An Improved Coarse-Mesh Nodal Integral Method for Partial Differential Equations

Numerical Methods for Partial Differential Equations

Volumn 13, Issue 2, 1997, Pages 113-145

  Rizwan uddin, ^a,b,c  

^a University of Illinois at Urbana Champaign   (United States)

^b Compl Sci and Engineering Program ^*  (United States)

^c UNIVERSITY OF VIRGINIA   (United States)

Author keywords

Burgers equation; Coarse mesh; Inherent upwinding; Nonlinear PDEs

Indexed keywords

EID: 0000765322     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199703)13:2<113::AID-NUM1>3.0.CO;2-S     Document Type: Article

References (17)

1. E. P. E. Michael, J. J. Doming, E. M. Gelbard, and Rizwan-uddin, "A nodal integral method for the convection-diffusion heat equation," Trans. Am. Nucl. Soc. 69, 239-241 (1993).
2. E. P. E. Michael, J. J. Dorning, and Rizwan-uddin, "A third order nodal integral method for the convection-diffusion equation," Trans. Am. Nucl. Soc. 71, 195-197 (1994).
3. C. A. J. Fletcher, "Burgers' equation: a model for all reasons," in Numerical Solutions of Partial Differential Equations, John Noye, Ed., North-Holland, Amsterdam, 1981, pp. 355-475.
4. W. J. Decker, "A block iterative nodal-integral method for fluid dynamics problems," M. S. Thesis, University of Virginia, 1995.
5. T. J. Burns and J. J. Dorning, "A new computational method for the solution of multidimensional neutron diffusion problems," in Proc. of the Joint NEACRP/CSNI Specialists' Meeting on New Developments in Three-Dimensional Neutron Kinetics and Review of Kinetics Benchmark Calculations, Garching, Munich, Germany, 1975, pp. 109-130. Laboratorium fur Reaktorregelung and Anlagensicherung.
6. William C. Horak, "Local Green's functions techniques for the solution of heat conduction and incompressible fluid flow problems," Ph. D. thesis, University of Illinois, 1980.
7. W. C. Horak and J. J. Dorning, "A nodal coarse-mesh method for the efficient numerical solution of laminar flow problems," J. Comp. Physics 59, 405-440 (1985).
8. R. D. Lawrence and J. J. Dorning, "A nodal green's function method for multidimensional neutron diffusion calculations," Nuclear Sci. Eng. 76, 218-231 (1980).
9. Y. Y. Azmy, "A nodal integral method for the numerical solution of incompressible fluid flow problems," Master's Thesis, University of Illinois, 1982.
10. Y. Y. Azmy and J. J. Dorning, "A nodal integral approach to the numerical solution of partial differential equations," in Advances in Reactor Computations, Vol. II, American Nuclear Society, LaGrange Park, IL, 1983, pp. 893-909.
11. Gary Wilson, "Time-dependent nodal integral method," Ph. D. thesis, University of Virginia, 1987.
12. G. L. Wilson, R. A. Rydin, and Y. Y. Azmy, "Time-dependent nodal integral method for the investigation of bifurcation and nonlinear phenomena in fluid flow and natural convection," Nucl. Sci. Eng. 100, 414-425 (1988).
13. C. A. J. Fletcher, "A comparison of finite element and finite difference solutions of the one- and two-dimensional Burgers' equations," J. Comp. Physics 51, 159-188 (1983).
14. P. L. Sachdev, Nonlinear Diffusive Waves, Cambridge University Press, New York, 1987.
15. C. A. J. Fletcher, Computational Techniques for Fluid Dynamics 1, Springer, New York, 1988.
16. C. Basdevant, M. Deville, P. Haldenwang, J. M. Lacroix, J. Ouazzani, R. Peyret, P. Orlandi, and A. T. Patera, "Spectral and finite difference solutions of the Burgers' equation," Computers & Fluids 14, 23-41 (1986).
17. D. G. Cacuci and O. A. Karakashian, "Benchmarking the propagator method for nonlinear systems: a Burgers-Korteweg-deVries equation," J. Comp. Physics 89, 63-79 (1990).