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v itilttttttttttflfff,
'
S i o i d P iifticlp Hydrodynamics
a meshfree particle method
G R Liu
National University of Singapore
M B Liu
SmoothPd Pdrticlp Hydrodyndmics
a meshfree particle method ''
i^11t'
World Scientific
NEW JERSEY • LONDON • SINGAPORE • SHANGHAI • HONGKONG • TAIPEI • BANGALORE
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: Suite 202, 1060 Main Street, River Edge, NJ 07661
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
SMOOTHED PARTICLE HYDRODYNAMICS
A Meshfree Particle Method
Copyright © 2003 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN 981-238-456-1
Printed in Singapore by World Scientific Printers (S) Pte Ltd
To Zuona
Yun, Kun, Run,
and my family
for the time and support they gave to me
G. R. Liu
To Huiqi
for her love, support and encouragement
M. B. Liu
V
Preface
Background
Numerical simulation using computers has increasingly become a very important
approach for solving problems in engineering and science. It plays a valuable
role in providing tests and examinations for theories, offering
insights to
complex physics, and assisting in the interpretation and even the discovery of
new phenomena. Grid or mesh based numerical methods such as the finite
difference methods (FDM) and the finite element methods (FDM) have been
widely applied to various areas of computational fluid dynamics (CFD) and
computational solid mechanics (CSM), and are currently the dominant methods
in numerical simulations for solving problems in engineering and science.
Despite the great success, grid-based numerical methods suffer
from
difficulties in some aspects, which limit their applications in many complex
problems. The major difficulties are inherited from the use of grid or mesh.
Because the entire formulation is based on the grid/mesh, a time-consuming and
costly process of generating/regenerating a quality grid/mesh is necessary. The
use of grid/mesh can lead to difficulties in dealing with problems with free
surface, deformable boundary, moving interface (for FDM), and extremely large
deformation (for FEM).
A recent strong interest is focused on the next generation computational
methods — meshfree methods, which are expected
to
conventional grid-based FDM and FEM in many applications. A large number
of meshfree methods have been proposed for different applications, as detailed in
the recent monograph on meshfree methods by G. R. Liu (2002). These
to be superior
vu
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