Six numerical schemes for parabolic initial boundary value problems with a priori bounded solution

Applied Numerical Mathematics

Volumn 46, Issue 3-4, 2003, Pages 353-377

  Makhanov, Stanislav S ^a   Semenov, Andrei Yu ^b  

^a THAMMASAT UNIVERSITY   (Thailand)

^b PROKHOROV GENERAL PHYSICS INSTITUTE   (Russian Federation)

Author keywords

Adaptive grid; Diffusion wave equation; Finite difference schemes; Parabolic initial boundary value problem; Richard's equation

Indexed keywords

APPROXIMATION THEORY; CONSTRAINT THEORY; DIFFUSION; FINITE DIFFERENCE METHOD; NUMERICAL METHODS;

DIFFUSION WAVE EQUATION;

BOUNDARY VALUE PROBLEMS;

EID: 0042170207     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(03)00038-2     Document Type: Conference Paper

References (54)

1. Abbot M.B., Rodenhuis G.S. Numerical modeling of water waves, flows and transport. Dan. Hydr. 3:1982;6-23.
2. Amano K. Approximate general solution of degenerate parabolic equations related to population genetics. Electron. J. Differential Equations. 15:1995;1-14.
3. Baker T.J. Delaunay-Voronoï methods. Thompson J.F., Soni B.K., Weatherill N.P. Handbook of Grid Generation. 1999;CRC, Boca Raton, FL. Chapter 16.
4. Barenblatt G.I., Vishik M.I. On a finite velocity in problems of non-stationary filtration of a liquid and gas. J. Appl. Math. Mech. 20:(3):1956;411-417. (in Russian).
5. Barenblatt G.I., Iooss G., Joseph D.D. Non-Linear Dynamics and Turbulence. 1983;Pitman, New York.
6. Bates P.D., Anderson M.G. A 2D finite element model for river flow inundation. Proc. Roy. Soc. London, Ser. A. 400:(1909):1993;481-491.
7. Belikov V.V., Semenov A.Yu. Non-Sibsonian interpolation on arbitrary system of points in Euclidean space and adaptive isolines generation. Appl. Numer. Math. 32:(4):2000;371-387.
8. Bergquist R.J., Ligteringen H. The BRANCH model and the Segara Anakan study. Proc. National Hydraulic Engineering Conf. 1988;794-799 American Society of Civil Engineers, New York.
9. Beyer N., Portner C. Mike11: Hydrodynamics simulation of flood protection systems. Proc. First Int. Conf. Hydroinformatics '94, Delft, the Netherlands, September 19-23. 1994;407-414.
10. Bras R.L. Hydrology: An Introduction to Hydrologic Science. 1990;Addison-Wesley, Reading, MA.
11. Brooks R.H., Corey A.T. Properties of porous media affecting fluid flow. J. Irrig. and Drain., ASCE. 92:1966;61-88.
12. Cappelaere B. Accurate diffusive wave routing. J. Hydraulic Engineering, ASCE. 123:(3):1997;174-181.
13. Chow V.T., Maidment D.R., Mays L.W. Applied Hydrology. 1988;McGraw-Hill, New York.
14. Cunningum A.B., Sinclair P.J. Application and analysis of coupled surface and groundwater models. J. Hydrology. 43:(1):1979;129-148.
15. Duru O.J., Hjelmfelt A.T. Investigating prediction capability of HEC-1 and KINEROS kinematic wave runoff models. J. Hydrology. 157:1994;87-103.
16. Eching S.O., Hopmans J.W., Wendroth O. Unsaturated hydraulic conductivity from a transient multi step outflow and soil water pressure. Soil. Sci. Soc. Amer. J. 58:1994;687-695.
17. Esteban J.R., Vazquez J.L. On the equation of turbulent filtration in one-dimensional porous media. Non-Linear Analysis, TMA. 10:(11):1986;1303-1325.
18. Fread D.L. Channel Routing: Hydrological Forecasting. 1985;John Wiley, New York.
19. Freeze R.A. Role of sub-surface flow in generating surface runoff, Part 1: Base flow contributions to channel flow. Water Resources Res. 8:(3):1972;609-623.
20. Hills R.G., Porro I., Hudson D.B., Wierenga P.J. Modeling one-dimensional infiltration into very dry soils 1. Model development and evaluation. Water Resources Res. 25:1989;1259-1269.
21. Jury W.A., Gardner W.R., Gardner W.H. Soil Physics. 1991;John Wiley, New York.
22. Kacur J. On a solution of degenerate elliptic-parabolic systems in Orlicz-Sobolev spaces I; II. Math. Z. 203:1990;153-171. 659-579.
23. Kacur J., Handlovicova A., Kacurova M. Solution of non-linear diffusion problems by linear approximation schemes. SIAM J. Numer. Anal. 30:(6):1993;1703-1722.
24. Kuchment L.S., Gel'fan A.N. Dynamic-probabilistic models for the formation of rainfall and snowmelt runoff. Water Resources. 18:(4):1992;335-343.
25. Kuchment L.S., O'Connel P.E. Construction of models of the global-scale hydrologic cyclic of land: analysis of the current state and prospects. Water Resources. 20:(2):1993;159-180.
26. Kulikovskii A.G., Pogorelov N.V., Semenov A.Yu. Mathematical Aspects of Numerical Solution of Hyperbolic Systems. Monographs and Surveys in Pure and Applied Mathematics. 118:2001;CRC, Boca Raton, FL.
27. Leendertse J.J., Criton E.C., A water quality simulation model for well-mixed estuaries and coastal seas, I/II, R-709-NYC, Rand Corporation, 1971.
28. Makhanov S.S. Flood modeling in East Bangkok. Proc. Civil and Environ. Eng. Conf., Pt. I: Water Eng. and Management, New Frontiers and Challenges, Bangkok. 5:1999;111-120.
29. Makhanov S.S., Semenov A.Yu. A stable non-negative numerical method for calculating the flow of a liquid in an open channel. Comput. Maths Math. Phys. 34:(1):1994;85-95.
30. Makhanov S.S., Semenov A.Yu. Modeling of motion of fluid with free surface under level recession. Water Resources. 22:(4):1995;357-362.
31. Makhanov S.S., Semenov A.Yu. A new technique for calculating surface runoff. Russ. Meteorol. Hydrol. 2:1995;44-52.
32. Makhanov S.S., Semenov A.Yu. A two-dimensional non-negative algorithm for calculating the flow of a liquid in an open channel. Comput. Maths Math. Phys. 36:(4):1996;501-507.
33. Makhanov S.S., Semenov A.Yu. The class of nonnegative numerical methods for open flows modeling. Computational Fluid Dynamics of Natural Flows. Trudy IOFAN Proc. Gen. Phys. Inst., Russian Acad. Sci. 53:1997;55-74 Nauka/Fizmatlit, Moscow. (in Russian).
34. Makhanov S.S., Semenov A.Yu. Numerical methods for non-linear parabolic boundary-value problems with a priory bounded solution. Papailiou K.D., Tsahalis D., Péraux T., Knorzer D. Proc. 4th Europ. Comput. Fluid Dyn. Conf., Athens, September 7-11, 1998. 1:1998;78-82 Wiley, Chichester.
35. Makhanov S.S., Vanderperre E.J., Sonthipaumpoon K. On generation of curvilinear grids. South-East Asian Bull. Math. 23:1999;131-241.
36. Makhanov S.S., Vannakrairojn S., Vanderperre E.J. A two-dimensional numerical model of flooding in East-Bangkok. J. Hydraulic Engineering, ASCE. 25:(4):1999;407-416.
37. Martinez A., Marquina A., Donat R. Shooting methods for 1D diffusion-absorption problems. SIAM J. Numer. Anal. 21:(2):1994;572-589.
38. Master plan study on the water management system and monitoring program in the Chao-Phraya river basin, Final Report, Ministry of Agriculture and Cooperatives of the Royal Irrigation Department, Thailand, 1989.
39. M.G. McDonald, A.W. Harbangh, A modular three-dimensional finite-difference groundwater flow model, U.S. Geolog. Survey Open-File Report, No. 83-875, Washington, D.C., 1988.
40. Moore I.D., Crayson R.B. Terrain-based catchment partitioning and runoff prediction using vector elevation data. Water Resources Res. 27:1991;1177-1191.
41. Querner E.P. Description and application of the combined surface and groundwater flow model MOGROW. J. Hydrology. 192:(1):1997;158-169.
42. Rasul A.Z.E., Rabbi M.F. GIS in flood mapping for improved flood management in Bangladesh. Proc. First Int. Conf. Hydroinformatics'94, Delft, The Netherlands, September 19-23. 1994;629-634.
43. Samarskii A.A., Nikolaev E.S. Numerical Methods for Grid Equations, Vol. 1. 1989;Birkhäuser Verlag, Basel.
44. Semenov A.Yu. A method of calculating the non-linear filtration equation for which the solution satisfies bilateral estimates. Comp. Maths Math. Phys. 36:(11):1996;1635-1636.
45. Semenov A.Yu. Numerical method for nonlinear filtration equation modeling providing the two-sides unequality. Computational Fluid Dynamics of Natural Flows. Trudy IOFAN Proc. Gen. Phys. Inst., Russian Acad. Sci. 53:1997;75-88 Nauka/Fizmatlit, Moscow. (in Russian).
46. Singh V.P., Prasana M. Generalized flux law, with application. Hydr. Processes. 13:1999;73-87.
47. Syme W.J., Paudyal G.N. Bangladesh flood management model. Proc. 2nd Int. Conf. on River Flood Hydraulics, York, UK, March 22-25. 1994;167-176.
48. Takasao T., Shiiba M. Incorporation of the effect of concentration of flow into the kinematic wave equations and its application to runoff system lumping. J. Hydrology. 102:1988;301-322.
49. Tingsanchai T., Lal N.K. Subsidence of flood waves in overbank flow areas. J. Hydrol. Res. 26:(5):1988;585-597.
50. van Genuchten M.Th. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil. Sci. Soc. Amer. J. 44:1980;892-898.
51. van Genuchten M.Th., Nielsen D.R. On describing and predicting the hydraulic properties of unsaturated soils. Annales Geophysicae. 3:1985;615-628.
52. Voltzinger N.E., Klevanny K.A., Matveyev G.V. An integrated modelling system for coastal area dynamics. Int. J. Numer. Methods Fluids. 19:(3):1994;181-206.
53. USGS General-Use Software, Water Resources Appl. Software, http://water.usgs.gov/software/general.html.
54. Wu W., Sidle R.C. A distributed slope stability model for steep forested basins. Water Resources Res. 31:(8):1995;2097-2110.