52. Define mixed element grids? Nowadays it becomes increasingly popular to build unstructured grids from various element types. For example, hexahedra or prisms are employed to discretise boundary layers. The rest of the flow domain is filled with tetrahedra. Pyramids are used as transitional elements between the hexahedra or the prisms and the tetrahedral. Hence the name mixed element grids .
COMPUTATIONAL FLUID DYNAMICS TWO MARKS QUESTION AND ANSWER 18 53. Write the unstructured grid generation methodology. Unstructured grid generation methodologies for CFD applications are mostly based on either an (1) Delaunay, method. or (2) Advancing-front method. 54. Define Dirichlet tessellatipn or Voronoj diagram? The Delaunay triangulation is based on a methodology proposed by Dirichlet in 1850 for the unique subdivision of space into a set of packed convex regions. Given a set of points, each region represents the space around the particular point, which is closer to that point than to any other. The regions form polygons (polyhedra in 3D) which are known as the Dirichlet tessellation or the Voronoj diagram . 55. Define Delaunay triangulation? If we connect point pairs which share some segment(face) of the Voronoj diagram by straight lines, we obtain the Delaunay triangulation. The triangulation defines a set of triangles (tetrahedra in 3D),which cover the convex hull of the points. This is displayed in Fig. a. The DeIaunay triangulation is the dual of the Voronoj diagram. The nodes of the Voronoj polygons are in 2D the centres of circumcircles of the triangles. In 3D, the nodes represent the centres of circumspheres of the tetrahedra. This implies that the circumcircle of every triangle (circumsphere of every tetrahedron) contains no point from the set in its interior . 56. Write the ‘Prandtl’s boundary layer equations’.
COMPUTATIONAL FLUID DYNAMICS TWO MARKS QUESTION AND ANSWER 19 57. Write Transformation of the Boundary Layer Equations e denotes the values at the outer edge of the boundary layer flow and R denotes the local radius of a body of revolution. 58. Write the governing equation of steady diffusion ?
COMPUTATIONAL FLUID DYNAMICS TWO MARKS QUESTION AND ANSWER 20 59. What is weak instability? The results of the calculation are displayed in Fig.a. One notices that the perturbation on u 1 gives rise to amplifying oscillations. In fact, as small as the initial perturbation may be - and there will always be one because of round off errors – it will eventually lead to an explosion of the numerical solution. This phenomenon is clearly inacceptable. It is named weak instability . 60. Define finite element method? The finite element method (FEM) is a numerical technique for solving partial differential equations (PDE’s). 61. Write the essential characteristic of FEM in CFD? Its first essential characteristic is that the continuum field, or domain , is subdivided into cells, called elements , which form a grid. The elements (in 2D) have a triangular or a quadrilateral form and can be rectilinear or curved. The grid itself need not be structured. With unstructured grids and curved cells , complex geometries can be handled with ease.
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- Summer '18