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Research papers

Timescale interpolation and no-neighbour discretization for a 1D finite-volume Saint-Venant solver

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Pages 738-754 | Received 18 Jun 2018, Accepted 18 Sep 2019, Published online: 05 Nov 2019

References

  • Aricò, C., & Tucciarelli, T. (2007). A marching in space and time (MAST) solver of the shallow water equations. Part I: The 1D model. Advances in Water Resources, 30(5), 1236–1252. doi:10.1016/j.advwatres.2006.11.003
  • Arora, M., & Roe, P. L. (1997). A well-behaved TVD limiter for high-resolution calculations of unsteady flow. Journal of Computational Physics, 132, 3–11. doi:10.1006/jcph.1996.5514
  • Audusse, E., Bouchut, F., Bristeau, M. O., Klein, R., & Perthame, B. (2004). A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM Journal on Scientific Computing, 25(6), 2050–2065. doi:10.1137/S1064827503431090
  • Balbás, J., & Karni, S. (2009). A central scheme for shallow water flows along channels with irregular geometry. ESAIM: Mathematical Modelling and Numerical Analysis, 43, 333–351. doi:10.1051/m2an:2008050
  • Bollermann, A., Chen, G., Kurganov, A., & Noelle, S. (2013). A well-balanced reconstruction of wet/dry fronts for the shallow water equations. Journal of Scientific Computing, 56(2), 267–290. doi:10.1007/s10915-012-9677-5
  • Bouchut, F., & de Luna, T. M. (2010). A subsonic-well-balanced reconstruction scheme for shallow water flows. SIAM Journal on Numerical Analysis, 48(5), 1733–1758. doi:10.1137/090758416
  • Buntina, M. V., & Ostapenko, V. V. (2008). TVD scheme for computing open channel wave flows. Computational Mathematics and Mathematical Physics, 48(12), 2241–2253. doi:10.1134/S0965542508120130
  • Burger, G., Sitzenfrei, R., Kleidorfer, M., & Rauch, W. (2014). Parallel flow routing in SWMM 5. Environmental Modelling & Software, 53, 27–34. doi:10.1016/j.envsoft.2013.11.002
  • Capart, H., Eldho, T. I., Huang, S. Y., Young, D. L., & Zech, Y. (2003). Treatment of natural geometry in finite volume river flow computations. Journal of Hydraulic Engineering, 129(5), 385–393. doi:10.1061/(ASCE)0733-9429(2003)129:5(385)
  • Capuano, F., Mastellone, A., & De Angelis, E. M. (2017). A conservative overlap method for multi-block parallelization of compact finite-volume schemes. Computers & Fluids, 159, 327–337. doi:10.1016/j.compfluid.2017.10.017
  • Catella, M., Paris, E., & Solari, L. (2008). Conservative scheme for numerical modeling of flow in natural geometry. Journal of Hydraulic Engineering, 134(6), 736–748. doi:10.1061/(ASCE)0733-9429(2008)134:6(736)
  • Coquel, F., Nguyen, Q. L., Postel, M., & Tran, Q. H. (2010). Local time stepping applied to implicit-explicit methods for hyperbolic systems. Multiscale Modeling & Simulation, 8(2), 540–570.
  • Crossley, A. J., Wright, N. G., & Whitlow, C. D. (2003). Local time stepping for modeling open channel flows. Journal of Hydraulic Engineering, 129(6), 455–462. doi:10.1061/(ASCE)0733-9429(2003)129:6(455)
  • Cunge, J. A., Holly, F. M., & Verwey, A. (1980). Practical aspects of computational river hydraulics. Boston, MA: Pitman Publishing Ltd.
  • Delestre, O., Lucas, C., Ksinant, P. A., Darboux, F., Laguerre, C., Tuoi Vo, T. N., & Cordier, S. (2013). SWASHES: A compilation of shallow water analytic solutions for hydraulic and environmental studies. International Journal for Numerical Methods in Fluids, 72(3), 269–300. doi:10.1002/fld.3741
  • Delis, A. I., & Skeels, C. P. (1998). TVD schemes for open channel flow. International Journal for Numerical Methods in Fluids, 26, 791–809.
  • Ferreira, V. G., de Queiroz, R. A. B., Lima, G. A. B., Cuenca, R. G., Oishi, C. M., Azevedo, J. L. F., & McKee, S. (2012). A bounded upwinding scheme for computing convection-dominated transport problems. Computers & Fluids, 57, 208–224. doi:10.1016/j.compfluid.2011.12.021
  • Flamm, K. (2017, March/April). Has Moore's Law been repealed? An economist's perspective. Computing in Science & Engineering, 19, 29–40.
  • Freitag, M. A., & Morton, K. W. (2007). The Preissmann box scheme and its modification for transcritical flows. International Journal for Numerical Methods in Engineering, 70(7), 791–811.
  • García-Navarro, P., & Vazquez-Cendon, M. E. (2000). On numerical treatment of the source terms in the shallow water equations. Computers & Fluids, 29(8), 951–979.
  • Goutal, N., & Maurel, F. (1997). Proceedings of the 2nd Workshop on Dam-break Wave Simulation (Tech. Rep. No. HE-43/97/016/B). Paris: Electricité de France, Direction des études et recherches.
  • Goutal, N., & Maurel, F. (2002). A finite volume solver for 1D shallow-water equations applied to an actual river. International Journal for Numerical Methods in Fluids, 38, 1–19.
  • Greenberg, J. M., & Leroux, A. Y. (1996). A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM Journal on Numerical Analysis, 33(1), 1–16.
  • Hernández-Dueñas, G., & Karni, S. (2011). Shallow water flows in channels. Journal of Scientific Computing, 48, 190–208. doi:10.1007/s10915-010-9430-x
  • Hodges, B. R. (2015). Representing hydrodynamically important blocking features in coastal or riverine lidar topography. Natural Hazards and Earth System Sciences, 15(5), 1011–1023. doi:10.5194/nhess-15-1011-2015
  • Hodges, B. R. (2019a). Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage. Hydrology and Earth System Sciences, 23, 1281–1304. doi:10.5194/hess-23-1281-2019
  • Hodges, B. R. (2019b). SvePy source code (Texas Data Repository). University of Texas at Austin. doi:10.18738/T8/EHHBNB.
  • Hodges, B. R., & Liu, F. (2019). Algorithms in the SvePy solver for the unsteady Saint-Venant equations (Technical Report). Center for Infrastructure Modeling and Management, University of Texas at Austin. doi:10.18738/T8/ETSJDJ.
  • Ivanova, K. A., Gavrilyuk, S. L., Nkonga, B., & Richard, G. L. (2017). Formation and coarsening of roll-waves in shear shallow water flows down an inclined rectangular channel. Computers & Fluids, 159, 189–203. doi:10.1016/j.compfluid.2017.10.004
  • Leonard, B. P. (1979). A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Computer Methods in Applied Mechanics And Engineering, 19, 59–98. doi:10.1016/0045-7825(79)90034-3
  • Leonard, B. P. (1995). Comments on the policy statement on numerical accuracy. Journal of Fluids Engineering, 117, 5–6.
  • Li, J. Q., & Chen, G. X. (2006). The generalized riemann problem method for the shallow water equations with bottom topography. International Journal for Numerical Methods in Engineering, 65(6), 834–862. doi:10.1002/nme.1471
  • Li, M., Guyenne, P., Li, F., & Xu, L. (2017). A positivity-preserving well-balanced central discontinuous Galerkin method for the nonlinear shallow water equations. Journal of Scientific Computing, 71(3), 994–1034. doi:10.1007/s10915-016-0329-z
  • Liggett, J. A. (1975). Unsteady flow in open channels. Fort Collins, CO: Water Resources Publications.
  • Liu, F., & Hodges, B. R. (2014). Applying microprocessor analysis methods to river network modelling. Environmental Modelling & Software, 52, 234–252. doi:10.1016/j.envsoft.2013.09.013
  • Morales-Hernández, M., Petaccia, G., Brufau, P., & García-Navarro, P. (2016). Conservative 1d-2d coupled numerical strategis applied to river flooding: The Tiber (Rome). Applied Mathematical Modelling, 40, 2087–2105. doi:10.1016/j.apm.2015.08.016
  • Patankar, S. V. (1980). Numerical heat transfer and fluid flow. New York: CRC Press.
  • Perthame, B., & Simeoni, C. (2001). A kinetic scheme for the Saint-Venant system with a source term. CALCOLO, 38(4), 201–231. doi:10.1007/s10092-001-8181-3
  • Pu, J. H., Cheng, N. S., Tan, S. K., & Shao, S. (2012). Source term treatment of SWEs using surface gradient upwind method. Journal of Hydraulic Research, 50(2), 145–153. doi:10.1080/00221686.2011.649838
  • Rosatti, G., Bonaventura, L., Deponti, A., & Garegnani, G. (2011). An accurate and efficient semi-implicit method for section-averaged free-surface flow modelling. International Journal for Numerical Methods in Fluids, 65(4), 448–473. doi:10.1002/fld.2191
  • Rossman, L. A. (2017). Storm Water Management Model Reference Manual, Volume II - Hydraulics (Tech. Rep. No. EPA/600/R-17/111). US EPA Office of Research and Development, Water Systems Division. Retrieved from https://nepis.epa.gov/Exe/ZyPDF.cgi?Dockey=P100S9AS.pdf.
  • Sart, C., Baume, J. P., Malaterre, P. O., & Guinot, V. (2010). Adaptation of Preissmann's scheme for transcritical open channel flows. Journal of Hydraulic Research, 48(4), 428–440. doi:10.1080/00221686.2010.491648
  • Schippa, L., & Pavan, S. (2008). Analytical treatment of source terms for complex channel geometry. Journal of Hydraulic Research, 46(6), 753–763. doi:10.3826/jhr.2008.3211
  • Trahan, C. J., & Dawson, C. (2012). Local time-stepping in Runge-Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations. Computer Methods in Applied Mechanics and Engineering, 217–220, 139–152.
  • Xing, Y. (2014). Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium. Journal of Computational Physics, 257(Part A), 536–553. doi:10.1016/j.jcp.2013.10.010
  • Ying, X., & Wang, S. S. Y. (2008). Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flows. Journal of Hydraulic Research, 46(1), 21–34.
  • Yu, C. W., Hodges, B. R., & Liu, F. (2019). Numerical modeling of the Saint-Venant equations: Effects and adaptions for bottom slope discontinuity. Water Resources Research (submitted).
  • Yu, C. W., Liu, F., & Hodges, B. R. (2017). Consistent initial conditions for the Saint-Venant equations in river network modeling. Hydrology and Earth System Sciences, 21, 4959–4972. doi:10.5194/hess-21-4959-2017

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