An improved multislope MUSCL scheme for solving shallow water equations on unstructured grids

Zhao, Jiaheng; Özgen-Xian, Ilhan; Liang, Dongfang; Wang, Tian; Hinkelmann, Reinhard

doi:10.1016/j.camwa.2018.09.059

Title: An improved multislope MUSCL scheme for solving shallow water equations on unstructured grids

Journal Article · 14 January 2019 · Computers and Mathematics with Applications (Oxford)

DOI: https://doi.org/10.1016/j.camwa.2018.09.059 · OSTI ID:1580349

^[1]; Özgen-Xian, Ilhan ^[2]; Liang, Dongfang ^[3]; Wang, Tian ^[4]; Hinkelmann, Reinhard ^[1]

Technical Univ. of Berlin (Germany)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Univ. of Cambridge (United Kingdom)
Technical Univ. of Berlin (Germany); Xi'an Jiaotong Univ., Shaanxi (China)

In this paper we describe an improved vector manipulation multislope monotone upstream-centred scheme for conservation laws (MUSCL) reconstruction for solving the shallow water equations on unstructured grids. This improved MUSCL reconstruction method includes a bigger stencil for the interpolation and saves time for determining the geometric relations compared to the original vector manipulation method, so it is computationally more efficient and straightforward to implement. Four examples involving an analytical solution, laboratory experiments and field-scale measurements are used to test the performance of the proposed scheme. It has been proven that the proposed scheme can provide comparable accuracy and higher efficiency compared to the original vector manipulation method. With the increasing of the number of cells, the advantage of the proposed scheme becomes more apparent.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1580349

Journal Information:: Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Journal Issue: 2 Vol. 77; ISSN 0898-1221

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (27)

Monoslope and multislope MUSCL methods for unstructured meshes Buffard, Thierry; Clain, Stéphane Journal of Computational Physics, Vol. 229, Issue 10 https://doi.org/10.1016/j.jcp.2010.01.026	journal	May 2010
TVD schemes for unstructured grids Darwish, M. S.; Moukalled, F. International Journal of Heat and Mass Transfer, Vol. 46, Issue 4 https://doi.org/10.1016/s0017-9310(02)00330-7	journal	February 2003
Improved total variation diminishing schemes for advection simulation on arbitrary grids: IMPROVED TVD SCHEMES FOR AS ON ARBITRARY GRIDS Hou, J.; Simons, F.; Hinkelmann, R. International Journal for Numerical Methods in Fluids, Vol. 70, Issue 3 https://doi.org/10.1002/fld.2700	journal	November 2011
A novel multidimensional solution reconstruction and edge-based limiting procedure for unstructured cell-centered finite volumes with application to shallow water dynamics: RECONSTRUCTION AND LIMITING FOR CELL-CENTERED FINITE VOLUMES Delis, A. I.; Nikolos, I. K. International Journal for Numerical Methods in Fluids, Vol. 71, Issue 5 https://doi.org/10.1002/fld.3674	journal	April 2012
A new TVD method for advection simulation on 2D unstructured grids: A NEW TVD METHOD FOR ADVECTION SIMULATION ON 2D UNSTRUCTURED GRIDS Hou, J.; Simons, F.; Hinkelmann, R. International Journal for Numerical Methods in Fluids, Vol. 71, Issue 10 https://doi.org/10.1002/fld.3709	journal	July 2012
Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters Venkatakrishnan, V. Journal of Computational Physics, Vol. 118, Issue 1 https://doi.org/10.1006/jcph.1995.1084	journal	April 1995
Restoration of the contact surface in the HLL-Riemann solver Toro, E. F.; Spruce, M.; Speares, W. Shock Waves, Vol. 4, Issue 1 https://doi.org/10.1007/BF01414629	journal	July 1994
Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method van Leer, Bram Journal of Computational Physics, Vol. 32, Issue 1 https://doi.org/10.1016/0021-9991(79)90145-1	journal	July 1979
TVD schemes for unstructured grids Darwish, M. S.; Moukalled, F. International Journal of Heat and Mass Transfer, Vol. 46, Issue 4 https://doi.org/10.1016/S0017-9310(02)00330-7	journal	February 2003
Numerical resolution of well-balanced shallow water equations with complex source terms Liang, Qiuhua; Marche, Fabien Advances in Water Resources, Vol. 32, Issue 6 https://doi.org/10.1016/j.advwatres.2009.02.010	journal	June 2009
A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment Hou, Jingming; Liang, Qiuhua; Simons, Franz Advances in Water Resources, Vol. 52 https://doi.org/10.1016/j.advwatres.2012.08.003	journal	February 2013
A robust well-balanced model on unstructured grids for shallow water flows with wetting and drying over complex topography Hou, Jingming; Simons, Franz; Mahgoub, Mohamed Computer Methods in Applied Mechanics and Engineering, Vol. 257 https://doi.org/10.1016/j.cma.2013.01.015	journal	April 2013
Adaptive quadtree simulation of shallow flows with wet–dry fronts over complex topography Liang, Qiuhua; Borthwick, Alistair G. L. Computers & Fluids, Vol. 38, Issue 2 https://doi.org/10.1016/j.compfluid.2008.02.008	journal	February 2009
MUSCL schemes for the shallow water sensitivity equations with passive scalar transport Guinot, Vincent; Delenne, Carole Computers & Fluids, Vol. 59 https://doi.org/10.1016/j.compfluid.2012.02.001	journal	April 2012
An efficient unstructured MUSCL scheme for solving the 2D shallow water equations Hou, Jingming; Liang, Qiuhua; Zhang, Hongbin Environmental Modelling & Software, Vol. 66 https://doi.org/10.1016/j.envsoft.2014.12.007	journal	April 2015
An improved r-factor algorithm for TVD schemes Li, Lian-xia; Liao, Hua-sheng; Qi, Li-jian International Journal of Heat and Mass Transfer, Vol. 51, Issue 3-4 https://doi.org/10.1016/j.ijheatmasstransfer.2007.04.051	journal	February 2008
Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids Park, Jin Seok; Yoon, Sung-Hwan; Kim, Chongam Journal of Computational Physics, Vol. 229, Issue 3 https://doi.org/10.1016/j.jcp.2009.10.011	journal	February 2010
Monoslope and multislope MUSCL methods for unstructured meshes Buffard, Thierry; Clain, Stéphane Journal of Computational Physics, Vol. 229, Issue 10 https://doi.org/10.1016/j.jcp.2010.01.026	journal	May 2010
Numerical modeling of dambreak-induced flood and inundation using smoothed particle hydrodynamics Kao, Hong-Ming; Chang, Tsang-Jung Journal of Hydrology, Vol. 448-449 https://doi.org/10.1016/j.jhydrol.2012.05.004	journal	July 2012
Case Study: Malpasset Dam-Break Simulation using a Two-Dimensional Finite Volume Method Valiani, Alessandro; Caleffi, Valerio; Zanni, Andrea Journal of Hydraulic Engineering, Vol. 128, Issue 5 https://doi.org/10.1061/(ASCE)0733-9429(2002)128:5(460)	journal	May 2002
Numerical Prediction of Dam-Break Flows in General Geometries with Complex Bed Topography Zhou, Jian G.; Causon, Derek M.; Mingham, Clive G. Journal of Hydraulic Engineering, Vol. 130, Issue 4 https://doi.org/10.1061/(ASCE)0733-9429(2004)130:4(332)	journal	April 2004
Flood Simulation Using a Well-Balanced Shallow Flow Model Liang, Qiuhua Journal of Hydraulic Engineering, Vol. 136, Issue 9 https://doi.org/10.1061/(ASCE)HY.1943-7900.0000219	journal	September 2010
Experimental study of dam-break flow against an isolated obstacle Soares-Frazão, S.; Zech, Y. Journal of Hydraulic Research, Vol. 45, Issue sup1 https://doi.org/10.1080/00221686.2007.9521830	journal	December 2007
A 2D shallow flow model for practical dam-break simulations Wang, Yueling; Liang, Qiuhua; Kesserwani, Georges Journal of Hydraulic Research, Vol. 49, Issue 3 https://doi.org/10.1080/00221686.2011.566248	journal	June 2011
A Maximum Principle Satisfying Modification of Triangle Based Adapative Stencils for the Solution of Scalar Hyperbolic Conservation Laws Liu, Xu-Dong SIAM Journal on Numerical Analysis, Vol. 30, Issue 3 https://doi.org/10.1137/0730034	journal	June 1993
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows Audusse, Emmanuel; Bouchut, François; Bristeau, Marie-Odile SIAM Journal on Scientific Computing, Vol. 25, Issue 6 https://doi.org/10.1137/S1064827503431090	journal	January 2004
Moving boundary shallow water flow above parabolic bottom topography Sampson, Joe; Easton, Alan; Singh, Manmohan ANZIAM Journal, Vol. 47 https://doi.org/10.21914/anziamj.v47i0.1050	journal	October 2006

Similar Records

Improved multislope MUSCL reconstruction on unstructured grids for shallow water equations

Journal Article · 2018 · International Journal for Numerical Methods in Fluids · OSTI ID:1483271

Zhao, J.; Özgen, I.; Liang, D.; +1 more

Convergence to steady state solutions of the Euler equations on unstructured grids with limiters

Journal Article · 1995 · Journal of Computational Physics · OSTI ID:121691

Venkatakrishnan, V

A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

Journal Article · 2015 · Computers and Fluids · OSTI ID:1214833

Charest, Marc R.J.; Canfield, Thomas R.; Morgan, Nathaniel R.; +2 more

Related Subjects

42 ENGINEERING
54 ENVIRONMENTAL SCIENCES
Finite volume method
MUSCL scheme
Shallow water
Total variation diminishing
Unstructured grids

Title: An improved multislope MUSCL scheme for solving shallow water equations on unstructured grids

Citation Formats

References (27)

Similar Records

Related Subjects