Lagrangian cell-centered conservative scheme

doi:10.1007/s10483-012-1625-9

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (10): 1329-1350.doi: https://doi.org/10.1007/s10483-012-1625-9

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Lagrangian cell-centered conservative scheme

葛全文

Institute of Applied Physics and Computational Mathematics, Beijing 100094, P. R. China

收稿日期:2011-08-29 修回日期:2012-05-02 出版日期:2012-10-10 发布日期:2012-10-10
通讯作者: Quan-wen GE, Associate Professor, Ph.D., E-mail: ge_quanwen@iapcm.ac.cn E-mail:ge_quanwen@iapcm.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11172050)

Lagrangian cell-centered conservative scheme

Quan-wen GE

Institute of Applied Physics and Computational Mathematics, Beijing 100094, P. R. China

Received:2011-08-29 Revised:2012-05-02 Online:2012-10-10 Published:2012-10-10
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11172050)

摘要/Abstract

摘要： This paper presents a Lagrangian cell-centered conservative gas dynamics scheme. The piecewise constant pressures of cells arising from the current time sub-cell densities and the current time isentropic speed of sound are introduced. Multipling the initial cell density by the initial sub-cell volumes obtains the sub-cell Lagrangian masses, and dividing the masses by the current time sub-cell volumes gets the current time sub- cell densities. By the current time piecewise constant pressures of cells, a scheme that conserves the momentum and total energy is constructed. The vertex velocities and the numerical fluxes through the cell interfaces are computed in a consistent manner due to an original solver located at the nodes. The numerical tests are presented, which are representative for compressible flows and demonstrate the robustness and accuracy of the Lagrangian cell-centered conservative scheme.

关键词: sub-cell force, Lagrange cell-centered scheme, Lagrangian cell-centered conservative gas dynamics scheme, piecewise constant pressure of cell, real noise, parametric excitation, co-dimension two bifurcation, detailed balance condition, FPK equation, singular boundary, maximal Lyapunov exponent, solvability condition

Abstract: This paper presents a Lagrangian cell-centered conservative gas dynamics scheme. The piecewise constant pressures of cells arising from the current time sub-cell densities and the current time isentropic speed of sound are introduced. Multipling the initial cell density by the initial sub-cell volumes obtains the sub-cell Lagrangian masses, and dividing the masses by the current time sub-cell volumes gets the current time sub- cell densities. By the current time piecewise constant pressures of cells, a scheme that conserves the momentum and total energy is constructed. The vertex velocities and the numerical fluxes through the cell interfaces are computed in a consistent manner due to an original solver located at the nodes. The numerical tests are presented, which are representative for compressible flows and demonstrate the robustness and accuracy of the Lagrangian cell-centered conservative scheme.

Key words: sub-cell force, Lagrange cell-centered scheme, Lagrangian cell-centered conservative gas dynamics scheme, piecewise constant pressure of cell, real noise, parametric excitation, co-dimension two bifurcation, detailed balance condition, FPK equation, singular boundary, maximal Lyapunov exponent, solvability condition

中图分类号:

O241.82

葛全文. Lagrangian cell-centered conservative scheme[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1329-1350.

Quan-wen GE . Lagrangian cell-centered conservative scheme[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1329-1350.

参考文献

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Lagrangian cell-centered conservative scheme

Lagrangian cell-centered conservative scheme

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