Computational Fluid Dynamics CFD - Lunds tekniska högskola

Computational Fluid Dynamics

CFD

Solving system of equations,

Grid generation

2

Basic steps of CFD

Problem

?

•Gov. Eq.

•BC

•Init. Cond.

...,, jijti uu

•Discretization •Result

•Solution•OK?

Discretisation and grid

Questions:

•How complex is the geometry?

•What accuracy is required? Grid quality?

•What about stability?

•Grid refinement?

Grid generation-classification

4

Structured

Number of blocks

Mono Multi

Hierarchy

Cartesian

Shape

H C O

Orthogonality

Orthogonal

Body-fitted

Oct-tree

Unstructured

Tetra-hedral

Poly-hedral

Cell types

2-dimensional 3-dimensional

Triangular

(tri)

Quadrilateral

(quad)

Tetrahedron

(tet)

Hexahedron

(hex)

pyramid wedge

Grid types

Structured grid Unstructured grid

Unstructured grid

Grid types

Structured grid

Multi-block

Grid types

Hybrid grid

Grid typesHybrid grid

10

Structured

• Easy to generate

• Inbuilt topology

• Low memory footprint

• Fast solution algorythms

• Easy to use high-order schemes

• Difficult for complex geometries

Unstructured

• Difficult to generate

• Topology has to be stored

• Lower mesh quality

• Slow algorythms

• Difficult for high-order

• Suitable for complex geometries

Mesh quality measures

11

• Stretching

• dy2/dy1

• Best: 1

• Aspect ratio

• dy1/dx

• Best: 1

• Skewness

a

• Best: equi-angle

a

dx

dy1

dy2

Efficient grids – grid stretching

12

Large gradients

Fine resolution

Efficient grids – grid stretching

13

i

i+1

i-1

...62 3

33

2

22

1

iii

iix

Tx

x

Tx

x

TxTT

...6

)(

2

)(3

33

2

22

1

iii

iix

Txr

x

Txr

x

TxrTT

)(2

)1(

)1(

2

2

2

11 xOx

Txr

xr

TT

x

T

i

ii

• Not second order any

more!

• Can be corrected

• Extra work

Grid stretching

Grid stretching

Efficient grids – local refinement

16

Efficient grids – adaptive

refinement

17

• Right marker parameter

• P, u, T, dt/dx, etc.

• Not too often

• Comp. Time

• Errors introduced

• Not too late

• Follow the flow

features

Refinement techniques

18

• Easier to implement

• Mesh quality

decreases

• Neighbours affected

• Better quality

Other grid related issues

• Grid generation strategies

• Moving boundaries