139 research outputs found
Vectorizable algorithms for adaptive schemes for rapid analysis of SSME flows
An initial study into vectorizable algorithms for use in adaptive schemes for various types of boundary value problems is described. The focus is on two key aspects of adaptive computational methods which are crucial in the use of such methods (for complex flow simulations such as those in the Space Shuttle Main Engine): the adaptive scheme itself and the applicability of element-by-element matrix computations in a vectorizable format for rapid calculations in adaptive mesh procedures
Adaptive computational methods for aerothermal heating analysis
The development of adaptive gridding techniques for finite-element analysis of fluid dynamics equations is described. The developmental work was done with the Euler equations with concentration on shock and inviscid flow field capturing. Ultimately this methodology is to be applied to a viscous analysis for the purpose of predicting accurate aerothermal loads on complex shapes subjected to high speed flow environments. The development of local error estimate strategies as a basis for refinement strategies is discussed, as well as the refinement strategies themselves. The application of the strategies to triangular elements and a finite-element flux-corrected-transport numerical scheme are presented. The implementation of these strategies in the GIM/PAGE code for 2-D and 3-D applications is documented and demonstrated
Analysis and Development of Finite Element Methods for the Study of Nonlinear Thermomechanical Behavior of Structural Components
Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states
Pre- and postprocessing techniques for determining goodness of computational meshes
Research in error estimation, mesh conditioning, and solution enhancement for finite element, finite difference, and finite volume methods has been incorporated into AUDITOR, a modern, user-friendly code, which operates on 2D and 3D unstructured neutral files to improve the accuracy and reliability of computational results. Residual error estimation capabilities provide local and global estimates of solution error in the energy norm. Higher order results for derived quantities may be extracted from initial solutions. Within the X-MOTIF graphical user interface, extensive visualization capabilities support critical evaluation of results in linear elasticity, steady state heat transfer, and both compressible and incompressible fluid dynamics
A hybrid-stress finite element for linear anisotropic elasticity
Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased
Corrector Operator to Enhance Accuracy and Reliability of Neural Operator Surrogates of Nonlinear Variational Boundary-Value Problems
This work focuses on developing methods for approximating the solution
operators of a class of parametric partial differential equations via neural
operators. Neural operators have several challenges, including the issue of
generating appropriate training data, cost-accuracy trade-offs, and nontrivial
hyperparameter tuning. The unpredictability of the accuracy of neural operators
impacts their applications in downstream problems of inference, optimization,
and control. A framework is proposed based on the linear variational problem
that gives the correction to the prediction furnished by neural operators. The
operator associated with the corrector problem is referred to as the corrector
operator. Numerical results involving a nonlinear diffusion model in two
dimensions with PCANet-type neural operators show almost two orders of increase
in the accuracy of approximations when neural operators are corrected using the
proposed scheme. Further, topology optimization involving a nonlinear diffusion
model is considered to highlight the limitations of neural operators and the
efficacy of the correction scheme. Optimizers with neural operator surrogates
are seen to make significant errors (as high as 80 percent). However, the
errors are much lower (below 7 percent) when neural operators are corrected
following the proposed method.Comment: 34 pages, 14 figure
Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity
Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory
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