Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves

被引:574
作者
Lind, S. J. [1 ]
Xu, R. [1 ]
Stansby, P. K. [1 ]
Rogers, B. D. [1 ]
机构
[1] Univ Manchester, Sch Mech Aerosp & Civil Engn, Manchester M13 9PL, Lancs, England
基金
英国工程与自然科学研究理事会;
关键词
Incompressible SPH; Free-surface flow simulation; Fick's law; Truncated-kernel error; SPH METHOD; SIMULATION;
D O I
10.1016/j.jcp.2011.10.027
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
The incompressible smoothed particle hydrodynamics (ISPH) method with projection-based pressure correction has been shown to be highly accurate and stable for internal flows and, importantly for many problems, the pressure field is virtually noise-free in contrast to the weakly compressible SPH approach (Xu et al., 2009 [31]). However for almost inviscid fluids instabilities at the free surface occur due to errors associated with the truncated kernels. A new algorithm is presented which remedies this issue, giving stable and accurate solutions to both internal and free-surface flows. Generalising the particle shifting approach of Xu et al. (2009) [31], the algorithm is based upon Fick's law of diffusion and shifts particles in a manner that prevents highly anisotropic distributions and the onset of numerical instability. The algorithm is validated against analytical solutions for an internal flow at higher Reynolds numbers than previously, the flow due to an impulsively started plate and highly accurate solutions for wet bed dam break problems at zero and small times. The method is then validated for progressive regular waves with paddle motion defined by linear theory. The accurate predictions demonstrate the effectiveness of the algorithm in stabilising solutions and minimising the surface instabilities generated by the inevitable errors associated with truncated kernels. The test cases are thought to provide a more thorough quantitative validation than previously undertaken. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:1499 / 1523
页数:25
相关论文
共 32 条
[1]  
Belytschko T, 1998, INT J NUMER METH ENG, V43, P785, DOI 10.1002/(SICI)1097-0207(19981115)43:5<785::AID-NME420>3.0.CO
[2]  
2-9
[3]   A CONTINUUM METHOD FOR MODELING SURFACE-TENSION [J].
BRACKBILL, JU ;
KOTHE, DB ;
ZEMACH, C .
JOURNAL OF COMPUTATIONAL PHYSICS, 1992, 100 (02) :335-354
[4]  
Buss G.Y., 1982, SAWW - a computer program to compute the properties of steady water waves
[5]   NUMERICAL SOLUTION OF NAVIER-STOKES EQUATIONS [J].
CHORIN, AJ .
MATHEMATICS OF COMPUTATION, 1968, 22 (104) :745-&
[6]   Numerical simulation of interfacial flows by smoothed particle hydrodynamics [J].
Colagrossi, A ;
Landrini, M .
JOURNAL OF COMPUTATIONAL PHYSICS, 2003, 191 (02) :448-475
[7]   An SPH projection method [J].
Cummins, SJ ;
Rudman, M .
JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 152 (02) :584-607
[8]  
Dean R.G., 1991, ADV SERIES OCEAN ENG
[9]  
Dold JW., 1986, NUMERICAL METHODS UI, P671
[10]   Incompressible smoothed particle hydrodynamics [J].
Ellero, Marco ;
Serrano, Mar ;
Espanol, Pep .
JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 226 (02) :1731-1752