×

Simulation of transients in natural gas pipelines using hybrid TVD schemes. (English) Zbl 0981.76065

From the summary: The mathematical model describing transients in natural gas pipelines constitutes a non-homogeneous system of nonlinear hyperbolic conservation laws. We adopt a time splitting approach to solve this non-homogeneous hyperbolic model. At each time step, the non-homogeneous hyperbolic model is split into a homogeneous hyperbolic model and an ODE operator. An explicit 5-point second-order-accurate total variation diminishing (TVD) scheme is formulated to solve the homogeneous system of nonlinear hyperbolic conservation laws. Special attention is given to the treatment of boundary conditions at the inlet and the outlet of the pipeline. Hybrid methods involving the Godunov scheme (TVD/Godunov scheme) or the Roe scheme (TVD/Roe scheme) or the Lax-Wendroff scheme (TVD/LW scheme) are used to achieve appropriate boundary handling strategy.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Heath, J. Inst. Gas Eng. 9 pp 261– (1969)
[2] Wylie, Soc. Pet. Eng. J. 3 pp 356– (1971) · doi:10.2118/2963-PA
[3] Streeter, Soc. Pet. Eng. J. 75 pp 357– (1970) · doi:10.2118/2555-PA
[4] Taylor, Soc. Pet. Eng. J. Trans. AIME 225 pp 297– (1962) · doi:10.2118/107-PA
[5] Yow, ASME Trans. Series D 94 pp 422– (1972) · doi:10.1115/1.3425438
[6] Wylie, Soc. Pet. Eng. J. 10 pp 35– (1974) · doi:10.2118/4004-PA
[7] Rachford, Soc. Pet. Eng. J. 15 pp 165– (1974) · doi:10.2118/4005-A
[8] Steger, J. Comput. Phys. 40 pp 263– (1981)
[9] Courant, Commun. Pure Appl. Math. 5 pp 243– (1952)
[10] Lax, Commun. Pure Appl. Math. 13 pp 217– (1960)
[11] ?The effects of viscosity in hypervelocity impact cratering?, AIAA Paper 69-354, 1969.
[12] Sod, J. Comput. Phys. 27 pp 1– (1984)
[13] Von Neumann, J. Appl. Phys. 21 pp 232– (1950)
[14] Boris, J. Comput. Phys. 11 pp 38– (1973)
[15] Van Leer, J. Comput. Phys. 14 pp 361– (1974)
[16] Sweby, SIAM J. Numer. Anal. 21 pp 995– (1984)
[17] Harten, J. Comput. Phys. 49 pp 357– (1983)
[18] Harten, SIAM J. Numer. Anal. 21 pp 1– (1984)
[19] Godunov, Mater. Sbornik, N.S. 47 pp 271– (1959)
[20] Chen, Ind. Eng. Chem. Fund. 15 pp 296– (1979)
[21] Dranchuk, J. Can. Pet. Technol. 15 pp 34– (1975)
[22] Numerical Computation of Internal and External Flows, Volume 2: Computational Methods for Inviscid and Viscous Flows, Wiley, New York, 1990, Chapters 16 and 19. · Zbl 0742.76001
[23] and ?The development and testing of a new flow equation?, Proc. PSIG (Pipeline Simulation Interest Group) 27th Annual Meeting, Albuquerque, NM, 19-20 October 1995.
[24] LeVeque, J. Comput. Phys. 86 pp 187– (1990)
[25] Roe, J. Comput. Phys. 43 pp 357– (1981)
[26] Numerical Methods for Conservation Laws, Birkhauser, Basel, 1990, pp. 156-157. · doi:10.1007/978-3-0348-5116-9
[27] and ?On the application and extension of Harten’s high-resolution scheme?, NASA 82-28063, June 1982.
[28] Chu, J. Comput. Phys. 15 pp 476– (1974)
[29] and The Finite Difference Method in Partial Differential Equations, Wiley, New York, 1980, pp. 190-191.
[30] Beam, J. Comput. Phys. 22 pp 87– (1976)
[31] Sundstrom, J. Comput. Phys. 17 pp 450– (1975)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.