Multi-layer non-hydrostatic free surface modelling using the discontinuous Galerkin method
Author(s)
Pan, Wei
Kramer, S
Piggott, M
Type
Journal Article
Abstract
A multi-layer non-hydrostatic version of the unstructured mesh, discontinuous Galerkin
finite element based coastal ocean model, Thetis, is developed. This is accomplished
using the PDE solver framework, Firedrake, which is used to automatically produce the
code for the discretised model equations in a rapid and efficient manner. The motivation
for this work is a need to accurately simulate dispersive nearshore free surface processes.
In order to resolve both frequency dispersion and non-linear effects accurately, additional non-hydrostatic terms are included in the layer-integrated hydrostatic equations,
producing a form similar to the layered non-linear shallow water equations, but with
extra vertical velocities at the layer interfaces. An implementation process is adopted
to easily handle the inter-layer connection, i.e. the governing equations are transformed
into a depth-integrated system through the introduction of depth-averaged variables.
The model is verified and validated through comparisons against several idealised
and experimentally-based test cases. All the comparisons demonstrate good agreement,
showing that the developed non-hydrostatic model has excellent capabilities in representing coastal wave phenomena including shoaling, refraction and diffraction of dispersive short waves, as well as propagation, run-up and inundation of non-linear tsunami
waves.
finite element based coastal ocean model, Thetis, is developed. This is accomplished
using the PDE solver framework, Firedrake, which is used to automatically produce the
code for the discretised model equations in a rapid and efficient manner. The motivation
for this work is a need to accurately simulate dispersive nearshore free surface processes.
In order to resolve both frequency dispersion and non-linear effects accurately, additional non-hydrostatic terms are included in the layer-integrated hydrostatic equations,
producing a form similar to the layered non-linear shallow water equations, but with
extra vertical velocities at the layer interfaces. An implementation process is adopted
to easily handle the inter-layer connection, i.e. the governing equations are transformed
into a depth-integrated system through the introduction of depth-averaged variables.
The model is verified and validated through comparisons against several idealised
and experimentally-based test cases. All the comparisons demonstrate good agreement,
showing that the developed non-hydrostatic model has excellent capabilities in representing coastal wave phenomena including shoaling, refraction and diffraction of dispersive short waves, as well as propagation, run-up and inundation of non-linear tsunami
waves.
Date Issued
2019-02-01
Date Acceptance
2019-01-08
Citation
Ocean Modelling, 2019, 134, pp.68-83
ISSN
1463-5003
Publisher
Elsevier
Start Page
68
End Page
83
Journal / Book Title
Ocean Modelling
Volume
134
Copyright Statement
© 2019 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/L000407/1
EP/M011054/1
EP/R029423/1
Subjects
Science & Technology
Physical Sciences
Meteorology & Atmospheric Sciences
Oceanography
Discontinuous Galerkin
Non-hydrostatic
Dispersion
Free surface
Unstructured mesh
FINITE-ELEMENT MODEL
NUMERICAL-SIMULATION
SOLITARY WAVES
ALGORITHM
FLOW
EQUATIONS
VOLUME
FORMULATIONS
TSUNAMI
RUNUP
0405 Oceanography
Publication Status
Published
Date Publish Online
2019-01-08