FluxCellv0.9

A second-order MUSCL-Hancock scheme with HLLC fluxes, in WebGPU.

References. The method, the benchmarks and cases, and the data behind the examples.

01 Method

  1. van Leer, B. (1979). Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. Journal of Computational Physics, 32(1), 101–136. https://doi.org/10.1016/0021-9991(79)90145-1
  2. Toro, E. F., Spruce, M., & Speares, W. (1994). Restoration of the contact surface in the HLL-Riemann solver. Shock Waves, 4(1), 25–34. https://doi.org/10.1007/BF01414629
  3. Toro, E. F. (2009). Riemann solvers and numerical methods for fluid dynamics: A practical introduction (3rd ed.). Springer. https://doi.org/10.1007/b79761
  4. 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. https://doi.org/10.1137/S1064827503431090
  5. Thornber, B., Mosedale, A., Drikakis, D., Youngs, D., & Williams, R. J. R. (2008). An improved reconstruction method for compressible flows with low Mach number features. Journal of Computational Physics, 227(10), 4873–4894. https://doi.org/10.1016/j.jcp.2008.01.036
  6. Smagorinsky, J. (1963). General circulation experiments with the primitive equations. Monthly Weather Review, 91(3), 99–164. https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
  7. Mehta, A. J. (1986). Characterization of cohesive sediment properties and transport processes in estuaries. In A. J. Mehta (Ed.), Estuarine cohesive sediment dynamics (Lecture Notes on Coastal and Estuarine Studies, Vol. 14, pp. 290–325). Springer New York. https://doi.org/10.1007/978-1-4612-4936-8_15
  8. Meyer-Peter, E., & Müller, R. (1948). Formulas for bed-load transport. In Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research (pp. 39–64). IAHR.
  9. Wu, J. (1982). Wind-stress coefficients over sea surface from breeze to hurricane. Journal of Geophysical Research: Oceans, 87(C12), 9704–9706. https://doi.org/10.1029/JC087iC12p09704

02 Benchmarks and cases

  1. Synolakis, C. E., Bernard, E. N., Titov, V. V., Kânoğlu, U., & González, F. I. (2007). Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models (NOAA Technical Memorandum OAR PMEL-135). NOAA Pacific Marine Environmental Laboratory.
  2. Briggs, M. J., Synolakis, C. E., Harkins, G. S., & Green, D. R. (1995). Laboratory experiments of tsunami runup on a circular island. Pure and Applied Geophysics, 144, 569–593.
  3. Liu, P. L.-F., Yeh, H., & Synolakis, C. (2008). Benchmark problems. In Advanced numerical models for simulating tsunami waves and runup (Advances in Coastal and Ocean Engineering, Vol. 10, pp. 223–230). World Scientific.
  4. Matsuyama, M., & Tanaka, H. (2001). An experimental study of the highest run-up height in the 1993 Hokkaido Nansei-Oki earthquake tsunami. In Proceedings of the International Tsunami Symposium 2001 (pp. 879–889).
  5. Fennema, R. J., & Chaudhry, M. H. (1990). Explicit methods for 2-D transient free surface flows. Journal of Hydraulic Engineering, 116(8), 1013–1034. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:8(1013)
  6. Michalke, A. (1964). On the inviscid instability of the hyperbolic-tangent velocity profile. Journal of Fluid Mechanics, 19(4), 543–556. https://doi.org/10.1017/S0022112064000908
  7. Williamson, C. H. K. (1996). Vortex dynamics in the cylinder wake. Annual Review of Fluid Mechanics, 28, 477–539. https://doi.org/10.1146/annurev.fl.28.010196.002401
  8. McWilliams, J. C. (1984). The emergence of isolated coherent vortices in turbulent flow. Journal of Fluid Mechanics, 146, 21–43. https://doi.org/10.1017/S0022112084001750

03 Data

  1. Cooperative Institute for Research in Environmental Sciences (CIRES) at the University of Colorado, Boulder. (2014). Continuously Updated Digital Elevation Model (CUDEM) – 1/9 arc-second resolution bathymetric-topographic tiles [tiles ncei19_n29x25_w090x00 and ncei19_n29x50_w090x00, 2020v1]. NOAA National Centers for Environmental Information. https://doi.org/10.25921/ds9v-ky35
  2. Sugarbaker, L. J., Constance, E. W., Heidemann, H. K., Jason, A. L., Lukas, V., Saghy, D. L., & Stoker, J. M. (2014). The 3D Elevation Program initiative: A call for action (U.S. Geological Survey Circular 1399). https://doi.org/10.3133/cir1399
  3. OpenStreetMap contributors. Building footprints and breakwaters, Grand Isle, Louisiana, retrieved through the Overpass API. Open Database License (ODbL) 1.0. https://www.openstreetmap.org/copyright
  4. NOAA National Ocean Service. Station 8761724, Grand Isle, LA: tidal datums (epoch 2012–2016) and record water level of 29 August 2021; NOAA VDatum for mean sea level relative to NAVD88. https://tidesandcurrents.noaa.gov/stationhome.html?id=8761724

04 Cite

  1. FluxCell: a MUSCL-Hancock/HLLC shallow-water and transport solver in WebGPU. HydroInformatics Lab. https://github.com/uihilab/fluxcell