The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

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Numerical Heat Transfer And Fluid Flow

SUMMARY
The open-source CFD library OpenFoam® contains a method for solving free surface Newtonian flows using the Reynolds averaged Navier–Stokes equations coupled with a volume of fluid method. In this paper, it is demonstrated how this has been extended with a generic wave generation and absorption method termed ‘wave relaxation zones’, on which a detailed account is given. The ability to use OpenFoam for the modelling of waves is demonstrated using two benchmark test cases, which show the ability to model wave propagation and wave breaking. Furthermore, the reflection coefficient from outlet relaxation zones is considered for a range of parameters. The toolbox is implemented in C++, and the flexibility in deriving new relaxation methods and implementing new wave theories along with other shapes of the relaxation zone is outlined. Subsequent to the publication of this paper, the toolbox has been made freely available through the OpenFoam-Extend Community. Copyright © 2011 John Wiley & Sons, Ltd.

A wave generation toolbox for the open‐source CFD library: OpenFoam®

SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters

/pdf/numerical-solutions-of-boussinesq-equations-for-fully-2d1s5nxbko.pdf

Numerical Solutions of Boussinesq Equations for Fully Nonlinear and Extremely Dispersive Water Waves

Full-scale CFD simulation of tsunamis. Part 2: Boundary layers and bed shear stresses

Numerical modeling of flow and morphology induced by a solitary wave on a sloping beach

https://orbit.dtu.dk/files/126135693/Bayraktaretal.pdf

David R. Fuhrman

Papers

Numerical Solutions of Boussinesq Equations for Fully Nonlinear and Extremely Dispersive Water Waves

Full-scale CFD simulation of tsunamis. Part 2: Boundary layers and bed shear stresses

Numerical modeling of flow and morphology induced by a solitary wave on a sloping beach

Experimental and Numerical Study of Wave-Induced Backfilling Beneath Submarine Pipelines

Span shoulder migration in three-dimensional current-induced scour beneath submerged pipelines