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