Optimization of numerical integration methods for shell models

Authors

  • R.A. Stepanov

Keywords:

численный анализ
численные методы
каскадные модели турбулентности обыкновенные дифференциальные уравнения
задача Коши
методы Рунге-Кутта
краевые задачи
разделение по физическим процессам
аппроксимация
сходимость

Abstract

We propose an algorithm devised to increase time steps for integrating a system of ordinary differential equations with a linear viscosity term. A special realization of this algorithm is considered for the classical fourth-order Runge-Kutta method. The efficiency of our approach is demonstrated by an example of shell models of turbulence. For problems of such a type, integration steps may increase by orders.

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Published

2002-10-08

Issue

Vol. 3 (2002): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biography

R.A. Stepanov

Institute of Continuous Media Mechanics of UB RAS (ICMM UB RAS)

References

  1. Гледзер E.Б. Система гидродинамического типа, допускающая два квадратичных интеграла движения // Докл. АН СССР. 1973. 209, № 5. 1046-1048.
  2. Yamada M., Okhitani K. GOY // J. Physical Society of Japan. 1987. 56 . 4210.
  3. Frick P., Sokoloff D. Cascade and dynamo action in a shell model of magnetohydrodynamic turbulence // Phys. Rev. E. 1998. 57, N 4. 4155-4164.
  4. Антонов Т.Ю., Фрик П.Г., Соколов Д.Д. Рост корреляций в свободно распадающейся МГД-турбулентности // Вычислительные методы и программирование. 2000. 1, № 1. 16-20 (http://num-meth.srcc.msu.su).
  5. Антонов Т.Ю., Фрик П.Г., Соколов Д.Д. Долговременная эволюция свободно распадающейся МГД-турбулентности // Докл. РАН. 2001. 377, № 2. 170-172.
  6. Корн Г., Корн Т. Справочник по математике для научных работников и инженеров. М.: Наука, 1984.
 How to cite   
Ryabov G.G. On the path coding of k-faces in an n-cube // Numerical Methods and Programming. 2008. 9, No 1. 16–18.

TEX CODE:

Ryabov G. , (2008) “On the path coding of k-faces in an n-cube,” Numerical Methods and Programming, vol. 9, no. 1, pp. 16–18.

TEX CODE:

G. Ryabov, “On the path coding of k-faces in an n-cube,” Numerical Methods and Programming 9, no. 1 (2008): 16–18

TEX CODE:

Ryabov G. On the path coding of k-faces in an n-cube. Numerical Methods and Programming. 2008;9(1):16–18.(In Russ.).

TEX CODE:

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