The Practical MFCAV Riemann Solver is Applied to a New Cell-centered Lagrangian Method
The MFCAV Riemann solver is practically used in many Lagrangian or ALE methods due to its merit of sharp shock profiles and rarefaction corners, though very often with numerical oscillations. By viewing it as a modification of the WWAM Riemann solver, we apply the MFCAV Riemann solver to the Lagrangian method recently developed by Maire. P. H et. al.. The numerical experiments show that the application is successful in that the shock profiles and rarefaction corners are sharpened compared with results obtained using other Riemann solvers. Though there are still numerical oscillations, they are within the range of the MFCAV applied in onther Lagrangian methods.
[1] Maire P. H., Abgralll R., Breil J., et al. A cell-centered lagrangian scheme
for multidimensional compressible flow problems[J]. SIAM J. Sci.
Comput, 2007,29(4): 1781-1824
[2] Von Neumann J. and Ritchimyer R. D.. A method for the numerical
calculations of hydrodynamical shocks[J]. J. Appl. Phys.,
1950,21:232-238.
[3] Wilkins M. L., Calculation of elastic plastic flow. Methods in
computational physics[J],3,1964
[4] Caramana E. J., Shashkov M. J., and Whalen P. P., Formulations of
artificial viscosity for multidimensional shock wave computations[J]. J.
Comput. Phys.,1998, 144:70-97.
[5] Godunov S. K., Zabrodine A., Ivanov M., Kraiko A., and Prokopov G.,
Mir.[J], 1979.
[6] Richtmyer R. D. and Morton K. W., Differencd methods for initial-value
problems. John Wiley, 1967
[7] Duckowicz J. K., Bertrand J. A. Meltz. Vorticity errors in
multidimensional Lagrangian codes [J].Comput. Phys,1992, 99:115-134.
[8] Addessio F. L., et,al. CAVEAT: A computer code for fluid dynamics
problem with large distortion and internal slip[M], Los Alamos report
LA-10613-MS,1992.
[9] Tian B, Shen W, Liu Y, etal, Numerical study on several Godunov-type
schemes with AlE formulation. Computational physics(Chinese Journal):
2007,24(5):537-542.
[10] Toro E. F., Riemann solvers and numerical methods for fluid dynamics, A
Practical Introduction, 2nd edition,Spring-verlag,1999.
[11] W. F. Noh, Errors for calculations of strong shocks using artifical
viscosity and artifical heat flux. J.Comput. Phys., 72:78-120,1987.
[12] P. Woodward and P. Colella, The numerical simulation of
two-dimensional fluid flow with strong shocks. J.Comput. Phys.,
54:115-173,1984.
[13] MAIRE P H, A high order cell-centered Lagrangian scheme for
two-dimensional compressible fluid flows on unstructured meshes.
[14] Li D, Xu G, Shui H, et.al., Numerical Methods for Two-dimensional
Unsteady Fluid Dynamics. The Science Press: Beijing, 1987; 246..
[15] Yan Liu, Baolin Tian, Weidong Shen, Comparing study on two
approximated Riemann solvers in a new cell-centered Lagrangian
method, GF report (GF-A0128959G),2010 (in Chinese).
[1] Maire P. H., Abgralll R., Breil J., et al. A cell-centered lagrangian scheme
for multidimensional compressible flow problems[J]. SIAM J. Sci.
Comput, 2007,29(4): 1781-1824
[2] Von Neumann J. and Ritchimyer R. D.. A method for the numerical
calculations of hydrodynamical shocks[J]. J. Appl. Phys.,
1950,21:232-238.
[3] Wilkins M. L., Calculation of elastic plastic flow. Methods in
computational physics[J],3,1964
[4] Caramana E. J., Shashkov M. J., and Whalen P. P., Formulations of
artificial viscosity for multidimensional shock wave computations[J]. J.
Comput. Phys.,1998, 144:70-97.
[5] Godunov S. K., Zabrodine A., Ivanov M., Kraiko A., and Prokopov G.,
Mir.[J], 1979.
[6] Richtmyer R. D. and Morton K. W., Differencd methods for initial-value
problems. John Wiley, 1967
[7] Duckowicz J. K., Bertrand J. A. Meltz. Vorticity errors in
multidimensional Lagrangian codes [J].Comput. Phys,1992, 99:115-134.
[8] Addessio F. L., et,al. CAVEAT: A computer code for fluid dynamics
problem with large distortion and internal slip[M], Los Alamos report
LA-10613-MS,1992.
[9] Tian B, Shen W, Liu Y, etal, Numerical study on several Godunov-type
schemes with AlE formulation. Computational physics(Chinese Journal):
2007,24(5):537-542.
[10] Toro E. F., Riemann solvers and numerical methods for fluid dynamics, A
Practical Introduction, 2nd edition,Spring-verlag,1999.
[11] W. F. Noh, Errors for calculations of strong shocks using artifical
viscosity and artifical heat flux. J.Comput. Phys., 72:78-120,1987.
[12] P. Woodward and P. Colella, The numerical simulation of
two-dimensional fluid flow with strong shocks. J.Comput. Phys.,
54:115-173,1984.
[13] MAIRE P H, A high order cell-centered Lagrangian scheme for
two-dimensional compressible fluid flows on unstructured meshes.
[14] Li D, Xu G, Shui H, et.al., Numerical Methods for Two-dimensional
Unsteady Fluid Dynamics. The Science Press: Beijing, 1987; 246..
[15] Yan Liu, Baolin Tian, Weidong Shen, Comparing study on two
approximated Riemann solvers in a new cell-centered Lagrangian
method, GF report (GF-A0128959G),2010 (in Chinese).
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57998", author = "Yan Liu and Weidong Shen and Dekang Mao and Baolin Tian", title = "The Practical MFCAV Riemann Solver is Applied to a New Cell-centered Lagrangian Method", abstract = "The MFCAV Riemann solver is practically used in many Lagrangian or ALE methods due to its merit of sharp shock profiles and rarefaction corners, though very often with numerical oscillations. By viewing it as a modification of the WWAM Riemann solver, we apply the MFCAV Riemann solver to the Lagrangian method recently developed by Maire. P. H et. al.. The numerical experiments show that the application is successful in that the shock profiles and rarefaction corners are sharpened compared with results obtained using other Riemann solvers. Though there are still numerical oscillations, they are within the range of the MFCAV applied in onther Lagrangian methods.
", keywords = "Cell-centered Lagrangian method, approximated Riemann solver, HLLC Riemann solver", volume = "5", number = "5", pages = "764-10", }
