Abstract. A numerical model, ISWFoam, for simulating internal solitary waves
(ISWs) in continuously stratified, incompressible, viscous fluids is
developed based on a fully three-dimensional (3D) Navier–Stokes equation
using the open-source code OpenFOAM®. This model combines the density
transport equation with the Reynolds-averaged Navier–Stokes equation with
the Coriolis force, and the model discrete equation adopts the finite-volume
method. The k–ω SST turbulence model has also been modified according to the variable density field. ISWFoam provides two initial wave generation
methods to generate an ISW in continuously stratified fluids, including
solving the weakly nonlinear models of the extended Korteweg–de Vries
(eKdV) equation and the fully nonlinear models of the Dubreil–Jacotin–Long
(DJL) equation. Grid independence tests for ISWFoam are performed, and
considering the accuracy and computing efficiency, the appropriate grid size
of the ISW simulation is recommended to be 1/150th of
the characteristic length and 1/25th of the ISW amplitude. Model
verifications are conducted through comparisons between the simulated and
experimental data for ISW propagation examples over a flat bottom section,
including laboratory scale and actual ocean scale, a submerged triangular
ridge, a Gaussian ridge, and slope. The laboratory test results, including
the ISW profile, wave breaking location, ISW arrival time, and the spatial
and temporal changes in the mixture region, are well reproduced by ISWFoam.
The ISWFoam model with unstructured grids and local mesh refinement can
effectively simulate the evolution of ISWs, the ISW breaking phenomenon,
waveform inversion of ISWs, and the interaction between ISWs and complex
topography.