of the equations. Computed results for flow over a two-dimensional backward-facing step and a three-dimensional cylinder mounted normal to a flat plate are presented for both the old and new algorithms. The accuracy and computing efficiency of these algorithms are compared.

Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Turchaninov, V. I.; Tsynkov, S. V.

1999-01-01

We propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.

Numerical approach for finite volume three-body interaction

NASA Astrophysics Data System (ADS)

Guo, Peng; Gasparian, Vladimir

2018-01-01

In the present work, we study a numerical approach to one dimensional finite volume three-body interaction, the method is demonstrated by considering a toy model of three spinless particles interacting with pair-wise δ -function potentials. The numerical results are compared with the exact solutions of three spinless bosons interaction when the strength of short-range interactions are set equal for all pairs.

Finite-Element Analysis of Residual Stresses Generated Under Nitriding Process: a Three-Dimensional Model

NASA Astrophysics Data System (ADS)

Sawicki, J.; Siedlaczek, P.; Staszczyk, A.

2018-03-01

A numerical three-dimensional model for computing residual stresses generated in cross section of steel 42CrMo4 after nitriding is presented. The diffusion process is analyzed by the finite-element method. The internal stresses are computed using the obtained profile of the distribution of the nitrogen concentration. The special features of the intricate geometry of the treated articles including edges and angles are considered. Comparative analysis of the results of the simulation and of the experimental measurement of residual stresses is performed by the Waisman-Philips method.

Three-dimensional finite element analysis of acoustic instability of solid propellant rocket motors

NASA Technical Reports Server (NTRS)

Hackett, R. M.; Juruf, R. S.

1976-01-01

A three dimensional finite element solution of the acoustic vibration problem in a solid propellant rocket motor is presented. The solution yields the natural circular frequencies of vibration and the corresponding acoustic pressure mode shapes, considering the coupled response of the propellant grain to the acoustic oscillations occurring in the motor cavity. The near incompressibility of the solid propellant is taken into account in the formulation. A relatively simple example problem is solved in order to illustrate the applicability of the analysis and the developed computer code.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rossow, C.-C.

2008-01-01

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1986-01-01

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

User's manual for three dimensional FDTD version B code for scattering from frequency-dependent dielectric materials

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.

1992-01-01

The Penn State Finite Difference Time Domain Electromagnetic Code Version B is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into 14 sections: introduction, description of the FDTD method, operation, resource requirements, Version B code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file, a discussion of radar cross section computations, a discussion of some scattering results, a sample problem setup section, a new problem checklist, references and figure titles.

The Time Course of Explicit and Implicit Categorization

PubMed Central

Zakrzewski, Alexandria C.; Herberger, Eric; Boomer, Joseph; Roeder, Jessica; Ashby, F. Gregory; Church, Barbara A.

2015-01-01

Contemporary theory in cognitive neuroscience distinguishes, among the processes and utilities that serve categorization, explicit and implicit systems of category learning that learn, respectively, category rules by active hypothesis testing or adaptive behaviors by association and reinforcement. Little is known about the time course of categorization within these systems. Accordingly, the present experiments contrasted tasks that fostered explicit categorization (because they had a one-dimensional, rule-based solution) or implicit categorization (because they had a two-dimensional, information-integration solution). In Experiment 1, participants learned categories under unspeeded or speeded conditions. In Experiment 2, they applied previously trained category knowledge under unspeeded or speeded conditions. Speeded conditions selectively impaired implicit category learning and implicit mature categorization. These results illuminate the processing dynamics of explicit/implicit categorization. PMID:26025556

A parallel finite-difference method for computational aerodynamics

NASA Technical Reports Server (NTRS)

Swisshelm, Julie M.

1989-01-01

A finite-difference scheme for solving complex three-dimensional aerodynamic flow on parallel-processing supercomputers is presented. The method consists of a basic flow solver with multigrid convergence acceleration, embedded grid refinements, and a zonal equation scheme. Multitasking and vectorization have been incorporated into the algorithm. Results obtained include multiprocessed flow simulations from the Cray X-MP and Cray-2. Speedups as high as 3.3 for the two-dimensional case and 3.5 for segments of the three-dimensional case have been achieved on the Cray-2. The entire solver attained a factor of 2.7 improvement over its unitasked version on the Cray-2. The performance of the parallel algorithm on each machine is analyzed.

Analytical modeling and analysis of magnetic field and torque for novel axial flux eddy current couplers with PM excitation

NASA Astrophysics Data System (ADS)

Li, Zhao; Wang, Dazhi; Zheng, Di; Yu, Linxin

2017-10-01

Rotational permanent magnet eddy current couplers are promising devices for torque and speed transmission without any mechanical contact. In this study, flux-concentration disk-type permanent magnet eddy current couplers with double conductor rotor are investigated. Given the drawback of the accurate three-dimensional finite element method, this paper proposes a mixed two-dimensional analytical modeling approach. Based on this approach, the closed-form expressions of magnetic field, eddy current, electromagnetic force and torque for such devices are obtained. Finally, a three-dimensional finite element method is employed to validate the analytical results. Besides, a prototype is manufactured and tested for the torque-speed characteristic.

An efficient, explicit finite-rate algorithm to compute flows in chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

An explicit finite-rate code was developed to compute hypersonic viscous chemically reacting flows about three-dimensional bodies. Equations describing the finite-rate chemical reactions were fully coupled to the gas dynamic equations using a new coupling technique. The new technique maintains stability in the explicit finite-rate formulation while permitting relatively large global time steps.

Computation of three-dimensional nozzle-exhaust flow fields with the GIM code

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Anderson, P. G.

1978-01-01

A methodology is introduced for constructing numerical analogs of the partial differential equations of continuum mechanics. A general formulation is provided which permits classical finite element and many of the finite difference methods to be derived directly. The approach, termed the General Interpolants Method (GIM), can combined the best features of finite element and finite difference methods. A quasi-variational procedure is used to formulate the element equations, to introduce boundary conditions into the method and to provide a natural assembly sequence. A derivation is given in terms of general interpolation functions from this procedure. Example computations for transonic and supersonic flows in two and three dimensions are given to illustrate the utility of GIM. A three-dimensional nozzle-exhaust flow field is solved including interaction with the freestream and a coupled treatment of the shear layer. Potential applications of the GIM code to a variety of computational fluid dynamics problems is then discussed in terms of existing capability or by extension of the methodology.

Three dimensional modeling of rigid pavement : executive summary, February 1995.

DOT National Transportation Integrated Search

1995-02-17

A finite-element program has been developed to model the response of rigid pavement to both static loads and temperature changes. The program is fully three-dimensional and incorporates not only the common twenty-node brick element but also a thin in...

Three-dimensional modeling of rigid pavement : final report, September 1995.

DOT National Transportation Integrated Search

1995-02-17

A finite-element program has been developed to model the response of rigid pavement to both static loads and temperature changes. The program is fully three-dimensional and incorporates not only the common twenty-node brick element but also a thin in...

Experiences with explicit finite-difference schemes for complex fluid dynamics problems on STAR-100 and CYBER-203 computers

NASA Technical Reports Server (NTRS)

Kumar, A.; Rudy, D. H.; Drummond, J. P.; Harris, J. E.

1982-01-01

Several two- and three-dimensional external and internal flow problems solved on the STAR-100 and CYBER-203 vector processing computers are described. The flow field was described by the full Navier-Stokes equations which were then solved by explicit finite-difference algorithms. Problem results and computer system requirements are presented. Program organization and data base structure for three-dimensional computer codes which will eliminate or improve on page faulting, are discussed. Storage requirements for three-dimensional codes are reduced by calculating transformation metric data in each step. As a result, in-core grid points were increased in number by 50% to 150,000, with a 10% execution time increase. An assessment of current and future machine requirements shows that even on the CYBER-205 computer only a few problems can be solved realistically. Estimates reveal that the present situation is more storage limited than compute rate limited, but advancements in both storage and speed are essential to realistically calculate three-dimensional flow.

A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

NASA Technical Reports Server (NTRS)

Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.

1977-01-01

An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

HYDRODYNAMIC SIMULATION OF THE UPPER POTOMAC ESTUARY.

USGS Publications Warehouse

Schaffranck, Raymond W.

1986-01-01

Hydrodynamics of the upper extent of the Potomac Estuary between Indian Head and Morgantown, Md. , are simulated using a two-dimensional model. The model computes water-surface elevations and depth-averaged velocities by numerically integrating finite-difference forms of the equations of mass and momentum conservation using the alternating direction implicit method. The fundamental, non-linear, unsteady-flow equations, upon which the model is formulated, include additional terms to account for Coriolis acceleration and meteorological influences. Preliminary model/prototype data comparisons show agreement to within 9% for tidal flow volumes and phase differences within the measured-data-recording interval. Use of the model to investigate the hydrodynamics and certain aspects of transport within this Potomac Estuary reach is demonstrated. Refs.

An exponential time-integrator scheme for steady and unsteady inviscid flows

NASA Astrophysics Data System (ADS)

Li, Shu-Jie; Luo, Li-Shi; Wang, Z. J.; Ju, Lili

2018-07-01

An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The effective and efficient implementation of PCEXP is realized by means of the Krylov method. The linear stability and truncation error are analyzed through a one-dimensional model equation. The proposed PCEXP scheme is applied to the Euler equations discretized with a discontinuous Galerkin method in both two and three dimensions. The effectiveness and efficiency of the PCEXP scheme are demonstrated for both steady and unsteady inviscid flows. The accuracy and efficiency of the PCEXP scheme are verified and validated through comparisons with the explicit third-order total variation diminishing Runge-Kutta scheme (TVDRK3), the implicit backward Euler (BE) and the implicit second-order backward difference formula (BDF2). For unsteady flows, the PCEXP scheme generates a temporal error much smaller than the BDF2 scheme does, while maintaining the expected acceleration at the same time. Moreover, the PCEXP scheme is also shown to achieve the computational efficiency comparable to the implicit schemes for steady flows.

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Wigner analysis of three dimensional pupil with finite lateral aperture

PubMed Central

Chen, Hsi-Hsun; Oh, Se Baek; Zhai, Xiaomin; Tsai, Jui-Chang; Cao, Liang-Cai; Barbastathis, George; Luo, Yuan

2015-01-01

A three dimensional (3D) pupil is an optical element, most commonly implemented on a volume hologram, that processes the incident optical field on a 3D fashion. Here we analyze the diffraction properties of a 3D pupil with finite lateral aperture in the 4-f imaging system configuration, using the Wigner Distribution Function (WDF) formulation. Since 3D imaging pupil is finite in both lateral and longitudinal directions, the WDF of the volume holographic 4-f imager theoretically predicts distinct Bragg diffraction patterns in phase space. These result in asymmetric profiles of diffracted coherent point spread function between degenerate diffraction and Bragg diffraction, elucidating the fundamental performance of volume holographic imaging. Experimental measurements are also presented, confirming the theoretical predictions. PMID:25836443

New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

NASA Astrophysics Data System (ADS)

Hano, Mitsuo; Hotta, Masashi

A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.

Three-dimensional vector modeling and restoration of flat finite wave tank radiometric measurements

NASA Technical Reports Server (NTRS)

Truman, W. M.; Balanis, C. A.; Holmes, J. J.

1977-01-01

In this paper, a three-dimensional Fourier transform inversion method describing the interaction between water surface emitted radiation from a flat finite wave tank and antenna radiation characteristics is reported. The transform technique represents the scanning of the antenna mathematically as a correlation. Computation time is reduced by using the efficient and economical fast Fourier transform algorithm. To verify the inversion method, computations have been made and compared with known data and other available results. The technique has been used to restore data of the finite wave tank system and other available antenna temperature measurements made at the Cape Cod Canal. The restored brightness temperatures serve as better representations of the emitted radiation than the measured antenna temperatures.

Numerical Modeling of Three-Dimensional Confined Flows

NASA Technical Reports Server (NTRS)

Greywall, M. S.

1981-01-01

A three dimensional confined flow model is presented. The flow field is computed by calculating velocity and enthalpy along a set of streamlines. The finite difference equations are obtained by applying conservation principles to streamtubes constructed around the chosen streamlines. With appropriate substitutions for the body force terms, the approach computes three dimensional magnetohydrodynamic channel flows. A listing of a computer code, based on this approach is presented in FORTRAN IV language. The code computes three dimensional compressible viscous flow through a rectangular duct, with the duct cross section specified along the axis.

Multi-dimensional multi-species modeling of transient electrodeposition in LIGA microfabrication.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Evans, Gregory Herbert; Chen, Ken Shuang

2004-06-01

This report documents the efforts and accomplishments of the LIGA electrodeposition modeling project which was headed by the ASCI Materials and Physics Modeling Program. A multi-dimensional framework based on GOMA was developed for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electro-chemical reactions on moving deposition surfaces. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation that explicitly describes the electrolyte potential was derived. The set of coupled, nonlinear equations governing species transport, electric potential, velocity, hydrodynamic pressure, and mesh motion were solved in GOMA, using themore » finite-element method and a fully-coupled implicit solution scheme via Newton's method. By treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and by repeatedly performing re-meshing with CUBIT and re-mapping with MAPVAR, the moving deposition surfaces were tracked explicitly from start of deposition until the trenches were filled with metal, thus enabling the computation of local current densities that potentially influence the microstructure and frictional/mechanical properties of the deposit. The multi-dimensional, multi-species, transient computational framework was demonstrated in case studies of two-dimensional nickel electrodeposition in single and multiple trenches, without and with bath stirring or forced flow. Effects of buoyancy-induced convection on deposition were also investigated. To further illustrate its utility, the framework was employed to simulate deposition in microscreen-based LIGA molds. Lastly, future needs for modeling LIGA electrodeposition are discussed.« less

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

An implicit spatial and high-order temporal finite difference scheme for 2D acoustic modelling

NASA Astrophysics Data System (ADS)

Wang, Enjiang; Liu, Yang

2018-01-01

The finite difference (FD) method exhibits great superiority over other numerical methods due to its easy implementation and small computational requirement. We propose an effective FD method, characterised by implicit spatial and high-order temporal schemes, to reduce both the temporal and spatial dispersions simultaneously. For the temporal derivative, apart from the conventional second-order FD approximation, a special rhombus FD scheme is included to reach high-order accuracy in time. Compared with the Lax-Wendroff FD scheme, this scheme can achieve nearly the same temporal accuracy but requires less floating-point operation times and thus less computational cost when the same operator length is adopted. For the spatial derivatives, we adopt the implicit FD scheme to improve the spatial accuracy. Apart from the existing Taylor series expansion-based FD coefficients, we derive the least square optimisation based implicit spatial FD coefficients. Dispersion analysis and modelling examples demonstrate that, our proposed method can effectively decrease both the temporal and spatial dispersions, thus can provide more accurate wavefields.

Modeling and analysis of visual digital impact model for a Chinese human thorax.

PubMed

Zhu, Jin; Wang, Kai-Ming; Li, Shu; Liu, Hai-Yan; Jing, Xiao; Li, Xiao-Fang; Liu, Yi-He

2017-01-01

To establish a three-dimensional finite element model of the human chest for engineering research on individual protection. Computed tomography (CT) scanning data were used for three-dimensional reconstruction with the medical image reconstruction software Mimics. The finite element method (FEM) preprocessing software ANSYS ICEM CFD was used for cell mesh generation, and the relevant material behavior parameters of all of the model's parts were specified. The finite element model was constructed with the FEM software, and the model availability was verified based on previous cadaver experimental data. A finite element model approximating the anatomical structure of the human chest was established, and the model's simulation results conformed to the results of the cadaver experiment overall. Segment data of the human body and specialized software can be utilized for FEM model reconstruction to satisfy the need for numerical analysis of shocks to the human chest in engineering research on body mechanics.

Solving the forward problem of magnetoacoustic tomography with magnetic induction by means of the finite element method

NASA Astrophysics Data System (ADS)

Li, Xun; Li, Xu; Zhu, Shanan; He, Bin

2009-05-01

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a recently proposed imaging modality to image the electrical impedance of biological tissue. It combines the good contrast of electrical impedance tomography with the high spatial resolution of sonography. In this paper, a three-dimensional MAT-MI forward problem was investigated using the finite element method (FEM). The corresponding FEM formulae describing the forward problem are introduced. In the finite element analysis, magnetic induction in an object with conductivity values close to biological tissues was first carried out. The stimulating magnetic field was simulated as that generated from a three-dimensional coil. The corresponding acoustic source and field were then simulated. Computer simulation studies were conducted using both concentric and eccentric spherical conductivity models with different geometric specifications. In addition, the grid size for finite element analysis was evaluated for the model calibration and evaluation of the corresponding acoustic field.

Solving the Forward Problem of Magnetoacoustic Tomography with Magnetic Induction by Means of the Finite Element Method

PubMed Central

Li, Xun; Li, Xu; Zhu, Shanan; He, Bin

2010-01-01

Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) is a recently proposed imaging modality to image the electrical impedance of biological tissue. It combines the good contrast of electrical impedance tomography with the high spatial resolution of sonography. In this paper, three-dimensional MAT-MI forward problem was investigated using the finite element method (FEM). The corresponding FEM formulas describing the forward problem are introduced. In the finite element analysis, magnetic induction in an object with conductivity values close to biological tissues was first carried out. The stimulating magnetic field was simulated as that generated from a three-dimensional coil. The corresponding acoustic source and field were then simulated. Computer simulation studies were conducted using both concentric and eccentric spherical conductivity models with different geometric specifications. In addition, the grid size for finite element analysis was evaluated for model calibration and evaluation of the corresponding acoustic field. PMID:19351978

[Finite Element Modelling of the Eye for the Investigation of Accommodation].

PubMed

Martin, H; Stachs, O; Guthoff, R; Grabow, N

2016-12-01

Background: Accommodation research increasingly uses engineering methods. This article presents the use of the finite element method in accommodation research. Material and Methods: Geometry, material data and boundary conditions are prerequisites for the application of the finite element method. Published data on geometry and materials are reviewed. It is shown how boundary conditions are important and how they influence the results. Results: Two dimensional and three dimensional models of the anterior chamber of the eye are presented. With simple two dimensional models, it is shown that realistic results for the accommodation amplitude can always be achieved. More complex three dimensional models of the accommodation mechanism - including the ciliary muscle - require further investigations of the material data and of the morphology of the ciliary muscle, if they are to achieve realistic results for accommodation. Discussion and Conclusion: The efficiency and the limitations of the finite element method are especially clear for accommodation. Application of the method requires extensive preparation, including acquisition of geometric and material data and experimental validation. However, a validated model can be used as a basis for parametric studies, by systematically varying material data and geometric dimensions. This allows systematic investigation of how essential input parameters influence the results. Georg Thieme Verlag KG Stuttgart · New York.

Three-dimensional finite elements for the analysis of soil contamination using a multiple-porosity approach

NASA Astrophysics Data System (ADS)

El-Zein, Abbas; Carter, John P.; Airey, David W.

2006-06-01

A three-dimensional finite-element model of contaminant migration in fissured clays or contaminated sand which includes multiple sources of non-equilibrium processes is proposed. The conceptual framework can accommodate a regular network of fissures in 1D, 2D or 3D and immobile solutions in the macro-pores of aggregated topsoils, as well as non-equilibrium sorption. A Galerkin weighted-residual statement for the three-dimensional form of the equations in the Laplace domain is formulated. Equations are discretized using linear and quadratic prism elements. The system of algebraic equations is solved in the Laplace domain and solution is inverted to the time domain numerically. The model is validated and its scope is illustrated through the analysis of three problems: a waste repository deeply buried in fissured clay, a storage tank leaking into sand and a sanitary landfill leaching into fissured clay over a sand aquifer.

Prediction of asymmetric vortical flows around slender bodies using Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Liu, C. H.; Wong, Tin-Chee; Kandil, Osama A.

1992-01-01

Steady and unsteady asymmetric vortical flows around slender bodies at high angles of attack are solved using the unsteady, compressible, thin-layer Navier-Stokes equations. An implicit, upwind-biased, flux-difference splitting, finite-volume scheme is used for the numerical computations. For supersonic flows past point cones, the locally conical flow assumption have been used for efficient computational studies of this phenomenon. Asymmetric flows past a 5-deg semiapex-angle circular cone at different angles of attack, free-stream Mach numbers, and Reynolds numbers have been studied in responses to different sources of disturbances. The effects of grid fineness and computational domain size have also been investigated. Next, the responses of three-dimensional supersonic asymmetric flow around a 5-deg circular cone at different angles of attack and Reynolds numbers to short-duration sideslip disturbances are presented. The results show that flow asymmetry becomes stronger as the Reynolds number and angles of attack are increased. One of the cases of flow over a cone-cylinder configuration is validated fairly well by experimental data.

Numerical computation of viscous flow about unconventional airfoil shapes

NASA Technical Reports Server (NTRS)

Ahmed, S.; Tannehill, J. C.

1990-01-01

A new two-dimensional computer code was developed to analyze the viscous flow around unconventional airfoils at various Mach numbers and angles of attack. The Navier-Stokes equations are solved using an implicit, upwind, finite-volume scheme. Both laminar and turbulent flows can be computed. A new nonequilibrium turbulence closure model was developed for computing turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present code was evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the present code in conjunction with the new nonequilibrium turbulence model gives excellent results.

Prediction of Film Cooling on Gas Turbine Airfoils

NASA Technical Reports Server (NTRS)

Garg, Vijay K.; Gaugler, Raymond E.

1994-01-01

A three-dimensional Navier-Stokes analysis tool has been developed in order to study the effect of film cooling on the flow and heat transfer characteristics of actual turbine airfoils. An existing code (Arnone et al., 1991) has been modified for the purpose. The code is an explicit, multigrid, cell-centered, finite volume code with an algebraic turbulence model. Eigenvalue scaled artificial dissipation and variable-coefficient implicit residual smoothing are used with a full-multigrid technique. Moreover, Mayle's transition criterion (Mayle, 1991) is used. The effects of film cooling have been incorporated into the code in the form of appropriate boundary conditions at the hole locations on the airfoil surface. Each hole exit is represented by several control volumes, thus providing an ability to study the effect of hole shape on the film-cooling characteristics. Comparison is fair with near mid-span experimental data for four and nine rows of cooling holes, five on the shower head, and two rows each on the pressure and suction surfaces. The computations, however, show a strong spanwise variation of the heat transfer coefficient on the airfoil surface, specially with shower-head cooling.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

NASA Astrophysics Data System (ADS)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Numerical analysis of three-dimensional viscous internal flows

NASA Technical Reports Server (NTRS)

Chima, Rodrick V.; Yokota, Jeffrey W.

1988-01-01

A 3-D Navier-Stokes code has been developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system rotating about the x-axis, and then mapped to a general body-fitted coordinate system. Streamwise viscous terms are neglected using the thin-layer assumption, and turbulence effects are modeled using the Baldwin-Lomax turbulence model. The equations are discretized using finite differences on stacked C-type grids and are solved using a multistage Runge-Kutta algorithm with a spatially-varying time step and implicit residual smoothing. Calculations have been made of a horseshoe vortex formed in front of a flat plate with a round leading edge standing in a turbulent endwall boundary layer. Comparisons are made with experimental data taken by Eckerle and Langston for a circular cylinder under similar conditions. Computer and measured results are compared in terms of endwall flow visualization pictures and total pressure loss contours and vector plots on the symmetry plane. Calculated details of the primary vortex show excellent agreement with the experimental data. The calculations also show a small secondary vortex not seen experimentally.

Dental application of novel finite element analysis software for three-dimensional finite element modeling of a dentulous mandible from its computed tomography images.

PubMed

Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich

2013-12-01

This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

Transpiration and film cooling boundary layer computer program. Volume 2: Computer program and user's manual

NASA Technical Reports Server (NTRS)

Gloss, R. J.

1971-01-01

A finite difference turbulent boundary layer computer program which allows for mass transfer wall cooling and equilibrium chemistry effects is presented. The program is capable of calculating laminar or turbulent boundary layer solutions for an arbitrary ideal gas or an equilibrium hydrogen oxygen system. Either two dimensional or axisymmetric geometric configurations may be considered. The equations are solved, in nondimension-alized physical coordinates, using the implicit Crank-Nicolson technique. The finite difference forms of the conservation of mass, momentum, total enthalpy and elements equations are linearized and uncoupled, thereby generating easily solvable tridiagonal sets of algebraic equations. A detailed description of the computer program, as well as a program user's manual is provided. Detailed descriptions of all boundary layer subroutines are included, as well as a section defining all program symbols of principal importance. Instructions are then given for preparing card input to the program and for interpreting the printed output. Finally, two sample cases are included to illustrate the use of the program.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

DOE PAGES

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

2016-10-21

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less

Implicit schemes and parallel computing in unstructured grid CFD

NASA Technical Reports Server (NTRS)

Venkatakrishnam, V.

1995-01-01

The development of implicit schemes for obtaining steady state solutions to the Euler and Navier-Stokes equations on unstructured grids is outlined. Applications are presented that compare the convergence characteristics of various implicit methods. Next, the development of explicit and implicit schemes to compute unsteady flows on unstructured grids is discussed. Next, the issues involved in parallelizing finite volume schemes on unstructured meshes in an MIMD (multiple instruction/multiple data stream) fashion are outlined. Techniques for partitioning unstructured grids among processors and for extracting parallelism in explicit and implicit solvers are discussed. Finally, some dynamic load balancing ideas, which are useful in adaptive transient computations, are presented.

Development of a finite element based delamination analysis for laminates subject to extension, bending, and torsion

NASA Technical Reports Server (NTRS)

Hooper, Steven J.

1989-01-01

Delamination is a common failure mode of laminated composite materials. This type of failure frequently occurs at the free edges of laminates where singular interlaminar stresses are developed due to the difference in Poisson's ratios between adjacent plies. Typically the delaminations develop between 90 degree plies and adjacent angle plies. Edge delamination has been studied by several investigators using a variety of techniques. Recently, Chan and Ochoa applied the quasi-three-dimensional finite element model to the analysis of a laminate subject to bending, extension, and torsion. This problem is of particular significance relative to the structural integrity of composite helicopter rotors. The task undertaken was to incorporate Chan and Ochoa's formulation into a Raju Q3DG program. The resulting program is capable of modeling extension, bending, and torsional mechanical loadings as well as thermal and hygroscopic loadings. The addition of the torsional and bending loading capability will provide the capability to perform a delamination analysis of a general unsymmetric laminate containing four cracks, each of a different length. The solutions obtained using this program are evaluated by comparing them with solutions from a full three-dimensional finite element solution. This comparison facilitates the assessment of three dimensional affects such as the warping constraint imposed by the load frame grips. It wlso facilitates the evaluation of the external load representation employed in the Q3D formulation. Finally, strain energy release rates computed from the three-dimensional results are compared with those predicted using the quasi-three-dimensional formulation.

Developments in the simulation of compressible inviscid and viscous flow on supercomputers

NASA Technical Reports Server (NTRS)

Steger, J. L.; Buning, P. G.

1985-01-01

In anticipation of future supercomputers, finite difference codes are rapidly being extended to simulate three-dimensional compressible flow about complex configurations. Some of these developments are reviewed. The importance of computational flow visualization and diagnostic methods to three-dimensional flow simulation is also briefly discussed.

Parallel Computation and Visualization of Three-dimensional, Time-dependent, Thermal Convective Flows

NASA Technical Reports Server (NTRS)

Wang, P.; Li, P.

1998-01-01

A high-resolution numerical study on parallel systems is reported on three-dimensional, time-dependent, thermal convective flows. A parallel implentation on the finite volume method with a multigrid scheme is discussed, and a parallel visualization systemm is developed on distributed systems for visualizing the flow.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aleman, S.E.

This report documents a finite element code designed to model subsurface flow and contaminant transport, named FACT. FACT is a transient three-dimensional, finite element code designed to simulate isothermal groundwater flow, moisture movement, and solute transport in variably saturated and fully saturated subsurface porous media.

User's guide to the NOZL3D and NOZLIC computer programs

NASA Technical Reports Server (NTRS)

Thomas, P. D.

1980-01-01

Complete FORTRAN listings and running instructions are given for a set of computer programs that perform an implicit numerical solution to the unsteady Navier-Stokes equations to predict the flow characteristics and performance of nonaxisymmetric nozzles. The set includes the NOZL3D program, which performs the flow computations; the NOZLIC program, which sets up the flow field initial conditions for general nozzle configurations, and also generates the computational grid for simple two dimensional and axisymmetric configurations; and the RGRIDD program, which generates the computational grid for complicated three dimensional configurations. The programs are designed specifically for the NASA-Langley CYBER 175 computer, and employ auxiliary disk files for primary data storage. Input instructions and computed results are given for four test cases that include two dimensional, three dimensional, and axisymmetric configurations.

User's manual for three dimensional FDTD version C code for scattering from frequency-independent dielectric and magnetic materials

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.

1991-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Version C is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into fourteen sections: introduction, description of the FDTD method, operation, resource requirements, Version C code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMONC.FOR), a section briefly discussing Radar Cross Section (RCS) computations, a section discussing some scattering results, a sample problem setup section, a new problem checklist, references and figure titles.

User's manual for three dimensional FDTD version D code for scattering from frequency-dependent dielectric and magnetic materials

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.

1991-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Version D is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into fourteen sections: introduction, description of the FDTD method, operation, resource requirements, Version D code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMOND.FOR), a section briefly discussing Radar Cross Section (RCS) computations, a section discussing some scattering results, a sample problem setup section, a new problem checklist, references and figure titles.

User's manual for three dimensional FDTD version A code for scattering from frequency-independent dielectric materials

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.

1992-01-01

The Penn State Finite Difference Time Domain (FDTD) Electromagnetic Scattering Code Version A is a three dimensional numerical electromagnetic scattering code based on the Finite Difference Time Domain technique. The supplied version of the code is one version of our current three dimensional FDTD code set. The manual provides a description of the code and the corresponding results for the default scattering problem. The manual is organized into 14 sections: introduction, description of the FDTD method, operation, resource requirements, Version A code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMONA.FOR), a section briefly discussing radar cross section (RCS) computations, a section discussing the scattering results, a sample problem setup section, a new problem checklist, references, and figure titles.

User's manual for three dimensional FDTD version C code for scattering from frequency-independent dielectric and magnetic materials

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.

1992-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Version C is a three-dimensional numerical electromagnetic scattering code based on the Finite Difference Time Domain (FDTD) technique. The supplied version of the code is one version of our current three-dimensional FDTD code set. The manual given here provides a description of the code and corresponding results for several scattering problems. The manual is organized into 14 sections: introduction, description of the FDTD method, operation, resource requirements, Version C code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMONC.FOR), a section briefly discussing radar cross section computations, a section discussing some scattering results, a new problem checklist, references, and figure titles.

User's manual for three dimensional FDTD version B code for scattering from frequency-dependent dielectric materials

NASA Technical Reports Server (NTRS)

Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.

1991-01-01

The Penn State Finite Difference Time Domain Electromagnetic Scattering Code Version B is a three dimensional numerical electromagnetic scattering code based upon the Finite Difference Time Domain Technique (FDTD). The supplied version of the code is one version of our current three dimensional FDTD code set. This manual provides a description of the code and corresponding results for several scattering problems. The manual is organized into fourteen sections: introduction, description of the FDTD method, operation, resource requirements, Version B code capabilities, a brief description of the default scattering geometry, a brief description of each subroutine, a description of the include file (COMMONB.FOR), a section briefly discussing Radar Cross Section (RCS) computations, a section discussing some scattering results, a sample problem setup section, a new problem checklist, references and figure titles.

Generation of three-dimensional delaunay meshes from weakly structured and inconsistent data

NASA Astrophysics Data System (ADS)

Garanzha, V. A.; Kudryavtseva, L. N.

2012-03-01

A method is proposed for the generation of three-dimensional tetrahedral meshes from incomplete, weakly structured, and inconsistent data describing a geometric model. The method is based on the construction of a piecewise smooth scalar function defining the body so that its boundary is the zero isosurface of the function. Such implicit description of three-dimensional domains can be defined analytically or can be constructed from a cloud of points, a set of cross sections, or a "soup" of individual vertices, edges, and faces. By applying Boolean operations over domains, simple primitives can be combined with reconstruction results to produce complex geometric models without resorting to specialized software. Sharp edges and conical vertices on the domain boundary are reproduced automatically without using special algorithms. Refs. 42. Figs. 25.

Temperature distributions and thermal stresses in a graded zirconia/metal gas path seal system for aircraft gas turbine engines

NASA Technical Reports Server (NTRS)

Taylor, C. M.; Bill, R. C.

1978-01-01

A ceramic/metallic aircraft gas turbine outer gas path seal designed for improved engine performance was studied. Transient temperature and stress profiles in a test seal geometry were determined by numerical analysis. During a simulated engine deceleration cycle from sea-level takeoff to idle conditions, the maximum seal temperature occurred below the seal surface, therefore the top layer of the seal was probably subjected to tensile stresses exceeding the modulus of rupture. In the stress analysis both two- and three-dimensional finite element computer programs were used. Predicted trends of the simpler and more easily usable two-dimensional element programs were borne out by the three-dimensional finite element program results.

A 3-D turbulent flow analysis using finite elements with k-ɛ model

NASA Astrophysics Data System (ADS)

Okuda, H.; Yagawa, G.; Eguchi, Y.

1989-03-01

This paper describes the finite element turbulent flow analysis, which is suitable for three-dimensional large scale problems. The k-ɛ turbulence model as well as the conservation equations of mass and momentum are discretized in space using rather low order elements. Resulting coefficient matrices are evaluated by one-point quadrature in order to reduce the computational storage and the CPU cost. The time integration scheme based on the velocity correction method is employed to obtain steady state solutions. For the verification of this FEM program, two-dimensional plenum flow is simulated and compared with experiment. As the application to three-dimensional practical problems, the turbulent flows in the upper plenum of the fast breeder reactor are calculated for various boundary conditions.

Direct Numerical Simulation of Fingering Instabilities in Coating Flows

NASA Astrophysics Data System (ADS)

Eres, Murat H.; Schwartz, Leonard W.

1998-11-01

We consider stability and finger formation in free surface flows. Gravity driven downhill drainage and temperature gradient driven climbing flows are two examples of such problems. The former situation occurs when a mound of viscous liquid on a vertical wall is allowed to flow. Constant surface shear stress due to temperature gradients (Marangoni stress) can initiate the latter problem. The evolution equations are derived using the lubrication approximation. We also include the effects of finite-contact angles in the evolution equations using a disjoining pressure model. Evolution equations for both problems are solved using an efficient alternating-direction-implicit method. For both problems a one-dimensional base state is established, that is steady in a moving reference frame. This base state is unstable to transverse perturbations. The transverse wavenumbers for the most rapidly growing modes are found through direct numerical solution of the nonlinear evolution equations, and are compared with published experimental results. For a range of finite equilibrium contact angles, the fingers can grow without limit leading to semi-finite steady fingers in a moving coordinate system. A computer generated movie of the nonlinear simulation results, for several sets of input parameters, will be shown.

Flow simulations about steady-complex and unsteady moving configurations using structured-overlapped and unstructured grids

NASA Technical Reports Server (NTRS)

Newman, James C., III

1995-01-01

The limiting factor in simulating flows past realistic configurations of interest has been the discretization of the physical domain on which the governing equations of fluid flow may be solved. In an attempt to circumvent this problem, many Computational Fluid Dynamic (CFD) methodologies that are based on different grid generation and domain decomposition techniques have been developed. However, due to the costs involved and expertise required, very few comparative studies between these methods have been performed. In the present work, the two CFD methodologies which show the most promise for treating complex three-dimensional configurations as well as unsteady moving boundary problems are evaluated. These are namely the structured-overlapped and the unstructured grid schemes. Both methods use a cell centered, finite volume, upwind approach. The structured-overlapped algorithm uses an approximately factored, alternating direction implicit scheme to perform the time integration, whereas, the unstructured algorithm uses an explicit Runge-Kutta method. To examine the accuracy, efficiency, and limitations of each scheme, they are applied to the same steady complex multicomponent configurations and unsteady moving boundary problems. The steady complex cases consist of computing the subsonic flow about a two-dimensional high-lift multielement airfoil and the transonic flow about a three-dimensional wing/pylon/finned store assembly. The unsteady moving boundary problems are a forced pitching oscillation of an airfoil in a transonic freestream and a two-dimensional, subsonic airfoil/store separation sequence. Accuracy was accessed through the comparison of computed and experimentally measured pressure coefficient data on several of the wing/pylon/finned store assembly's components and at numerous angles-of-attack for the pitching airfoil. From this study, it was found that both the structured-overlapped and the unstructured grid schemes yielded flow solutions of comparable accuracy for these simulations. This study also indicated that, overall, the structured-overlapped scheme was slightly more CPU efficient than the unstructured approach.

Three-dimensional calculations of rotor-airframe interaction in forward flight

NASA Technical Reports Server (NTRS)

Zori, Laith A. J.; Mathur, Sanjay R.; Rajagopalan, R. G.

1992-01-01

A method for analyzing the mutual aerodynamic interaction between a rotor and an airframe model has been developed. This technique models the rotor implicitly through the source terms of the momentum equations. A three-dimensional, incompressible, laminar, Navier-Stokes solver in cylindrical coordinates was developed for analyzing the rotor/airframe problem. The calculations are performed on a simplified model at an advance ratio of 0.1. The airframe surface pressure predictions are found to be in good agreement with wind tunnel test data. Results are presented for velocity and pressure field distributions in the wake of the rotor.

Three-dimensional aerodynamic shape optimization of supersonic delta wings

NASA Technical Reports Server (NTRS)

Burgreen, Greg W.; Baysal, Oktay

1994-01-01

A recently developed three-dimensional aerodynamic shape optimization procedure AeSOP(sub 3D) is described. This procedure incorporates some of the most promising concepts from the area of computational aerodynamic analysis and design, specifically, discrete sensitivity analysis, a fully implicit 3D Computational Fluid Dynamics (CFD) methodology, and 3D Bezier-Bernstein surface parameterizations. The new procedure is demonstrated in the preliminary design of supersonic delta wings. Starting from a symmetric clipped delta wing geometry, a Mach 1.62 asymmetric delta wing and two Mach 1. 5 cranked delta wings were designed subject to various aerodynamic and geometric constraints.

Vectorization on the star computer of several numerical methods for a fluid flow problem

NASA Technical Reports Server (NTRS)

Lambiotte, J. J., Jr.; Howser, L. M.

1974-01-01

A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.

A History of the Description of the Three-Dimensional Finite Rotation

NASA Astrophysics Data System (ADS)

Fraiture, Luc

2009-01-01

A history of the description of a three-dimensional finite rotation is given starting with Cardano in the middle of the sixteenth century and ending with Bryan in the beginning of the past century. Description means both a textual description and/or a mathematical representation. To appreciate the historical context of the milestones reached over the centuries, the background and personality of the main players in this history are given. At the end, a short critical discussion is added, reviewing the present names of rotation parameters in use related to the scientists which have been considered here.

MHOST version 4.2. Volume 1: Users' manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1989-01-01

This manual describes the user options available for running the MHOST finite element analysis package. MHOST is a solid and structural analysis program based on mixed finite element technology, and is specifically designed for three-dimensional inelastic analysis. A family of two- and three-dimensional continuum elements along with beam and shell structural elements can be utilized. Many options are available in the constitutive equation library, the solution algorithms and the analysis capabilities. An overview of the algorithms, a general description of the input data formats, and a discussion of input data for selecting solution algorithms are given.

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro

2017-04-01

We present an efficient implicit incompressible smoothed particle hydrodynamics (I2SPH) discretization of Navier-Stokes, Poisson-Boltzmann, and advection-diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The I2SPH's accuracy and convergence are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. The new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

NASA Astrophysics Data System (ADS)

Xing, F.; Masson, R.; Lopez, S.

2017-09-01

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.

Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course

ERIC Educational Resources Information Center

Kull, Trent C.

2011-01-01

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)

NASA Astrophysics Data System (ADS)

Lee, Jin

2014-05-01

The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.

Finite element probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bacvarov, D.C.

1981-01-01

A new method for probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes is presented. The utilized approach of applying the finite element method for probabilistic risk assessment is demonstrated to be very powerful. The reasons for this are two. First, the finite element method is inherently suitable for analysis of three dimensional spaces where the parameters, such as three variate probability densities of the lightning currents, are non-uniformly distributed. Second, the finite element method permits non-uniform discretization of the three dimensional probability spaces thus yielding high accuracy in critical regions, such as the area of themore » low probability events, while at the same time maintaining coarse discretization in the non-critical areas to keep the number of grid points and the size of the problem to a manageable low level. The finite element probabilistic risk assessment method presented here is based on a new multidimensional search algorithm. It utilizes an efficient iterative technique for finite element interpolation of the transmission line insulation flashover criteria computed with an electro-magnetic transients program. Compared to other available methods the new finite element probabilistic risk assessment method is significantly more accurate and approximately two orders of magnitude computationally more efficient. The method is especially suited for accurate assessment of rare, very low probability events.« less

A comparison of three-dimensional nonequilibrium solution algorithms applied to hypersonic flows with stiff chemical source terms

NASA Technical Reports Server (NTRS)

Palmer, Grant; Venkatapathy, Ethiraj

1993-01-01

Three solution algorithms, explicit underrelaxation, point implicit, and lower upper symmetric Gauss-Seidel (LUSGS), are used to compute nonequilibrium flow around the Apollo 4 return capsule at 62 km altitude. By varying the Mach number, the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness. The performance of the solution algorithms degraded as the Mach number and stiffness of the flow increased. At Mach 15, 23, and 30, the LUSGS method produces an eight order of magnitude drop in the L2 norm of the energy residual in 1/3 to 1/2 the Cray C-90 computer time as compared to the point implicit and explicit under-relaxation methods. The explicit under-relaxation algorithm experienced convergence difficulties at Mach 23 and above. At Mach 40 the performance of the LUSGS algorithm deteriorates to the point it is out-performed by the point implicit method. The effects of the viscous terms are investigated. Grid dependency questions are explored.

Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite element method

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1992-01-01

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique.

Finite element analysis of helicopter structures

NASA Technical Reports Server (NTRS)

Rich, M. J.

1978-01-01

Application of the finite element analysis is now being expanded to three dimensional analysis of mechanical components. Examples are presented for airframe, mechanical components, and composite structure calculations. Data are detailed on the increase of model size, computer usage, and the effect on reducing stress analysis costs. Future applications for use of finite element analysis for helicopter structures are projected.

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

PubMed

Deng, Yongbo; Korvink, Jan G

2016-05-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

PubMed Central

Korvink, Jan G.

2016-01-01

This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable. PMID:27279766

Implicit solution of three-dimensional internal turbulent flows

NASA Technical Reports Server (NTRS)

Michelassi, V.; Liou, M.-S.; Povinelli, Louis A.; Martelli, F.

1991-01-01

The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.

Development and Application of a Numerical Framework for Improving Building Foundation Heat Transfer Calculations

NASA Astrophysics Data System (ADS)

Kruis, Nathanael J. F.

Heat transfer from building foundations varies significantly in all three spatial dimensions and has important dynamic effects at all timescales, from one hour to several years. With the additional consideration of moisture transport, ground freezing, evapotranspiration, and other physical phenomena, the estimation of foundation heat transfer becomes increasingly sophisticated and computationally intensive to the point where accuracy must be compromised for reasonable computation time. The tools currently available to calculate foundation heat transfer are often either too limited in their capabilities to draw meaningful conclusions or too sophisticated to use in common practices. This work presents Kiva, a new foundation heat transfer computational framework. Kiva provides a flexible environment for testing different numerical schemes, initialization methods, spatial and temporal discretizations, and geometric approximations. Comparisons within this framework provide insight into the balance of computation speed and accuracy relative to highly detailed reference solutions. The accuracy and computational performance of six finite difference numerical schemes are verified against established IEA BESTEST test cases for slab-on-grade heat conduction. Of the schemes tested, the Alternating Direction Implicit (ADI) scheme demonstrates the best balance between accuracy, performance, and numerical stability. Kiva features four approaches of initializing soil temperatures for an annual simulation. A new accelerated initialization approach is shown to significantly reduce the required years of presimulation. Methods of approximating three-dimensional heat transfer within a representative two-dimensional context further improve computational performance. A new approximation called the boundary layer adjustment method is shown to improve accuracy over other established methods with a negligible increase in computation time. This method accounts for the reduced heat transfer from concave foundation shapes, which has not been adequately addressed to date. Within the Kiva framework, three-dimensional heat transfer that can require several days to simulate is approximated in two-dimensions in a matter of seconds while maintaining a mean absolute deviation within 3%.

Three-dimensional whispering gallery modes in InGaAs nanoneedle lasers on silicon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tran, T.-T. D.; Chen, R.; Ng, K. W.

2014-09-15

As-grown InGaAs nanoneedle lasers, synthesized at complementary metal–oxide–semiconductor compatible temperatures on polycrystalline and crystalline silicon substrates, were studied in photoluminescence experiments. Radiation patterns of three-dimensional whispering gallery modes were observed upon optically pumping the needles above the lasing threshold. Using the radiation patterns as well as finite-difference-time-domain simulations and polarization measurements, all modal numbers of the three-dimensional whispering gallery modes could be identified.

A diagonal implicit scheme for computing flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Eberhardt, Scott; Imlay, Scott

1990-01-01

A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

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.

Implicit time-marching solution of the Navier-Stokes equations for thrust reversing and thrust vectoring nozzle flows

NASA Technical Reports Server (NTRS)

Imlay, S. T.

1986-01-01

An implicit finite volume method is investigated for the solution of the compressible Navier-Stokes equations for flows within thrust reversing and thrust vectoring nozzles. Thrust reversing nozzles typically have sharp corners, and the rapid expansion and large turning angles near these corners are shown to cause unacceptable time step restrictions when conventional approximate factorization methods are used. In this investigation these limitations are overcome by using second-order upwind differencing and line Gauss-Siedel relaxation. This method is implemented with a zonal mesh so that flows through complex nozzle geometries may be efficiently calculated. Results are presented for five nozzle configurations including two with time varying geometries. Three cases are compared with available experimental data and the results are generally acceptable.

Implicit approximate-factorization schemes for the low-frequency transonic equation

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Steger, J. L.

1975-01-01

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

Modeling of high pressure arc-discharge with a fully-implicit Navier-Stokes stabilized finite element flow solver

NASA Astrophysics Data System (ADS)

Sahai, A.; Mansour, N. N.; Lopez, B.; Panesi, M.

2017-05-01

This work addresses the modeling of high pressure electric discharge in an arc-heated wind tunnel. The combined numerical solution of Poisson’s equation, radiative transfer equations, and the set of Favre-averaged thermochemical nonequilibrium Navier-Stokes equations allows for the determination of the electric, radiation, and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles with the Chapman-Enskog method. A multi-temperature formulation is used to account for thermal non-equilibrium. Finally, the turbulence closure of the flow equations is obtained by means of the Spalart-Allmaras model, which requires the solution of an additional scalar transport equation. A Streamline upwind Petrov-Galerkin stabilized finite element formulation is employed to solve the Navier-Stokes equation. The electric field equation is solved using the standard Galerkin formulation. A stable formulation for the radiative transfer equations is obtained using the least-squares finite element method. The developed simulation framework has been applied to investigate turbulent plasma flows in the 20 MW Aerodynamic Heating Facility at NASA Ames Research Center. The current model is able to predict the process of energy addition and re-distribution due to Joule heating and thermal radiation, resulting in a hot central core surrounded by colder flow. The use of an unsteady three-dimensional treatment also allows the asymmetry due to a dynamic electric arc attachment point in the cathode chamber to be captured accurately. The current work paves the way for detailed estimation of operating characteristics for arc-heated wind tunnels which are critical in testing thermal protection systems.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Holographically Fabricated Photonic Crystals with Large Reflectance

DTIC Science & Technology

2008-07-16

CLASSIFICATION OF: We report reflection and transmission spectra from three-dimensional polymer photonic crystals fabricated by holographic...transmission spectra from three-dimensional polymer photonic crystals fabricated by holographic lithography. The measured peak reflectance matches that... polymer photonic crystals fabricated by holographic lithography. The measured peak reflectance matches that predicted by both a finite-difference time

Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsuchiya, Shunji; Department of Physics, Waseda University, 3-4-1 Okubo, Tokyo 169-8555; Griffin, Allan

2005-11-15

We study the Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures, extending our recent work on one-dimensional (1D) optical lattices. We use a Bose-Hubbard tight-binding model and the Popov approximation to calculate the temperature dependence of the number of condensate atoms n{sup c0}(T) in each lattice well. As with 1D optical lattices, damping only occurs if the Bogoliubov excitations exhibit anomalous dispersion (i.e., the excitation energy bends upward at low momentum), analogous to the case of phonons in superfluid {sup 4}He. This leads to the disappearance of all damping processes in a D-dimensional simplemore » cubic optical lattice when Un{sup c0}{>=}6DJ, where U is the on-site interaction, and J is the hopping matrix element.« less

Implicit flux-split schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Thomas, J. L.; Walters, R. W.; Van Leer, B.

1985-01-01

Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.

Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Efficient Numerical Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Bardina, J. E.

1994-01-01

A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in complex geometries with good accuracy.

ANSYS duplicate finite-element checker routine

NASA Technical Reports Server (NTRS)

Ortega, R.

1995-01-01

An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.

Human vocal tract resonances and the corresponding mode shapes investigated by three-dimensional finite-element modelling based on CT measurement.

PubMed

Vampola, Tomáš; Horáček, Jaromír; Laukkanen, Anne-Maria; Švec, Jan G

2015-04-01

Resonance frequencies of the vocal tract have traditionally been modelled using one-dimensional models. These cannot accurately represent the events in the frequency region of the formant cluster around 2.5-4.5 kHz, however. Here, the vocal tract resonance frequencies and their mode shapes are studied using a three-dimensional finite element model obtained from computed tomography measurements of a subject phonating on vowel [a:]. Instead of the traditional five, up to eight resonance frequencies of the vocal tract were found below the prominent antiresonance around 4.7 kHz. The three extra resonances were found to correspond to modes which were axially asymmetric and involved the piriform sinuses, valleculae, and transverse vibrations in the oral cavity. The results therefore suggest that the phenomenon of speaker's and singer's formant clustering may be more complex than originally thought.

[Nasolabial muscle finite-element study and clinical application].

PubMed

Yin, Ningbei; Wu, Jiajun; Chen, Bo; Wang, Yongqian; Song, Tao; Ma, Hengyuan

2015-05-01

To investigate the nasolabial muscle anatomy and biomechanical characteristics. Micro-computed tomography scan was performed in 8 cases of spontaneous abortion fetus lip nasal specimens to construct a three-dimensional model. The nasolabial muscle structure was analyzed using Mimics software. The three-dimensional configuration model of nasolabial muscle was established based on local anatomy and tissue section, and compared with tissue section. Three dimensional finite element analysis was performed on lip nasal muscle related biomechanics and surface deformation in Application verification was carried out in 263 cases of microform cleft lip surgery. There was close relationship between nasolabial muscle. The nasolabial muscle tension system was constituted, based on which a new cleft lip repair surgery was designed and satisfied results were achieved. There is close relationship among nasolabial muscle in anatomy, histology and biomechanics. To obtain better effect, cleft lip repair should be performed on the basis of recovering muscle tension system.

Coarse-grained mechanics of viral shells

NASA Astrophysics Data System (ADS)

Klug, William S.; Gibbons, Melissa M.

2008-03-01

We present an approach for creating three-dimensional finite element models of viral capsids from atomic-level structural data (X-ray or cryo-EM). The models capture heterogeneous geometric features and are used in conjunction with three-dimensional nonlinear continuum elasticity to simulate nanoindentation experiments as performed using atomic force microscopy. The method is extremely flexible; able to capture varying levels of detail in the three-dimensional structure. Nanoindentation simulations are presented for several viruses: Hepatitis B, CCMV, HK97, and φ29. In addition to purely continuum elastic models a multiscale technique is developed that combines finite-element kinematics with MD energetics such that large-scale deformations are facilitated by a reduction in degrees of freedom. Simulations of these capsid deformation experiments provide a testing ground for the techniques, as well as insight into the strength-determining mechanisms of capsid deformation. These methods can be extended as a framework for modeling other proteins and macromolecular structures in cell biology.

WIND: Computer program for calculation of three dimensional potential compressible flow about wind turbine rotor blades

NASA Technical Reports Server (NTRS)

Dulikravich, D. S.

1980-01-01

A computer program is presented which numerically solves an exact, full potential equation (FPE) for three dimensional, steady, inviscid flow through an isolated wind turbine rotor. The program automatically generates a three dimensional, boundary conforming grid and iteratively solves the FPE while fully accounting for both the rotating cascade and Coriolis effects. The numerical techniques incorporated involve rotated, type dependent finite differencing, a finite volume method, artificial viscosity in conservative form, and a successive line overrelaxation combined with the sequential grid refinement procedure to accelerate the iterative convergence rate. Consequently, the WIND program is capable of accurately analyzing incompressible and compressible flows, including those that are locally transonic and terminated by weak shocks. The program can also be used to analyze the flow around isolated aircraft propellers and helicopter rotors in hover as long as the total relative Mach number of the oncoming flow is subsonic.

a Cell Vertex Algorithm for the Incompressible Navier-Stokes Equations on Non-Orthogonal Grids

NASA Astrophysics Data System (ADS)

Jessee, J. P.; Fiveland, W. A.

1996-08-01

The steady, incompressible Navier-Stokes (N-S) equations are discretized using a cell vertex, finite volume method. Quadrilateral and hexahedral meshes are used to represent two- and three-dimensional geometries respectively. The dependent variables include the Cartesian components of velocity and pressure. Advective fluxes are calculated using bounded, high-resolution schemes with a deferred correction procedure to maintain a compact stencil. This treatment insures bounded, non-oscillatory solutions while maintaining low numerical diffusion. The mass and momentum equations are solved with the projection method on a non-staggered grid. The coupling of the pressure and velocity fields is achieved using the Rhie and Chow interpolation scheme modified to provide solutions independent of time steps or relaxation factors. An algebraic multigrid solver is used for the solution of the implicit, linearized equations.A number of test cases are anlaysed and presented. The standard benchmark cases include a lid-driven cavity, flow through a gradual expansion and laminar flow in a three-dimensional curved duct. Predictions are compared with data, results of other workers and with predictions from a structured, cell-centred, control volume algorithm whenever applicable. Sensitivity of results to the advection differencing scheme is investigated by applying a number of higher-order flux limiters: the MINMOD, MUSCL, OSHER, CLAM and SMART schemes. As expected, studies indicate that higher-order schemes largely mitigate the diffusion effects of first-order schemes but also shown no clear preference among the higher-order schemes themselves with respect to accuracy. The effect of the deferred correction procedure on global convergence is discussed.

Second order tensor finite element

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.

1990-01-01

The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.

Transonic flow analysis for rotors. Part 2: Three-dimensional, unsteady, full-potential calculation

NASA Technical Reports Server (NTRS)

Chang, I. C.

1985-01-01

A numerical method is presented for calculating the three-dimensional unsteady, transonic flow past a helicopter rotor blade of arbitrary geometry. The method solves the full-potential equations in a blade-fixed frame of reference by a time-marching implicit scheme. At the far-field, a set of first-order radiation conditions is imposed, thus minimizing the reflection of outgoing wavelets from computational boundaries. Computed results are presented to highlight radial flow effects in three dimensions, to compare surface pressure distributions to quasi-steady predictions, and to predict the flow field on a swept-tip blade. The results agree well with experimental data for both straight- and swept-tip blade geometries.

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

Three-dimensional structural analysis using interactive graphics

NASA Technical Reports Server (NTRS)

Biffle, J.; Sumlin, H. A.

1975-01-01

The application of computer interactive graphics to three-dimensional structural analysis was described, with emphasis on the following aspects: (1) structural analysis, and (2) generation and checking of input data and examination of the large volume of output data (stresses, displacements, velocities, accelerations). Handling of three-dimensional input processing with a special MESH3D computer program was explained. Similarly, a special code PLTZ may be used to perform all the needed tasks for output processing from a finite element code. Examples were illustrated.

Comparison of Gap Elements and Contact Algorithm for 3D Contact Analysis of Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Tiku, K.; Kumar, A.; Handschuh, R.

1994-01-01

Three dimensional stress analysis of spiral bevel gears in mesh using the finite element method is presented. A finite element model is generated by solving equations that identify tooth surface coordinates. Contact is simulated by the automatic generation of nonpenetration constraints. This method is compared to a finite element contact analysis conducted with gap elements.

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

NASA Astrophysics Data System (ADS)

Regnier, D.; Dubray, N.; Verrière, M.; Schunck, N.

2018-04-01

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the large amplitude collective motion of quantum many-body systems such as atomic nuclei. Under the Gaussian Overlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in a multi-dimensional collective space. In this paper, we present the version 2.0 of the code FELIX that solves the collective Schrödinger equation in a finite element basis. This new version features: (i) the ability to solve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) support for new kinds of finite elements and different types of quadrature to compute the discretized Hamiltonian and overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylov approximation of the time propagator for time integration instead of the implicit Crank-Nicolson method implemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on an analytic problem as well as on realistic two-dimensional calculations of the low-energy fission of 240Pu and 256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplex elements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectral element method with a degree 4 polynomial basis. We emphasize that in a realistic calculation of fission mass distributions of 240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numerical precision of a few percents).

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

NASA Technical Reports Server (NTRS)

Rao, K. V.; Pletcher, R. H.; Steger, J. L.; Vandalsem, W. R.

1987-01-01

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

A three-dimensional finite element model of near-field scanning microwave microscopy

NASA Astrophysics Data System (ADS)

Balusek, Curtis; Friedman, Barry; Luna, Darwin; Oetiker, Brian; Babajanyan, Arsen; Lee, Kiejin

2012-10-01

A three-dimensional finite element model of an experimental near-field scanning microwave microscope (NSMM) has been developed and compared to experiment on non conducting samples. The microwave reflection coefficient S11 is calculated as a function of frequency with no adjustable parameters. There is qualitative agreement with experiment in that the resonant frequency can show a sizable increase with sample dielectric constant; a result that is not obtained with a two-dimensional model. The most realistic model shows a semi-quantitative agreement with experiment. The effect of different sample thicknesses and varying tip sample distances is investigated numerically and shown to effect NSMM performance in a way consistent with experiment. Visualization of the electric field indicates that the field is primarily determined by the shape of the coupling hooks.

Visions of visualization aids - Design philosophy and observations

NASA Technical Reports Server (NTRS)

Ellis, Stephen R.

1989-01-01

Aids for the visualization of high-dimensional scientific or other data must be designed. Simply casting multidimensional data into a two-dimensional or three-dimensional spatial metaphor does not guarantee that the presentation will provide insight or a parsimonious description of phenomena implicit in the data. Useful visualization, in contrast to glitzy, high-tech, computer-graphics imagery, is generally based on preexisting theoretical beliefs concerning the underlying phenomena. These beliefs guide selection and formatting of the plotted variables. Visualization tools are useful for understanding naturally three-dimensional data bases such as those used by pilots or astronauts. Two examples of such aids for spatial maneuvering illustrate that informative geometric distortion may be introduced to assist visualization and that visualization of complex dynamics alone may not be adequate to provide the necessary insight into the underlying processes.

A semi-implicit level set method for multiphase flows and fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Cottet, Georges-Henri; Maitre, Emmanuel

2016-06-01

In this paper we present a novel semi-implicit time-discretization of the level set method introduced in [8] for fluid-structure interaction problems. The idea stems from a linear stability analysis derived on a simplified one-dimensional problem. The semi-implicit scheme relies on a simple filter operating as a pre-processing on the level set function. It applies to multiphase flows driven by surface tension as well as to fluid-structure interaction problems. The semi-implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost. It is validated through comparisons with the original explicit scheme and refinement studies on two-dimensional benchmarks.

A cell-vertex multigrid method for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Radespiel, R.

1989-01-01

A cell-vertex scheme for the Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, very good convergence rates are obtained for a wide range of two- and three-dimensional flows over airfoils and wings. The accuracy of the code is examined by grid refinement studies and comparison with experimental data. For an accurate prediction of turbulent flows with strong separations, a modified version of the nonequilibrium turbulence model of Johnson and King is introduced, which is well suited for an implementation into three-dimensional Navier-Stokes codes. It is shown that the solutions for three-dimensional flows with strong separations can be dramatically improved, when a nonequilibrium model of turbulence is used.

Three-Dimensional Ignition and Flame Propagation Above Liquid Fuel Pools: Computational Analysis

NASA Technical Reports Server (NTRS)

Cai, Jinsheng; Sirignano, William A.

2001-01-01

A three-dimensional unsteady reactive Navier-Stokes code is developed to study the ignition and flame spread above liquid fuels initially below the flashpoint temperature. Opposed air flow to the flame spread due to forced and/or natural convection is considered. Pools of finite width and length are studied in air channels of prescribed height and width. Three-dimensional effects of the flame front near the edge of the pool are captured in the computation. The formation of a recirculation zone in the gas phase similar to that found in two-dimensional calculations is also present in the three-dimensional calculations. Both uniform spread and pulsating spread modes are found in the calculated results.

Calculation of three-dimensional compressible laminar and turbulent boundary layers. Calculation of three-dimensional compressible boundary layers on arbitrary wings

NASA Technical Reports Server (NTRS)

Cebeci, T.; Kaups, K.; Ramsey, J.; Moser, A.

1975-01-01

A very general method for calculating compressible three-dimensional laminar and turbulent boundary layers on arbitrary wings is described. The method utilizes a nonorthogonal coordinate system for the boundary-layer calculations and includes a geometry package that represents the wing analytically. In the calculations all the geometric parameters of the coordinate system are accounted for. The Reynolds shear-stress terms are modeled by an eddy-viscosity formulation developed by Cebeci. The governing equations are solved by a very efficient two-point finite-difference method used earlier by Keller and Cebeci for two-dimensional flows and later by Cebeci for three-dimensional flows.

Analysis of high-rise constructions with the using of three-dimensional models of rods in the finite element program PRINS

NASA Astrophysics Data System (ADS)

Agapov, Vladimir

2018-03-01

The necessity of new approaches to the modeling of rods in the analysis of high-rise constructions is justified. The possibility of the application of the three-dimensional superelements of rods with rectangular cross section for the static and dynamic calculation of the bar and combined structures is considered. The results of the eighteen-story spatial frame free vibrations analysis using both one-dimensional and three-dimensional models of rods are presented. A comparative analysis of the obtained results is carried out and the conclusions on the possibility of three-dimensional superelements application in static and dynamic analysis of high-rise constructions are given on its basis.

A gradient enhanced plasticity-damage microplane model for concrete

NASA Astrophysics Data System (ADS)

Zreid, Imadeddin; Kaliske, Michael

2018-03-01

Computational modeling of concrete poses two main types of challenges. The first is the mathematical description of local response for such a heterogeneous material under all stress states, and the second is the stability and efficiency of the numerical implementation in finite element codes. The paper at hand presents a comprehensive approach addressing both issues. Adopting the microplane theory, a combined plasticity-damage model is formulated and regularized by an implicit gradient enhancement. The plasticity part introduces a new microplane smooth 3-surface cap yield function, which provides a stable numerical solution within an implicit finite element algorithm. The damage part utilizes a split, which can describe the transition of loading between tension and compression. Regularization of the model by the implicit gradient approach eliminates the mesh sensitivity and numerical instabilities. Identification methods for model parameters are proposed and several numerical examples of plain and reinforced concrete are carried out for illustration.

Computational plasticity algorithm for particle dynamics simulations

NASA Astrophysics Data System (ADS)

Krabbenhoft, K.; Lyamin, A. V.; Vignes, C.

2018-01-01

The problem of particle dynamics simulation is interpreted in the framework of computational plasticity leading to an algorithm which is mathematically indistinguishable from the common implicit scheme widely used in the finite element analysis of elastoplastic boundary value problems. This algorithm provides somewhat of a unification of two particle methods, the discrete element method and the contact dynamics method, which usually are thought of as being quite disparate. In particular, it is shown that the former appears as the special case where the time stepping is explicit while the use of implicit time stepping leads to the kind of schemes usually labelled contact dynamics methods. The framing of particle dynamics simulation within computational plasticity paves the way for new approaches similar (or identical) to those frequently employed in nonlinear finite element analysis. These include mixed implicit-explicit time stepping, dynamic relaxation and domain decomposition schemes.

A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES

EPA Science Inventory

A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...

Effect of Surface Nonequilibrium Thermochemistry in Simulation of Carbon Based Ablators

NASA Technical Reports Server (NTRS)

Chen, Yih-Kang; Gokcen, Tahir

2012-01-01

This study demonstrates that coupling of a material thermal response code and a flow solver using finite-rate gas/surface interaction model provides time-accurate solutions for multidimensional ablation of carbon based charring ablators. The material thermal response code used in this study is the Two-dimensional Implicit Thermal Response and Ablation Program (TITAN), which predicts charring material thermal response and shape change on hypersonic space vehicles. Its governing equations include total energy balance, pyrolysis gas momentum conservation, and a three-component decomposition model. The flow code solves the reacting Navier-Stokes equations using Data Parallel Line Relaxation (DPLR) method. Loose coupling between material response and flow codes is performed by solving the surface mass balance in DPLR and the surface energy balance in TITAN. Thus, the material surface recession is predicted by finite-rate gas/surface interaction boundary conditions implemented in DPLR, and the surface temperature and pyrolysis gas injection rate are computed in TITAN. Two sets of gas/surface interaction chemistry between air and carbon surface developed by Park and Zhluktov, respectively, are studied. Coupled fluid-material response analyses of stagnation tests conducted in NASA Ames Research Center arc-jet facilities are considered. The ablating material used in these arc-jet tests was a Phenolic Impregnated Carbon Ablator (PICA). Computational predictions of in-depth material thermal response and surface recession are compared with the experimental measurements for stagnation cold wall heat flux ranging from 107 to 1100 Watts per square centimeter.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

DCOMP Award Lecture (Metropolis): A 3D Spectral Anelastic Hydrodynamic Code for Shearing, Stratified Flows

NASA Astrophysics Data System (ADS)

Barranco, Joseph

2006-03-01

We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (eg, the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The time-independent background state is stably stratified in the vertical direction and has a unidirectional linear shear flow aligned with one horizontal axis. Superposed on this background state is an unsteady, subsonic flow that is evolved with the Euler equations subject to the anelastic approximation to filter acoustic phenomena. A Fourier-Fourier basis in a set of quasi-Lagrangian coordinates that advect with the background shear is used for spectral expansions in the two horizontal directions. For the vertical direction, two different sets of basis functions have been implemented: (1) Chebyshev polynomials on a truncated, finite domain, and (2) rational Chebyshev functions on an infinite domain. Use of this latter set is equivalent to transforming the infinite domain to a finite one with a cotangent mapping, and using cosine and sine expansions in the mapped coordinate. The nonlinear advection terms are time integrated explicitly, whereas the Coriolis force, buoyancy terms, and pressure/enthalpy gradient are integrated semi- implicitly. We show that internal gravity waves can be damped by adding new terms to the Euler equations. The code exhibits excellent parallel performance with the Message Passing Interface (MPI). As a demonstration of the code, we simulate vortex dynamics in protoplanetary disks and the Kelvin-Helmholtz instability in the dusty midplanes of protoplanetary disks.

A 3D spectral anelastic hydrodynamic code for shearing, stratified flows

NASA Astrophysics Data System (ADS)

Barranco, Joseph A.; Marcus, Philip S.

2006-11-01

We have developed a three-dimensional (3D) spectral hydrodynamic code to study vortex dynamics in rotating, shearing, stratified systems (e.g., the atmosphere of gas giant planets, protoplanetary disks around newly forming protostars). The time-independent background state is stably stratified in the vertical direction and has a unidirectional linear shear flow aligned with one horizontal axis. Superposed on this background state is an unsteady, subsonic flow that is evolved with the Euler equations subject to the anelastic approximation to filter acoustic phenomena. A Fourier Fourier basis in a set of quasi-Lagrangian coordinates that advect with the background shear is used for spectral expansions in the two horizontal directions. For the vertical direction, two different sets of basis functions have been implemented: (1) Chebyshev polynomials on a truncated, finite domain, and (2) rational Chebyshev functions on an infinite domain. Use of this latter set is equivalent to transforming the infinite domain to a finite one with a cotangent mapping, and using cosine and sine expansions in the mapped coordinate. The nonlinear advection terms are time-integrated explicitly, the pressure/enthalpy terms are integrated semi-implicitly, and the Coriolis force and buoyancy terms are treated semi-analytically. We show that internal gravity waves can be damped by adding new terms to the Euler equations. The code exhibits excellent parallel performance with the message passing interface (MPI). As a demonstration of the code, we simulate the merger of two 3D vortices in the midplane of a protoplanetary disk.

Analysis of Aerospike Plume Induced Base-Heating Environment

NASA Technical Reports Server (NTRS)

Wang, Ten-See

1998-01-01

Computational analysis is conducted to study the effect of an aerospike engine plume on X-33 base-heating environment during ascent flight. To properly account for the effect of forebody and aftbody flowfield such as shocks and to allow for potential plume-induced flow-separation, thermo-flowfield of trajectory points is computed. The computational methodology is based on a three-dimensional finite-difference, viscous flow, chemically reacting, pressure-base computational fluid dynamics formulation, and a three-dimensional, finite-volume, spectral-line based weighted-sum-of-gray-gases radiation absorption model computational heat transfer formulation. The predicted convective and radiative base-heat fluxes are presented.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.

PubMed

Xu, X Q

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Four-Dimensional Continuum Gyrokinetic Code: Neoclassical Simulation of Fusion Edge Plasmas

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2005-10-01

We are developing a continuum gyrokinetic code, TEMPEST, to simulate edge plasmas. Our code represents velocity space via a grid in equilibrium energy and magnetic moment variables, and configuration space via poloidal magnetic flux and poloidal angle. The geometry is that of a fully diverted tokamak (single or double null) and so includes boundary conditions for both closed magnetic flux surfaces and open field lines. The 4-dimensional code includes kinetic electrons and ions, and electrostatic field-solver options, and simulates neoclassical transport. The present implementation is a Method of Lines approach where spatial finite-differences (higher order upwinding) and implicit time advancement are used. We present results of initial verification and validation studies: transition from collisional to collisionless limits of parallel end-loss in the scrape-off layer, self-consistent electric field, and the effect of the real X-point geometry and edge plasma conditions on the standard neoclassical theory, including a comparison of our 4D code with other kinetic neoclassical codes and experiments.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (ψ,θ,γ,μ) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Recognition of 3-D symmetric objects from range images in automated assembly tasks

NASA Technical Reports Server (NTRS)

Alvertos, Nicolas; Dcunha, Ivan

1990-01-01

A new technique is presented for the three dimensional recognition of symmetric objects from range images. Beginning from the implicit representation of quadrics, a set of ten coefficients is determined for symmetric objects like spheres, cones, cylinders, ellipsoids, and parallelepipeds. Instead of using these ten coefficients trying to fit them to smooth surfaces (patches) based on the traditional way of determining curvatures, a new approach based on two dimensional geometry is used. For each symmetric object, a unique set of two dimensional curves is obtained from the various angles at which the object is intersected with a plane. Using the same ten coefficients obtained earlier and based on the discriminant method, each of these curves is classified as a parabola, circle, ellipse, or hyperbola. Each symmetric object is found to possess a unique set of these two dimensional curves whereby it can be differentiated from the others. It is shown that instead of using the three dimensional discriminant which involves evaluation of the rank of its matrix, it is sufficient to use the two dimensional discriminant which only requires three arithmetic operations.

THREE-DIMENSIONAL MODELING OF COHESIVE SEDIMENT TRANSPORT IN A PARTIALLY STRATIFIED MICRO-TIDAL ESTUARY TO ASSESS EFFECTIVENESS OF SEDIMENT TRAPS

EPA Science Inventory

The three-dimensional (3D) finite difference model Environmental Fluid Dynamics Code (EFDC) was used to simulate the hydrodynamics and sediment transport in a partially stratified micro-tidal estuary. The estuary modeled consisted of a 16-km reach of the St. Johns River, Florida,...

Generation of a composite grid for turbine flows and consideration of a numerical scheme

NASA Technical Reports Server (NTRS)

Choo, Y.; Yoon, S.; Reno, C.

1986-01-01

A composite grid was generated for flows in turbines. It consisted of the C-grid (or O-grid) in the immediate vicinity of the blade and the H-grid in the middle of the blade passage between the C-grids and in the upstream region. This new composite grid provides better smoothness, resolution, and orthogonality than any single grid for a typical turbine blade with a large camber and rounded leading and trailing edges. The C-H (or O-H) composite grid has an unusual grid point that is connected to more than four neighboring nodes in two dimensions (more than six neighboring nodes in three dimensions). A finite-volume lower-upper (LU) implicit scheme to be used on this grid poses no problem and requires no special treatment because each interior cell of this composite grid has only four neighboring cells in two dimensions (six cells in three dimensions). The LU implicit scheme was demonstrated to be efficient and robust for external flows in a broad flow regime and can be easily applied to internal flows and extended from two to three dimensions.

Real-time, interactive animation of deformable two- and three-dimensional objects

DOEpatents

Desbrun, Mathieu; Schroeder, Peter; Meyer, Mark; Barr, Alan H.

2003-06-03

A method of updating in real-time the locations and velocities of mass points of a two- or three-dimensional object represented by a mass-spring system. A modified implicit Euler integration scheme is employed to determine the updated locations and velocities. In an optional post-integration step, the updated locations are corrected to preserve angular momentum. A processor readable medium and a network server each tangibly embodying the method are also provided. A system comprising a processor in combination with the medium, and a system comprising the server in combination with a client for accessing the server over a computer network, are also provided.

Viscous real gas flowfields about three dimensional configurations

NASA Technical Reports Server (NTRS)

Balakrishnan, A.; Davy, W. C.

1983-01-01

Laminar, real gas hypersonic flowfields over a three dimensional configuration are computed using an unsteady, factored implicit scheme. Local chemical and thermodynamic properties are evaluated by an equilibrium composition method. Transport properties are obtained from individual species properties and application of a mixture rule. Numerical solutions are presented for an ideal gas and equilibrium air for free-stream Mach numbers of 13 and 15 and at various angles of attack. The effect of real gas is to decrease the shock-layer thickness resulting from decreased shock-layer temperatures and corresponding increased density. The combined effects of viscosity and real gas are to increase the subsonic layer near the wall.

ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noble, Charles R.; Anderson, Andrew T.; Barton, Nathan R.

ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.

Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics

DOE PAGES

Pan, Wenxiao; Kim, Kyungjoo; Perego, Mauro; ...

2017-01-03

In this paper, we present a consistent implicit incompressible smoothed particle hydrodynamics (I 2SPH) discretization of Navier–Stokes, Poisson–Boltzmann, and advection–diffusion equations subject to Dirichlet or Robin boundary conditions. It is applied to model various two and three dimensional electrokinetic flows in simple or complex geometries. The accuracy and convergence of the consistent I 2SPH are examined via comparison with analytical solutions, grid-based numerical solutions, or empirical models. Lastly, the new method provides a framework to explore broader applications of SPH in microfluidics and complex fluids with charged objects, such as colloids and biomolecules, in arbitrary complex geometries.

Improved Design of Tunnel Supports : Volume 3 : Finite Element Analysis of the Peachtree Center Station in Atlanta

DOT National Transportation Integrated Search

1980-06-01

Volume 3 contains the application of the three-dimensional (3-D) finite element program, Automatic Dynamic Incremental Nonlinear Analysis (ADINA), which was designed to replace the traditional 2-D plane strain analysis, to a specific location. The lo...