A Numerical Solution of the Kinetic Collection Equation Using High Spectral Grid Resolution: A Proposed Reference

Shalva Tzivion, Tamir G. Reisin, Zev Levin

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)527-544
Number of pages18
JournalJournal of Computational Physics
Volume148
Issue number2
DOIs
StatePublished - 20 Jan 1999

Funding

FundersFunder number
Rain Enhancement Project of Israel
Water Commissioner of Israel

    Keywords

    • Kinetic collection equation
    • Numerical solutions of integro-differential equations

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