Distributed approximating functional approach to Burgers' equation in one and two space dimensions

Computer Physics Communications

Volumn 111, Issue 1-3, 1998, Pages 93-109

  Wei, G W ^a   Zhang, D S ^a   Kouri, D J ^a   Hoffman, D K ^b  

^a University of Houston   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; NONLINEAR EQUATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; REYNOLDS NUMBER;

BURGERS' EQUATION; DISTRIBUTED APPROXIMATING FUNCTIONALS (DAF); TAYLOR EXPANSION;

APPROXIMATION THEORY;

EID: 0032097865     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0010-4655(98)00041-1     Document Type: Article

References (26)

1. J. Burgers, A Mathematical Model Illustrating the Theory of Turbulence, Advances in Applied Mechanics (Academic Press, New York, 1948).
2. P. Jamet, R. Bonnerot, Numerical solution of compressible flow by finite element method which follows the free boundary and the interfaces, J. Comput. Phys. 18 (1975) 21-45.
3. E. Varoglu, W.D.L. Finn, Space-time finite elements incorporating characteristics for the Burgers' equation, Int. J. Numer. Methods Eng. 16 (1980) 171-184.
4. H. Nguyen, J. Reynen, A space-time finite element approach to Burgers' equation, in: C. Taylor et al., eds., Numerical Methods for Non-Linear Problems, Vol. 2, Proc. Int. Conf., Universidal Poltecnica de Barcelona, Spain (Pineridge Press, Swansea, UK, 1984).
5. J. Caldwell, P. Wanless, A.E. Cook, A finite element approach to Burgers' equation, Appl. Math. Modelling 5 (1981) 189; J. Caldwell, P. Smith, Solution of Burgers' equation with a large Reynolds number, Appl. Math. Modelling 6 (1982) 381-385.
6. J. Caldwell, P. Wanless, A.E. Cook, A finite element approach to Burgers' equation, Appl. Math. Modelling 5 (1981) 189; J. Caldwell, P. Smith, Solution of Burgers' equation with a large Reynolds number, Appl. Math. Modelling 6 (1982) 381-385.
7. K. Kakuda, N. Tosaka, The generalized boundary element approach to Burgers' equation, Int. J. Numer. Methods Eng. 29 (1990) 245-261.
8. P. Bar-Yoseph, E. Moses, U. Zrahia, A.L. Yarin, Space-time spectral element methods for one-dimensional nonlinear advection-diffusion problems, J. Comput. Phys. 119 (1995) 62-74.
9. R. Arina, C. Canuto, A self-adaptive domain decomposition for the viscous/inviscid coupling. I. Burgers equation, J. Comput. Phys. 105 (1993) 290-300.
10. S. Biringen, A. Saati, Comparison of several finite-difference methods, J. Aircraft. 27 (1990) 90-92.
11. G. Mansell, W. Merryfield, B. Shizgal, U. Weinert, A comparison of differential quadrature methods for the solution of partial differential equations, Comput. Meth. Appl. Mech. Eng. 104 (1993) 295-316.
12. P. Arminjon, C. Beauchamp, Numerical solution of Burgers' equations in two space dimensions, Comput. Meth. Appl. Mech. Eng. 19 (1979) 351-365.
13. D.K. Hoffman, N. Nayar, O.A. Sharafeddin, D.J. Kouri, Analytic banded approximation for the discretized free propagator, J. Phys. Chem. 95 (1991) 8299-8305.
14. D.K. Hoffman, D.J. Kouri, Distributed approximating function theory: A general, fully quantal approach to wave propagation, J. Phys. Chem. 96 (1992) 1179-1184.
15. W. Zhu, Y. Huang, D.J. Kouri, C. Chandler, D.K. Hoffman, Orthogonal polynomial expansion of the spectral density operator and the calculation of bound state energies and eigenfunctions, Chem. Phys. Lett. 217 (1993) 73-79.
16. D.J. Kouri, W. Zhu, X. Ma, B.M. Pettitt, D.K. Hoffman, Monte Carlo evaluation of real-time path intergrals for quantal many-body dynamics: Distributed approximating functions and Gaussian sampling, J. Phys. Chem. 96 (1992) 9622-9630.
17. D.J. Kouri, D.K. Hoffman, Toward a new time-dependent path integral formalism based on restricted quantum propagators for physically realizable systems, J. Phys. Chem. 95 (1992) 9631-9636.
18. D.K. Hoffman, M. Arnold, D.J. Kouri, Traveling distributed approximating function approach to wave packet propagation: Explicit inclusion of a local wave velocity, J. Phys. Chem. 97 (1993) 1110-1118.
19. D.K. Hoffman, M. Arnold, W. Zhu, D.J. Kouri, Interacting distributed approximating functions for real-time quantum dynamics, J. Phys. Chem. 99 (1993) 1124-1134.
20. D.K. Hoffman, D.J. Kouri, Distributed approximating function theory for an arbitrary number of particles in a coordinate system-independent formalism, J. Phys. Chem. 97 (1993) 4984-4988.
21. D.K. Hoffman, D.J. Kouri, in: Time-Dependent Quantum Molecular Dynamics, J. Broeckhove, L. Lathouwers, eds., NATO ASI Series B 299 (1992) 117-129.
22. D.K. Hoffman, T.L. Marchioro II, M. Arnold, Y. Huang, W. Zhu, D.J. Kouri, Variational derivation and extensions of distributed approximating functionals, J. Math. Chem. 20 (1996) 117-139.
23. D.S. Zhang, G.W. Wei, D.J. Kouri, D.K. Hoffman, Distributed approximating functional approach to the Fokker-Planck equation: Eigenfunction Expansion, J. Chem. Phys., in press.
24. J.D. Cole, On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Appl. Math. 9 (1951) 225-236.
25. xx, Commun. Pure Appl. Math. 3 (1950) 201-230.
26. E.L. Miller, M.S. Thesis (University of Delaware, Newark, Delaware, 1966).