TY - JOUR

T1 - A Numerical Solution of the Kinetic Collection Equation Using High Spectral Grid Resolution

T2 - A Proposed Reference

AU - Tzivion, Shalva

AU - Reisin, Tamir G.

AU - Levin, Zev

N1 - Funding Information:
Special thanks are due to Mrs. Zipi Rosen and Mrs. Sara Rehavi for their help with the programming and the testing of the code, without whom this work would have never been accomplished. Part of this work was conducted under a grant from the Water Commissioner of Israel as part of of the Rain Enhancement Project of Israel.

PY - 1999/1/20

Y1 - 1999/1/20

N2 - The multi-moments method of S. Tzivion, G. Feingold, and Z. Levin was applied to the original kinetic collection equation in order to obtain a set of equations with respect to moments in spectral bins. For solving this set of equations an accurate and efficient method is proposed. The method conserves total mass independently of the number of bins, time step, initial conditions, or kernel of interaction. In the present paper the number of bins was varied from 36, 72, 108, and 144 in order to study the behavior of the solutions. Different kernels and initial conditions were tested. In all cases the results show that when the number of bins increases from 36 to 144 the numerical solution of the KCE gradually converges. Increasing the number of bins from 108 to 144 produces only a small difference in the numerical solution, indicating that the solution obtained for 144 bins approaches the "real" solution of the KCE. The use of this solution for evaluating the accuracy of other numerical methods that solve the KCE is suggested.

AB - The multi-moments method of S. Tzivion, G. Feingold, and Z. Levin was applied to the original kinetic collection equation in order to obtain a set of equations with respect to moments in spectral bins. For solving this set of equations an accurate and efficient method is proposed. The method conserves total mass independently of the number of bins, time step, initial conditions, or kernel of interaction. In the present paper the number of bins was varied from 36, 72, 108, and 144 in order to study the behavior of the solutions. Different kernels and initial conditions were tested. In all cases the results show that when the number of bins increases from 36 to 144 the numerical solution of the KCE gradually converges. Increasing the number of bins from 108 to 144 produces only a small difference in the numerical solution, indicating that the solution obtained for 144 bins approaches the "real" solution of the KCE. The use of this solution for evaluating the accuracy of other numerical methods that solve the KCE is suggested.

KW - Kinetic collection equation

KW - Numerical solutions of integro-differential equations

UR - http://www.scopus.com/inward/record.url?scp=0000970875&partnerID=8YFLogxK

U2 - 10.1006/jcph.1998.6128

DO - 10.1006/jcph.1998.6128

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AN - SCOPUS:0000970875

SN - 0021-9991

VL - 148

SP - 527

EP - 544

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 2

ER -