Lagrangian Cell-Centered Conservative Scheme

GE Quan-wen

doi:10.3879/j.issn.1000-0887.2012.10.009

Volume 33 Issue 10

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GE Quan-wen. Lagrangian Cell-Centered Conservative Scheme[J]. Applied Mathematics and Mechanics, 2012, 33(10): 1239-1256. doi: 10.3879/j.issn.1000-0887.2012.10.009

Citation:

GE Quan-wen. Lagrangian Cell-Centered Conservative Scheme[J]. Applied Mathematics and Mechanics, 2012, 33(10): 1239-1256. doi: 10.3879/j.issn.1000-0887.2012.10.009

Citation:

GE Quan-wen. Lagrangian Cell-Centered Conservative Scheme[J]. Applied Mathematics and Mechanics, 2012, 33(10): 1239-1256. doi: 10.3879/j.issn.1000-0887.2012.10.009

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Lagrangian Cell-Centered Conservative Scheme

doi: 10.3879/j.issn.1000-0887.2012.10.009

GE Quan-wen

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

Received Date: 2011-08-29
Rev Recd Date: 2012-05-02
Publish Date: 2012-10-15

Abstract

Abstract

A Lagrangian cell-centered conservative gas dynamics scheme was presented. It introduced the piecewise constant pressures of cell, which arose from the current time sub cell densities and the current time isentropic speed of sound of cell. The sub cell Lagrangian masses which the initial cell density multiplied by the initial sub cell volumes, divided by the current time sub cell volumes, the current time sub cell densities were obtained. Using the current time piecewise constant pressures of cell, the scheme which conserved momentum, total energy was constructed. The vertex velocities and the numerical fluxes through the cell interfaces were computed in a consistent manner due to an original solver located at the nodes. Many numerical tests were presented. They are representative test cases for compressible flows and demonstrate the robustness and the accuracy of Lagrangian cell-centered conservative scheme.

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References(16)

References

[1]	Maire P H, Abgrall R, Breil J, Ovadia J. A cell-centered Lagrangian scheme for compressible flow problems[J]. SIAM J Scien Comp, 2007, 29(4): 1781-1824.
[2]	von Neumann J, Richtmyer R D. A method for the numerical calculations of hydrodynamica shocks[J]. J Appl Phys, 1950, 21, 232-238.
[3]	Wilkins M L. Calculation of elastic plastic flow[C]Blder B, Fernbach S.Methods in Computationnal Physics. 3. New York: Academic, 1964.
[4]	Caramana E J, Shashkov M J . Elimination of artificial grid distorsion and hourglass-type motions by means of Lagrangian subzonal masses and pressures[J]. J Comput Phys, 1998, 142(2): 521-561.
[5]	Caramana E J, Shashkov M J, Whalen P P. Formulations of artificial viscosity for multidimensional shock wave computations[J]. J Comput Phys, 1998, 144(1): 70-97.
[6]	Campbell J C, Shashov J C. A tensor artificial viscosity using a mimetic finite difference algorithm[J]. J Comput Phys, 2001, 172(4): 739-765.
[7]	Caramana E J, Burton D E, Shashov M J, Whalen P P. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy[J]. J Comput Phys, 1998, 146(1): 227-262.
[8]	Campbell J C, Shashov M J. A compatible Lagrangian hydrodynamics algorithm for unstructured grids[J]. Seluk J Appl Math, 2003, 4(2): 53-70.
[9]	Scovazzi G, Christon M A, Hughes T J R, Shadid J N. Stabilized shock hydrodynamics—Ⅰ: a Lagrangian method[J]. Comput Methods Appl Mech and Engrg, 2007, 196(4): 923-966.
[10]	Scovazzi G. Stabilized shock hydrodynamicsⅡ: design and physical interpretation of the SUPG operator for Lagrangian computations[J]. Comput Methods Appl Mech and Engrg, 2007, 196(4/6): 966-978.
[11]	Scovazzi G, Love E, Shashkov M J. Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: theoretical framework and two-dimensional computations[J]. Comput Methods Appl Mech and Engrg, 2008, 197(9/12): 1056-1079.
[12]	Godunov S K, Zabrodine A, Ivanov M, Kraiko A, Prokopov G.Résolution Numérique des Problèmes Multidimensionnels de la Dynamique des Gaz[M]. Mir, 1979.
[13]	Adessio F L, Carroll D E, Dukowicz K K, Johnson J N, Kashiwa B A, Maltrud M E, Ruppel H M . Caveat: a computer code for fluid dynamics problems with large distortion and internal slip[R]. Technical Report LA-10613-MS, Los Alamos National Laboratory, 1986.
[14]	Dukowicz J K, Meltz B . Vorticity errors in multidimensional Lagrangian codes[J]. J Comput Phys, 1992, 99(1): 115-134.
[15]	Despr＇es B, Mazeran C. Lagrangian gas dynamics in two dimensions and Lagrangian systems[J]. Arch Rational Mech Anal, 2005, 178(3): 327-372.
[16]	Carré G, Delpino S, Despr＇es B, Labourasse E . A cell-centered Lagrangian hydrodynamics scheme in arbitrary dimension[J]. J Comput Phys, 2009, 228(14): 5160-5183.