Efficiently and Discretely Modelling Shallow Water Flows

Natural disasters involving flow such as flooding and tsunamis often lead to a loss of lives and considerable economic damage.
For example, in 1993 a tsunami generated by a magnitude-7.8 earthquake inundated Okushiri, Japan causing the death of 165 people; in the UK flooding causes £1.3 billion of economic loss each year1. Understanding these flows is a crucial step towards mitigating their devastation, and the application of computational modelling techniques is one important method contributing to this field of research.
1993 Hokkaido earthquake and tsunami: Aonae, Okushiri Island, looking southeast. Structures in the foreground were damaged by fires fueled by above-ground kerosene and propane tanks following the tsunami. The concrete steps provided a means of escape for some residents following the strong earthquake2.
UKCOMES community software is developed to simulate the flow behaviour of a tsunami inundation
Dr. Jianping Meng, Dr. Xiaojun Gu, and Prof. David Emerson, (computational engineers at the Science and Technologies Facilities Council (STFC)) describe how their work with Mr Yunlong Fei, Dr. Peng Yong3, and Prof. Jianmin Zhang (at the State Key Laboratory of Hydraulics and Mountain River Engineering (SKLH), Sichuan University, China) contributes to the understanding of fluid flows present in natural disasters. The team developed software to simulate realistic flow problems such as a tsunami inundation.

Photo Credit: Pixabay
Enhancing the lattice Boltzmann method
The lattice Boltzmann method (LBM) has emerged as an easy-to-understand modelling tool for fluid flows. Rooted in the kinetic theory of gases – where identical particles move in random directions – the LBM is formed by discretizing the statistical Boltzmann equation on a grid (‘lattice’). Although used in the shallow water model, LBM needed further development to make it applicable to supercritical flows that occur in natural disasters4. To simulate these more realistic problems, e.g., tsunami inundation, it is necessary to model the drying-wetting interface that is moving during the inundation. ‘Vanilla’ LBM lacked this capability, and was in need of development.
Discrete Boltzmann model (DBM)
To tackle this challenge, the team developed a type of discrete Boltzmann model (DBM) by applying a specific type of polynomial expansion i.e., the Hermite expansion approach4 to the LBM. This extended the model’s capability to supercritical flows without much loss in efficiency and simplicity. The model was then implemented into the multiple platform lattice Boltzmann (MPLB) code within STFC’s general purpose mesoscale simulation package – DL-MESO.
High-resolution snapshots of a discrete Boltzmann model (DBM) simulation of a tsunami run-up onto a complex beach profile showing the 3D water height distributions at different times, (T). Grey denotes the sea bathymetry (surface of the underwater floors); and blue is the height of the surface of the water.
To simulate the drying-wetting phenomenon seen, for example, in a tsunami inundation the research team implemented various schemes based on the MPLB code and tested them over a range of benchmark problems. In particular, they compared the DBM simulations with the experimental data produced using a large-scale tank for exploring the extreme run-up of 32m height observed near the village of Monai during the 1993 Okushiri tsunami5. The computer simulations were conducted to model a sub-region of the tank where there are complex bathymetry (underwater floor surface profiles) and coastal topography. Preliminary testing demonstrated promising results, confirming the successful implementation and application of the MPLB code to such shallow water flows.
Tsunami run-up onto a complex 3D beach
The movie shows a discrete Boltzmann model (DBM) simulation of a tsunami run-up onto a complex beach profile showing the 3D water height distributions at different times. (Grey denotes the sea bathymetry (surface of the underwater floors); and blue is the height of the surface of the water)
This work complements a wave tank experiment5 of a 1:400 scale model of the coastline bathymetry near Monai in Japan, Okushiri – the location of the 1993 tsunami inundation.
The developed software has been implemented in DL_MESO and is one of the codes supported by UKCOMES.
How to obtain DL-MESO
Follow the instructions on this page to register: https://www.scd.stfc.ac.uk/Pages/DL_MESO-register.aspx. Then follow the instructions that are emailed to you on successful registration. DL_MESO is one of the software codes developed by UKCOMES (ucl.ac.uk/mesoscale-modelling-consortium) that is one of the 19 communities supported by STFC scientists and engineers through the CoSeC project. (cosec.stfc.ac.uk).
1Flood risk and the UK Energy & Climate Intelligence Unit
eciu.net/analysis/briefings/climate-impacts/flood-risk-and-the-uk
2National Centers for Environmental Information
ngdc.noaa.gov/hazardimages/#/all/46
3Dr. Yong Peng’s present address – School of Natural and Built Environment, Environmental Change and Resilience, Queens’ University Belfast
4Meng JP, Gu XJ, Emerson DR, Peng Y, Zhang JM (2018), Discrete Boltzmann model of shallow water equations with polynomial equilibria, International Journal of Modern Physics C 29: 1850080-15;
5Liu P. L.-F, Yeh H, Synolakis C (Eds.), Advanced numerical models for simulating tsunami waves and run-up, Vol. 10. World Scientific, 2008.
Funding: This work was sponsored by: The Royal Society – 2015 China (NSFC) Cost share programme; UK Consortium on Mesoscale Engineering Sciences (UKCOMES, EP/R029598/1). This work used the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk). The Computational Science Centre for Research Communities (CoSeC) (cosec.stfc.ac.uk) provided STFC staff support.
Further Information: Dr. Yong Peng’s present address -School of Natural and Built Environment, Environmental Change and Resilience, Queens’ University Belfast (https://pure.qub.ac.uk/en/organisations/school-of-natural-and-built-environment)
Contact: jianping.meng@stfc.ac.uk
This BBC Radio 4 program ‘The Reunion: The Boxing Day Tsunami‘ is a moving account of the first-hand experiences of 5 people caught-up in the 2004 tsunami.
