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1

Introduction to numerical grid generation for fluid flow problems

Zimoń M., Karczewski M.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2011

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nr 139

87-98

EN

The grid construction process and the use thereof in numerical solutions of Navier-Stokes equations are both discussed. The necessary basic information is provided, from the simplified stand point of mathematical background. The emphasis throughout is on grids formed by the intersections of coordinate lines of a curvilinear coordinate system, as opposed to covering a field wit h triangular elements or a random distribution of points.

PL

Niniejszy artykuł przedstawia procedury tworzenia siatek obliczeniowych dla potrzeb symulacji przepływów, a więc zadań, w których zastosowanie ma równanie Naviera-Stokesa. Omówiony jest opis matematyczny równań transformacji konforemnej oraz metod wyższego rzędu, tj. Poisson, Laplace, hiperboliczna. Artykuł skupia się głównie na sposobach tworzenia siatek w krzywoliniowym układzie współrzędnych.

2

Volume meshing using a coupled Delaunay triangulation with advancing front technique - mathematical foundation

Kucwaj J.

Czasopismo Techniczne. Nauki Podstawowe

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2011

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R. 108, z. 1-NP

103-119

EN

The paper presents an algorithm of volume meshing by using the Advancing Front Technique (AFT) combined with the Delaunay triangulation. The tetrahedronization starts with the surface mesh with elements oriented towards the interior 3-D domain. The main idea is based upon AFT, with simultaneous points insertion and tetrahedra creation. The characteristic feature of the approach is the part of AFT in case, when a new calculated point on the current face of the front is not accepted then the existing point in the front is found to create a new tetrahedron by using Delaunay triangulation on the given set of points. Additionally the algorithm takes into account a mesh size function.

PL

Artykuł zawiera podstawowe definicje i własności podziału Dirichleta, wielościanów Voronoi oraz triangularyzacji Delaunaya. W dalszej części przedstawione są twierdzenia Delaunaya będące podstawą algorytmu triangularyzacji łączącego metody frontowe z triangularyzacją Delaunaya. Następnie przedstawiony jest algorytm łączący triangularyzację Delaunaya z metodą postępującego frontu. Artykuł kończy punkt z wynikami numerycznymi w postaci graficznej.

3

The efficiency of the application of the heap lists to the algorithm of mesh generation

Kucwaj J.

Computer Assisted Mechanics and Engineering Sciences

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2010

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Vol. 17, no. 2-3-4

137-145

EN

The paper presents an analysis of the efficiency of the application of heap lists data structures to the 2D triangular mesh generation algorithms. Such efficiency is especially important for the frontal methods for which the size of the generated mesh is controlled by a prescribed function in the considered domain. In the presented approach two advancing front procedures are presented: first for points insertion and the second for the Delaunay triangulation. If the heap lists are applied to the minimal size of frontal segment selection, a better quality mesh is obtained.

4

Numerical investigations of the convergence of a remeshing algorithm on an example of subsonic flow

Kucwaj J.

Computer Assisted Mechanics and Engineering Sciences

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2010

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Vol. 17, no. 2-3-4

149-160

EN

The main goal of the paper is to analyze convergence of a remeshing scheme evaluated by the author [8] on the example of a potential flow around a profile. It is assumed that flow is stationary, irrotational, inviscid and compressible. The problem is led to solving nonlinear differential equation with additional nonlinear algebraic equation representing the so called Kutta-Joukovsky condition. For adaptation a remeshing scheme is applied. For every adaptation step mesh is generated using grid generator [7], which generates meshes with mesh size function. The mesh size function is modified at every adaptation step by nodal values of the error indicator interpolation. The nonlinear algebraic system of equations obtained from discretizing of the problem, is solved by the application of the Newton-Raphson method.