Download presentation

Published byHannah Kelley Modified over 4 years ago

1
**Fast Adaptive Hybrid Mesh Generation Based on Quad-tree Decomposition**

Mohamed Ebeida Mechanical and Aeronautical Eng. Dept –UCDavis Bay Area Scientific Computing Day 2008 March 29, 2008

2
**Motivation Structured Grids Unstructured Grids**

Relatively simple geometries Algebraic – Elliptic – Hyperbolic methods Line relaxation solvers Structured Multigrid solvers Adaptation using quad-tree or oct-tree decomp (FEM) Grid quality Unstructured Grids Complex geometries Delaunay point insertion algorithms / advancing front re-triangulation mesh points can move Agglomeration Multigrid solvers Adaptation using quad-tree or oct-tree (FEM) Grid quality

3
Motivation Sophisticated Multiblock and Overlapping Structured Grid Techniques are required for Complex Geometries Overlapping grid system on space shuttle (Slotnick, Kandula and Buning 1994)

4
**Motivation Multigrid solvers**

Multigrid techniques enable optimal O(N) solution complexity Based on sequence of coarse and fine meshes Originally developed for structured grids

5
Motivation Agglomeration Multigrid solvers for unstructured meshes

6
**Quad-tree decomposition**

Fast Adaptive Grid Quality Line solvers Hanging nodes Multigrid Complex geometries

7
**Our Goals A fast technique Quality Complex geometries**

Adaptive (geometries – solution variables) Multigrid Line relaxation solvers No hanging nodes Simple optimization steps (3D) Parallelizable

8
**Spatial Decomposition**

9
**Strategy Algorithm Algorithm 1 Adaptive grid based on the geometries**

Adaptive grid based on the Simulation

10
**Algorithm 1 - Geometries**

Start with a coarse Cartesian grid with aspect ratio = 1.0 Dim: 30x30 Sp = 2.0 256 points

11
**Algorithm 1 - Geometries**

Perform successive refinements till you reach a level that resolves the curvature of the geometries of the domain

12
**Algorithm 1 - Geometries**

Level of refinements depend on the curvature of each shape

13
**Algorithm 1 - Geometries**

Define a buffer zone and delete any element with a node in that zone

14
**Algorithm 1 - Geometries**

Project nodes on the edge of the buffer zone orthogonally to the geometry

15
**Algorithm 1 - Geometries**

Move nodes on the edge of the buffer zone orthogonally to the geometry to adjust B.L. elements

16
**Algorithm 1 - Geometries**

17
Another way ! Increase the width of the buffer zone and create boundary elements explicitly better bounds!

19
**Algorithm 1 - Geometries**

Final mesh 22416 pts 22064 elem. Quad dom % Min edge length 7.6 x 10 Max A.R. = 64 -6

20
Complex geometries

21
**Testing Algorithm 1 output**

22
**Algorithm 2 – Simulation based**

Use the output of Algorithm 1 as a base mesh for the spatial decomposition Run the simulation for n time steps (unsteady) or n iterations (steady) Perform Spatial decomposition on the base mesh based on a level set function. Map the variables from the grid used in the last simulation

23
**How about transition elements?**

In order to ensure quality, transition element has to advance one step per spatial decomposition level x x

24
Results

26
Multigrid Levels Spatial decomposition allows us to generate prolongation and restriction operators easily How about the elements of each grid level? We already have them

27
Multigrid Levels

28
Multigrid Results For elliptic equations, the application of Multigrid is straight forward once we have the grid levels. For convection diffusion equations, line solvers are crucial for good results

29
**Checking our Goals A fast technique Quality Complex geometries**

Adaptive with a starting coarse grid Multigrid Line relaxation solvers No hanging nodes Simple optimization steps (3D) Parallelizable

30
Thank you!

Similar presentations

OK

THREE-DIMENSIONAL UNSTRUCTURED MESH GENERATION FOR ARBITRARY DOMAINS WITH CRACKS Joaquim Bento Cavalcante-Neto Department of Computing Federal University.

THREE-DIMENSIONAL UNSTRUCTURED MESH GENERATION FOR ARBITRARY DOMAINS WITH CRACKS Joaquim Bento Cavalcante-Neto Department of Computing Federal University.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on self development definition Ppt on world diabetes day theme Ppt on bio battery download Option call put ppt on loop Ppt on amplitude shift keying modem Ppt on carbon and its compounds elements Ppt on water resources in india Ppt on producers consumers and decomposers ecosystem Ppt on fire alarm system Ppt on synthesis and degradation of purines and pyrimidines a g