Boundary Layer Initialization

In order to avoid instabilities and help the convergence of the numerical system this tecnique is adopted. It is based on the resolution of the p-poisson, [5]. The algorithm used to solve the non-linear p-Poisson, equation \eqref{equ:ppoisson} equation resembles the Picard method.

$\nabla \cdot (|\nabla u_p|^{p-2} \nabla u_p) = -1 , x\in \Omega$ $u_p = 0 , x\in \Omega_D$

The idea is to compute the wall-normal distance, from the airfoil, for each point of the domain. Then setting a threshold based on the Reynolds number, the velocity in the area close to the airfoil follows a cubic function.

How to use it

It is possible to initialize the airfoil simulation using the WallDistance module. It works only in serial and for 2D meshes but it is possible to initialize a 3D solution from a 2D results.

using SegregatedVMSSolver
using SegregatedVMSSolver.WallDistance


mesh_file = joinpath(@__DIR__, "../../models", "DU89_2D_A1_M.msh")

D = 2
u_in = 1.0
Re = 500e3
chord = 1.0
walltag = ["airfoil"]

df_start = get_initial_conditions(mesh_file, u_in, Re, walltag; D=D, chord=chord)

This will create a Initial_Conditions.vtu which can be open in ParaView and BoundaryLayerInit.csv which can be used to restart the simulation. Only the velocity is initilized, not the pressure.