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�������պ����ѧѧ�� 2009, Vol. 35 Issue (11) :1335-1338    DOI:
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����ƽ1, �Ž���1, ������2*
1. �������պ����ѧ ���տ�ѧ�빤��ѧԺ, ���� 100191;
2. �������պ����ѧ �ѧԺ, ���� 100191
Correction of conservative smoothing approach used in SPH method
Long Liping1, Zhang Jianyu1, Zhao Libin2*
1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;

2. School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

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ժҪ �غ�⻬��CSA(Conservative Smoothing Approach)�ǽ����ͳSPH(Smoothed Particle Hydrodynamics)���ȶ��������һ�ֺ���Ч�ķ���.�о�������SPH����������ν���غ�⻬�������ܱ�֤ϵͳ����������(������������������)��ÿ��ʱ�䲽���غ�,��������ʱ��������ֵ��������,�Լ������ľ�����һ����Ӱ��.�Դ�������غ�⻬����������ʽ,��SPH���Ʒ��̵õ��ĸ������ӵ�����������CSA�⻬,Ȼ���������������CSA��������ʽ�ѶԸ������������ĸı�����Ȩƽ���������ڸ�������,�Ӷ�ȷ����SPH�㷨��ϵͳ����������(�����������Լ�������)��ÿ��ʱ�䲽���غ�,�������ڼ�����CSA��SPH�õ��ĸ��������������Ĺ��ֹ⻬,�Ӷ�����˼��㾫��.�������塢�����Ƶ��Լ����е�������֤����������������Ч��.
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Abstract�� The conservative smoothing approach (CSA) is a kind of methods which is very efficient for eliminating the instability of traditional smoothed particle hydrodynamics (SPH) method. Research discovered that total physical quantities of system (such as mass, moment and energy) were no longer strictly conservative in each time step with the use of CSA. The calculated value fluctuated around the theoretical value with time and affected the result precision. Correction of CSA(CCSA) was proposed. Used CSA to smooth the physical variables obtained from SPH governing equations and then used CCSA to weighted average the change of the physical variables to each neighbor node, thus ensured the conservation of total physical quantities of system (such as mass, moment or energy) in each time step. Owing to reduce of the excessive smoothness which CSA acted on physical variables, calculation accuracy was improved. Physical meaning, theoretical derivation and numerical test show the efficiency of this correction.
Keywords�� CSA(conservative smoothing approach)   SPH(smoothed particle hydrodynamics)   stability     
Received 2008-11-03;
About author: ����ƽ(1977-),Ů,������,��ʿ��,longliping@buaa.edu.cn.
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����ƽ, �Ž���, ������.������SPH�����غ�⻬��������[J]  �������պ����ѧѧ��, 2009,V35(11): 1335-1338
Long Liping, Zhang Jianyu, Zhao Libin.Correction of conservative smoothing approach used in SPH method[J]  JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2009,V35(11): 1335-1338
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http://bhxb.buaa.edu.cn//CN/     ��     http://bhxb.buaa.edu.cn//CN/Y2009/V35/I11/1335
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