High-order Lagrangian cell-centered conservative scheme on unstructured meshes

doi:10.1007/s10483-014-1856-6

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (9): 1203-1222.doi: https://doi.org/10.1007/s10483-014-1856-6

• • 上一篇

High-order Lagrangian cell-centered conservative scheme on unstructured meshes

葛全文

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

收稿日期:2013-07-26 修回日期:2014-01-11 出版日期:2014-09-01 发布日期:2014-09-01
通讯作者: Quan-wen GE, 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 (Nos. 11172050, 11372051, and 11001027)

High-order Lagrangian cell-centered conservative scheme on unstructured meshes

Quan-wen GE

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

Received:2013-07-26 Revised:2014-01-11 Online:2014-09-01 Published:2014-09-01
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11172050, 11372051, and 11001027)

摘要/Abstract

摘要： A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is introduced. With the high-order piecewise pressure of the cell, the high-order spatial discretization fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.

关键词: high-order piecewise pressure of cell, high-order sub-cell force, high-order Lagrangian cell-centered conservative scheme, unstructured mesh

Abstract: A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is introduced. With the high-order piecewise pressure of the cell, the high-order spatial discretization fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.

Key words: high-order sub-cell force, high-order piecewise pressure of cell, high-order Lagrangian cell-centered conservative scheme, unstructured mesh

中图分类号:

O241.82

葛全文. High-order Lagrangian cell-centered conservative scheme on unstructured meshes[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1203-1222.

Quan-wen GE. High-order Lagrangian cell-centered conservative scheme on unstructured meshes[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1203-1222.

参考文献

[1] Von Neumann, J. and Richtmyer, R. D. A method for the numerical calculations of hydrodynamical shocks. Journal of Applied Physics, 21, 232-238 (2009)
[2] Wilkins, M. L. Calculation of elastic plastic flow. Methods in Computationnal Physics, 3, 211-263 (1964)
[3] Caramana, E. J. and Shashkov, M. J. Elimination of artificial grid distorsion and hourglasstype motions by means of Lagrangian subzonal masses and pressures. Journal of Computational Physics, 142, 521-561 (2009)
[4] Caramana, E. J., Shashkov, M. J., and Whalen, P. P. Formulations of artificial viscosity for multidimensional shock wave computations. Journal of Computational Physics, 144, 70-97 (2009)
[5] Campbell, J. C. and Shashov, J. C. A tensor artificial viscosity using a mimetic finite difference algorithm. Journal of Computational Physics, 172, 739-765 (2009)
[6] Caramana, E. J., Burton, D. E., Shashkov, M. J., and Whalen, P. P. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. Journal of Computational Physics, 146, 227-262 (1998)
[7] Campbell, J. C. and Shashkov, M. J. A compatible Lagrangian hydrodynamics algorithm for unstructured grids. Selcuk Journal of Appllied Mathematics, 4, 53-70 (2003)
[8] Godunov, S. K., Zabrodine, A., Ivanov, M., Kraiko, A., and Prokopov, G. Résolution Numérique des Probl mes Multidimensionnels de la Dynamique des Gaz, Mir, Moscou (1979)
[9] Adessio, F. L., CarrollD, E., Dukowicz, K. K., Johnson, J. N., Kashiwa, B. A., Maltrud, M. E., and Ruppel, H. M. Caveat: a Computer Code for Fluid Dynamics Problems with Large Distortion and Internal Slip, Technical Report LA-10613-MS, Los Alamos National Laboratory, Los Alamos (1986)
[10] Dukowicz, J. K. and Meltz, B. Vorticity errors in multidimensional Lagrangian codes. Journal of Computational Physics, 99, 115-134 (1992)
[11] Desp?es, B. and Mazeran, C. Lagrangian gas dynamics in two dimensions and Lagrangian systems. Archive for Rational Mechanics and Analysis, 178, 327-372 (2005)
[12] Carré, G., Delpino, S., Desprées, B., and Labourasse, E. A cell-centered Lagrangian hydrodynamics scheme in arbitrary dimension. Journal of Computational Physics, 228, 5160-5183 (2009)
[13] Ge, Q. W. A Lagrangian cell-centered conservative scheme. Applied Mathematics and Mechanics (English Edition), 33(10), 1329-1350 (2012) DOI 10.1007/s10483-012-1625-9
[14] Maire, P. H. A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes. Journal of Computational Physics, 228, 2391-2425 (2009)

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High-order Lagrangian cell-centered conservative scheme on unstructured meshes

High-order Lagrangian cell-centered conservative scheme on unstructured meshes

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