Prediction of three-dimensional general shape extrudates by an implicit iterative scheme

1992 ◽  
Vol 14 (5) ◽  
pp. 609-625 ◽  
Author(s):  
Vincent Legat ◽  
Jean-Marie Marchal
Keyword(s):  
Iterative Scheme ◽  
Three Dimensional ◽  
General Shape ◽  
Implicit Iterative Scheme

Numerical Analysis of Turbine Coolant Passage Flows

1998 ◽  
Author(s):  
Meng-Sing Liou ◽  
K. P. Singh
Keyword(s):  
Iterative Scheme ◽  
Three Dimensional ◽  
Nasa Lewis Research ◽  
Reynolds Stresses ◽  
Complex Flow ◽  
Internal Flows ◽  
The Matrix ◽  
Turbine Component ◽  
Unstructured Tetrahedral Meshes ◽  
Matrix Bandwidth

We report in this paper a project undertaken at NASA Lewis Research Center with an aim at achieving a timely, reliable, and high-fidelity CFD prediction of aeropropulsion systems. The present paper specifically addresses issues relevant to internal flows in a turbine component. The flows are three dimensional, highly viscous and turbulent and the geometry is complex. We choose to discretize the computation domain with unstructured tetrahedral meshes and approximate the inviscid fluxes with the recent upwind scheme, AUSM+. An implicit discrete system of unknowns is solved by the Gauss-Seidel Jacobi iterative scheme with a coloring strategy to reduce the matrix bandwidth. A one-equation turbulence model is used to represent the Reynolds stresses. To calculate the complex flow in a turbine coolant passage, we first validate the code for unit problems that contain some subset features. The calculations show excellent results for the backward-facing step and the 180-degree-turn duct. Finally we provide a detailed analysis of the flow in the simulated geometry of th turbine coolant passage.

Irrotational flow past bodies close to a plane surface

1971 ◽  
Vol 50 (3) ◽  
pp. 481-491 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Asymptotic Expansion ◽  
Numerical Computation ◽  
Potential Flow ◽  
Close Agreement ◽  
Plane Surface ◽  
Three Dimensional ◽  
Ground Surface ◽  
Two Dimensional ◽  
General Shape ◽  
Irrotational Flow

A theroetical analysis is given for potential flow over, around and under a vehicle of general shape moving close to a plane ground surface. Solutions are given both in the form of a small-gap asymptotic expansion and a direct numerical computation, with close agreement between the two for two-dimensional flows with and without circulation. Some results for three-dimensional bodies are discussed.

scholarly journals Implicit Iterative Method for Hierarchical Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
L.-C. Ceng ◽  
Q. H. Ansari ◽  
N.-C. Wong ◽  
J.-C. Yao
Keyword(s):  
Variational Inequality ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Fixed Point Set ◽  
Implicit Iterative Method ◽  
Point Set ◽  
Implicit Iterative Scheme ◽  
Necessary And Sufficient

We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained.

Identification of nonlinear B–H curves based on magnetic field computations and multigrid methods for ill-posed problems

2003 ◽  
Vol 14 (1) ◽  
pp. 15-38 ◽  
Author(s):  
BARBARA KALTENBACHER ◽  
MANFRED KALTENBACHER ◽  
STEFAN REITZINGER
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Three Dimensional ◽  
Multigrid Methods ◽  
Stopping Criterion ◽  
Nonlinear Inverse Problem ◽  
Field Problem ◽  
Ill Posed

Our task is the identification of the reluctivity $\nu\,{=}\,\nu(B)$ in $\vec{H}\,{=}\,\nu(B) \vec{B}$, ($B\,{=}\,|\vec{B}|$) from measurements of the magnetic flux for different excitation currents in a driving coil, in the context of a nonuniform magnetic field distribution. This is a nonlinear inverse problem and ill-posed in the sense of unstable data dependence, whose solution is done numerically by a Newton type iterative scheme, regularized by an appropriate stopping criterion. The computational complexity of this method is determined by the number of necessary forward evaluations, i.e. the number of numerical solutions to the three-dimensional magnetic field problem. We keep the effort minimal by applying a special discretization strategy to the inverse problem, based on multigrid methods for ill-posed problems. Numerical results demonstrate the efficiency of the proposed method.

scholarly journals Fixed point results of an implicit iterative scheme for fractal generations

2021 ◽  
Vol 6 (12) ◽  
pp. 13170-13186
Author(s):  
Haixia Zhang ◽  
◽  
Muhammad Tanveer ◽  
Yi-Xia Li ◽  
Qingxiu Peng ◽  
...  
Keyword(s):  
Fixed Point ◽  
Iterative Scheme ◽  
Mandelbrot Set ◽  
Complex Polynomial ◽  
Ishikawa Iteration ◽  
General Complex ◽  
Implicit Iterative Scheme ◽  
Implicit Iteration

<abstract><p>In this paper, we derive the escape criteria for general complex polynomial $ f(x) = \sum_{i = 0}^{p}a_{i}x^{i} $ with $ p\geq2 $, where $ a_{i} \in \mathbb{C} $ for $ i = 0, 1, 2, \dots, p $ to generate the fractals. Moreover, we study the orbit of an implicit iteration (i.e., Jungck-Ishikawa iteration with $ s $-convexity) and develop algorithms for Mandelbrot set and Multi-corn or Multi-edge set. Moreover, we draw some complex graphs and observe how the graph of Mandelbrot set and Multi-corn or Multi-edge set vary with the variation of $ a_{i} $'s.</p></abstract>

An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow

2000 ◽  
Vol 422 ◽  
pp. 207-223 ◽  
Author(s):  
SØREN OTT ◽  
JAKOB MANN
Keyword(s):  
Experimental Data ◽  
Experimental Investigation ◽  
Turbulent Flow ◽  
Particle Tracking ◽  
Three Dimensional ◽  
Direct Interaction ◽  
General Shape ◽  
Particle Pairs ◽  
Oscillating Grids ◽  
A Minor

The particle tracking (PT) technique is used to study turbulent diffusion of particle pairs in a three-dimensional turbulent flow generated by two oscillating grids. The experimental data show a range where the Richardson–Obukhov law 〈r2〉 = Cεt3 is satisfied, and the Richardson–Obukhov constant is found to be C = 0.5. A number of models predict much larger values. Furthermore, the distance–neighbour function is studied in detail in order to determine its general shape. The results are compared with the predictions of three models: Richardson (1926), Batchelor (1952) and Kraichnan (1966a). These three models predict different behaviours of the distance–neighbour function, and of the three, only Richardson's model is found to be consistent with the measurements. We have corrected a minor error in Kraichnan's (1996a) Lagrangian history direct interaction calculations with the result that we had to increase his theoretical value from C = 2.42 to C = 5.5.

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