The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy

Journal of Computational Physics

Volumn 146, Issue 1, 1998, Pages 227-262

  Caramana, E J ^a   Burton, D E ^a   Shashkov, M J ^a   Whalen, P P ^a  

^a Hydrodynamics Methods Group   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE EVENT SIMULATION; ERRORS; FLUID DYNAMICS; MOMENTUM;

CONTINUUM EQUATION; CONTINUUM SYSTEMS; DISCRETIZATION METHOD; FLUID-DYNAMICS; GLOBAL PROPERTIES; LOCAL TRUNCATION ERRORS; NUMERICAL ALGORITHMS; NUMERICAL SOLUTION; TOTAL ENERGY; TRUNCATION ERRORS;

NUMERICAL METHODS;

EID: 0000142136     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6029     Document Type: Article

References (25)

1. Burton D. E. Exact conservation of energy and momentum in staggered-grid hydrodynamics with arbitrary connectivity. Advances in the Free Lagrange Method. 1990.
2. Samarskii A. A., Tishkin V. F., Favorskii A. P., Shashkov M. J. Operational finite difference schemes. Differential Equations. 17:1981;854.
3. Shashkov M. J. Conservative Finite-Difference Methods on General Grids. 1996.
4. Caramana E. J., Shashkov M. J. Elimination of artificial grid distortion and hourglass-type motions by means of Lagrangian subzonal masses and pressures. J. Comput. Phys. 142:1998;521.
5. E. J. Caramana, M. J. Shashkov, P. P. Whalen, Formulations of artificial viscosity for multi-dimensional shock wave computations, J. Comput. Phys.
6. Landau L. D., Lifshitz E. M. Course in Theoretical Physics. Vol. 1. Mechanics. 1960.
7. Benson D. J. Computational methods in Lagrangian and Eulerian hydrocodes. Comput. Methods Appl. Mech. Eng. 99:1992;235.
8. Favorskii A. P. Variational-discrete models of hydrodynamics equations. Differential Equations. 16:1980;834.
9. Holm D. D., Kupershmidt B. A., Levermore C. D. Hamiltonian differencing of fluid dynamics. Adv. in Appl. Math. 1:1985;52.
10. Wilkins M. L. Calculations of elastic-plastic flow. Methods Comput. Phys. 3:1964;211.
11. Schulz W. D. Two-dimensional Lagrangian hydrodynamic difference equations. Methods Comput. Phys. 3:1964;1.
12. V. F. Tishkin, N. N. Tiurina, A. P. Favorskii, Finite-difference schemes for calculating hydrodynamic flows in cylindrical coordinates, preprint, No. 23, Keldysh Institute of Applied Mathematics, Moscow, Russia, 1978.
13. Caramana E. J., Whalen P. P. Numerical preservation of symmetry properties of continuum problems. J. Comput. Phys. 141:1998;174.
14. Solov'ev A., Shashkov M. Difference scheme for the Dirichlet particle method in cylindrical method in cylindrical coordinates, conserving symmetry of gas-dynamical flow. Differential Equations. 24:1988;817.
15. Whalen P. P. Algebraic limitations on two-dimensional hydrodynamics simulations. J. Comput. Phys. 124:1996;46.
16. Shashkov M., Steinberg S. Solving diffusion equations with rough coefficients in rough grids. J. Comput. Phys. 129:1996;383.
17. Solov'ev A., Solov'eva E., Tishkin V., Favorskii A., Shashkov M. Approximation of finite-difference operators on a mesh of Dirichlet cells. Differential Equations. 22:1986;863.
18. Mikhailova N., Tishkin V., Turina N., Favorskii A., Shashkov M. Numerical modelling of two-dimensional gas dynamic flows on a variable-structure mesh. U.S.S.R. Comput. Math. Math. Phys. 26:1986;74.
19. Shashkov M., Solov'ov A. Numerical Simulation of Two-Dimensional Flows by the Free-Lagrangian Method. May 1991.
20. Monaghan J. J. Particle methods for hydrodynamics. Comput. Phys. Rep. 3:1985;71.
21. Dukowicz J. K., Meltz B. Vorticity errors in multidimensional Lagrangian codes. J. Comput. Phys. 99:1992;115.
22. M. Hyman.
23. Sedov L. I. Similarity and Dimensional Methods in Mechanics. 1959.
24. Burton D. E. Multidimensional Discretizations of Conservation Laws for Unstructured Ployhedral Grids. 1994.
25. Margolin L. G., Adams T. F. Spatial Differencing for Finite Difference Codes. January 1985.