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NASA NTRS1988

Nonconforming mortar element methods: Application to spectral discretizations

Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.

Maday, Yvon↗

NASA NTRS1989

A three-node C deg element for analysis of laminated composite sandwich shells

A three-node flat shell element with C deg rotation fields has been developed for analysis of arbitrary composite shells. The element may consist of any number of orthotropic layers, each layer having different material properties and angular orientation. The formulation includes coupling between bending and extension, which is essential for analysis of unsymmetric laminates. Shearing deflections are included, since laminated and sandwich construction frequently results in shear stiffness much smaller than bending stiffness. Formulation of the element is straightforward, and calculation of its stiffness matrix is simple and fast. Convergence of solutions with mesh refinement is uniform for both thin and thick shells and is insensitive to element shape, although not as rapid as some other elements that lack one or more capabilities of the newly developed element. An experimental verification of the shall element is reported in the appendix.

Martin, C. Wayne↗

NASA NTRS1989

Vortex breakdown simulation - A circumspect study of the steady, laminar, axisymmetric model

The incompressible axisymmetric steady Navier-Stokes equations are written using the streamfunction-vorticity formulation. The resulting equations are discretized using a second-order central-difference scheme. The discretized equations are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers (based on vortex core radius) 100-1800 and swirl parameter 0.9-1.1. The effects of inflow boundary conditions, the location of farfield and outflow boundaries, and mesh refinement are examined. Finally, the stability of the steady solutions is investigated by solving the time-dependent equations.

Salas, M. D.↗

NASA NTRS1989

Low Reynolds number numerical solutions of chaotic flow

Numerical computations of two-dimensional flow past an airfoil at low Mach number, large angle of attack, and low Reynolds number are reported which show a sequence of flow states leading from single-period vortex shedding to chaos via the period-doubling mechanism. Analysis of the flow in terms of phase diagrams, Poincare sections, and flowfield variables are used to substantiate these results. The critical Reynolds number for the period-doubling bifurcations is shown to be sensitive to mesh refinement and the influence of large amounts of numerical dissipation. In extreme cases, large amounts of added dissipation can delay or completely eliminate the chaotic response. The effect of artificial dissipation at these low Reynolds numbers is to produce a new effective Reynolds number for the computations.

Pulliam, Thomas H.↗

NASA NTRS1988

Finite element substructuring methods for composite mechanics

Finite element substructuring strategies are presented to obtain numerical solutions for three typical problems of interest to the composites community: (1) impact and toughness characterization of composites using Charpy's impact test specimen; (2) free-edge stress analysis of composite laminates; and (3) fracture toughness predictions of composites for individual and combined fracture of modes I, II, and III. The key issue common to these problems is the presence of singular or near singular stress fields. The regions prone to see steep stress gradients are substructured with progressively refined meshes to study the local response simultaneously with the global response. The results from the select examples indicate that finite element substructuring methods are computationally effective for composite singularity mechanics.

Murthy, P. L. N.↗

NASA NTRS1989

International Conference on Numerical Methods in Fluid Dynamics, 11th, Williamsburg, VA, June 27-July 1, 1988, Proceedings

Recent advances in computational fluid dynamics (CFD) are discussed in reviews and reports. Topics addressed include CFD models in plasma dynamics, parallel computation for simulation studies, CFD for hypersonic airbreathing aircraft, multigrid methods for the steady incompressible Navier-Stokes equations, upwind differencing techniques, TV stable schemes for shock-interacting flows, Euler models of hypersonic vortex flows, parallel multilevel adaptive methods, and vortex methods for slightly viscous three-dimensional flows. Consideration is given to the accuracy of node-based solutions on irregular meshes, multigrid calculations for cascades, a finite-volume-element method for planar cavity flow, parallel heterogeneous mesh refinement for advection-diffusion equations, the convergence of the spectral-viscosity method for nonlinear conservation laws, and numerical simulations of Taylor vortices in a spherical gap.

Dwoyer, D. L.↗

NASA NTRS1989

Modeling of turbulence for compression corner flows and internal flows

A compressible Reynolds averaged Navier-Stokes code is applied to examine the performances of basic turbulence models for unseparated and separated flows. The turbulence models considered are a zero-equation model and several two-equation models, including a new k-epsilon model with an eddy viscosity damping function depending upon the Reynolds number and the distance from the wall. The turbulence models are assessed using the following experimental flows: a channel flow, a backward facing step, and a two-dimensional compression corner at Mach 2.8. Discussions and comparisons of the experimental and numerical results are given. Mesh refinement is shown to have a significant beneficial effect on free shear layer flow results obtained with two-equation turbulence models. The results illustrate the usefulness of several turbulence models as a design tool for fluid engineering systems.

Champney, J. M.↗

NASA NTRS1989

Evaluation of the heat transfer module (FAHT) of Failure Analysis Nonlinear Thermal And Structural Integrated Code (FANTASTIC)

The heat transfer module of FANTASTIC Code (FAHT) is studied and evaluated to the extend possible during the ten weeks duration of this project. A brief background of the previous studies is given and the governing equations as modeled in FAHT are discussed. FAHT's capabilities and limitations based on these equations and its coding methodology are explained in detail. It is established that with improper choice of element size and time step FAHT's temperature field prediction at some nodes will be below the initial condition. The source of this unrealistic temperature prediction is identified and a procedure is proposed for avoiding this phenomenon. It is further shown that the proposed procedure will converge to an accurate prediction upon mesh refinement. Unfortunately due to lack of time FAHT's ability to accurately account for pyrolysis and surface ablation has not been verified. Therefore, at the present time it can be stated with confidence that FAHT can accurately predict the temperature field for a transient multi-dimensional, orthotropic material with directional dependence, variable property, with nonlinear boundary condition. Such a prediction will provide an upper limit for the temperature field in an ablating decomposing nozzle liner. The pore pressure field, however, will not be known.

Keyhani, Majid↗

NASA NTRS1990

Reliability analysis of a structural ceramic combustion chamber

The Weibull modulus, fracture toughness and thermal properties of a silicon nitride material used to make a gas turbine combustor were experimentally measured. The location and nature of failure origins resulting from bend tests were determined with fractographic analysis. The measured Weibull parameters were used along with thermal and stress analysis to determine failure probabilities of the combustor with the CARES design code. The effect of data censoring, FEM mesh refinement, and fracture criterion were considered in the analysis.

Salem, Jonathan A.↗

NASA NTRS1990

Adaptive quadrilateral and triangular finite-element scheme for compressible flows

The development of an adaptive mesh refinement procedure for analyzing high-speed compressible flows using the finite-element method is described. This new adaptation procedure, which uses both quadrilateral and triangular elements, was implemented with two explicit finite-element algorithms - the two-step Taylor-Galerkin and the multistep Galerkin-Runge-Kutta schemes. A von Neumann stability analysis and a rotating 'cosine hill'problem demonstrate the instability of the Taylor-Galerkin scheme when coupled with the adaptation procedure. For the same adaptive refinement scheme, the Galerkin-Runge-Kutta procedure yields stable solutions within its explicit stability limit. The utility of this new adaptation procedure for the prediction of compressible flow features is illustrated for inviscid problems involving strong shock interactions at hypersonic speeds.

Ramakrishnan, R.↗

NASA NTRS1989

Finite element analysis of high speed compressible flows using mesh refinement/movement procedures

An adaptive mesh refinement procedure for analyzing high-speed inviscid and viscous compressible flows is described. The adaptation procedure which uses both quadrilateral and triangular elements is implemented with an explicit finite element formulation. Elements in regions of strong and weak gradients are refined or coarsened based on inviscid and viscous indicators. Nodal locations are also adaptively moved to better resolve flow features. The effectiveness of the finite element procedure is demonstrated by modeling flows with complex shock structure and viscous-inviscid interactions. Numerical results are compared with experimental data.

Ramakrishnan, R.↗

NASA NTRS1990

Numerical simulation of an F-16A at angle of attack

The transonic flowfield around an F-16A fighter configuration at a moderate incidence angle is simulated by solving the Navier-Stokes equations on a single-block grid. The numerical solution matches experimental freestream conditions with a mach number of 0.85, 16 degrees angle of attack, and a characteristic Reynolds number of 12.75 million. MacCormack's explicit algorithm is used in conjuction with a local time step and consecutive mesh refinement procedure to accelerate numerical convergence. The Baldwin-Lomax algebraic model provides turbulent closure. Computed surface pressure distributions and the aircraft lift coefficient compare favorably with wind tunnel data. The drag coefficient in the simulation overpredicts the experimental value by 8 percent.

Huband, G. W.↗

NASA NTRS1990

Multigrid Calculations of a Jet in Crossflow

A series of numerical calculations are made of a jet in crossflow using progressive mesh refinement up to 2.4 million grid points. A solution algorithm that combined the features of a point-coupled solution of the momentum and continuity equations with multigrid acceleration demonstrated efficient convergence of the governing equations. In comparisons with experimental data, some features of the jet flow field were found to be predicted reasonably well, but the results still remain affected by numerical diffusion.

Claus, R. W.↗

NASA NTRS1990

Behaviour of plate elements based on the first-order shear deformation theory

A new analytical technique to assess the performance of shear deformable elements is presented, which makes it possible to determine a priori whether a given element will lock when used to model thin structures. The role that shear constraints play in determining the behavior of thin elements was established by comparing the results of key numerical tests with the predictions of element behavior made by studying the form of the shear constraints. Conclusions regarding locking behavior and the effects of reduced integration in thin shear deformable elements are presented, including the findings (1) that singularity of the shear stiffness matrix is not sufficient to avoid locking; (2) that the effect of mesh refinement on an element that contains spurious constraints is two-fold; and (3) that reduced integration does not remove spurious constraints but rather relaxes them. The results of the study are in agreement with previous studies of Mindlin plate elements in regarding Lagrangian elements as superior to serendipity elements when either full or reduced integration is employed.

Averill, R. C.↗

NASA NTRS1991

Developing and utilizing an Euler computational method for predicting the airframe/propulsion effects for an aft-mounted turboprop transport. Volume 1: Theory document

An Euler flow solver was developed for predicting the airframe/propulsion integration effects for an aft-mounted turboprop transport. This solver employs a highly efficient multigrid scheme, with a successive mesh-refinement procedure to accelerate the convergence of the solution. A new dissipation model was also implemented to render solutions that are grid insensitive. The propeller power effects are simulated by the actuator disk concept. An embedded flow solution method was developed for predicting the detailed flow characteristics in the local vicinity of an aft-mounted propfan engine in the presence of a flow field induced by a complete aircraft. Results from test case analysis are presented. A user's guide for execution of computer programs, including format of various input files, sample job decks, and sample input files, is provided in an accompanying volume.

Chen, H. C.↗

NASA NTRS1991

A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems

An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction.

Thompson, C. P.↗

NASA NTRS1990

An isoparametric finite-element Stokes flow test problem

Two-dimensional Stokes flow of an incompressible Newtonian fluid about a horizontal cylinder situated next to a moving wall is presented and suggested as a nontrivial benchmark problem. Both the primitive variable Galerkin finite-element and the exact solutions are generated on a sequence of refined meshes. Error norms and convergence rates are presented for the C(o) bilinear-velocity/C(-1) piecewise constant-pressure and the C(o) biquadratic-velocity/C(-1) linear-pressure quadrilateral elements.

Maslanik, Miriam K.↗

NASA NTRS1991

Adaptive finite element analysis of hypersonic laminar flows for aerothermal load predictions

The use of an adaptive mesh refinement procedure for analyzing hypersonic laminar flows with application to aerothermal load predictions is described. The adaptation procedure, which uses both quadrilateral and triangular elements, is implemented with the multistep Galerkin-Runge-Kutta scheme. Elements that lie in regions of strong gradients are refined based on indicators to obtain better definition of flow features. The effectiveness of the adaptive procedure is demonstrated by modeling Mach 11.7 flow over a 15-deg ramp. Numerical results are compared with predictions of strong interaction theories and experimental data. Surface quantities such as heating rates and pressure loads, critical for the effective design of high-speed vehicles, are found to be in good agreement with experimental values.

Ramakrishnan, R.↗