Shang-Gui Cai

In this paper, we study the stability of breakwaters made of discrete ar-mour units, which requires specialized numerical methods to account foreach block’s shape, motion, and inter-element contact. Furthermore, theeffects of the porosity and thickness of the porous layer on stability are as-sessed. Therefore, a fluid-porous-solid coupling model is developed to investi-gate the stability of discrete composite breakwater. The fluid-porous modelis formulated from the Volume-Averaged Reynolds-Averaged Navier-Stokes(VARANS) equations, in which nonlinear Forchheimer terms have been incor-porated to describe flow through the porous layer. The solid model is basedon the Nodal-based Discontinuous Deformation Analysis (NDDA) method tocompute the displacements of individual blocks. This coupled model enablesexamination of how the thickness and porosity of porous layer influence themaximum impacting wave height (IWHmax) and the generation of turbulentkinetic energy (TKE). Then to investigate the stability of breakwater withdifferent kinds of armour units.

A strongly coupled algorithm is presented for the incompressible fluid–rigid body interaction using the moving immersed boundary method. The pressure and the boundary force are treated as Lagrange multipliers to enforce the incompressibility and no-slip wall constraints. To compute the two unknowns from the velocity field, we adopt the fractional step algorithm and successively apply the two constraints. A Poisson equation and a moving force equation are derived for the pressure and the boundary force, respectively. As both coefficient matrices are formulated to be symmetric and positive-definite, the resulting linear systems are solved efficiently with the conjugate gradient solver. The strongly coupled nonlinear fluid–solid system is achieved by a fixed-point iteration. To improve the computational efficiency, we only iterate the moving force equation with the rigid body motion equation, and the time-consuming pressure Poisson equation is solved once the sub-iteration is finished. The proposed method is validated with various benchmark tests, and the results compare well with the literature.

Algebraic explicit wall models covering the entire inner region of the turbulent boundary layer are proposed to reduce the computational effort for large eddy simulation of wall-bounded turbulent flows. The proposed formulas are given in closed forms with either logarithmic- or power-function-based laws of the wall, allowing straightforward evaluation of the friction velocity on near wall grids independent of their locations in the turbulent boundary layer. The performance of the proposed models is demonstrated by the wall modeled large eddy simulation of a turbulent plane channel flow.

Summary: A novel implicit immersed boundary method of high accuracy and efficiency is presented for the simulation of incompressible viscous flow over complex stationary or moving solid boundaries. A boundary force is often introduced in many immersed boundary methods to mimic the presence of solid boundary, such that the overall simulation can be performed on a simple Cartesian grid. The current method inherits this idea and considers the boundary force as a Lagrange multiplier to enforce the no‐slip constraint at the solid boundary, instead of applying constitutional relations for rigid bodies. Hence excessive constraint on the time step is circumvented, and the time step only depends on the discretization of fluid Navier‐Stokes equations, like the CFL condition in present work. To determine the boundary force, an additional moving force equation is derived. The dimension of this derived system is proportional to the number of Lagrangian points describing the solid boundaries, which makes the method very suitable for moving boundary problems since the time for matrix update and system solving is not significant. The force coefficient matrix is made symmetric and positive definite so that the conjugate gradient method can solve the system quickly. The proposed immersed boundary method is incorporated into the fluid solver with a second‐order accurate projection method as a plug‐in. The overall scheme is handled under an efficient fractional step framework, namely, prediction, forcing, and projection. Various simulations are performed to validate current method, and the results compare well with previous experimental and numerical studies.