A collocation-grid method on moving grids for the numerical modelling of boundary layers

Numerical models of jet flows of a viscous incompressible fluid

“…Analysing the works on the numerical integration of the boundarylayer equations, we can emphasize the trend associated with the use of adaptive grids [15,18,21,23,27]. First of all, this is the use of Euler -Lagrange Prandtl-Mises variables [18,21,23].…”

“…First of all, this is the use of Euler -Lagrange Prandtl-Mises variables [18,21,23]. The finite difference method and the collocation grid method with the use of adaptive grids were developed in [15,27], respectively. The flows in the boundary layer itself were considered in [15,27].…”

“…We carried out the numerical experiments that demonstrate the convergence of the algorithms considered. Using the modified turbulent e -ε model, we numerically simulate the dynamics of two-dimensional and axisymmetric turbulent wakes with zero and small nonzero excess momenta.The approximation of a boundary (thin shear) layer is a classical approximation when studying the two-dimensional and axisymmetric jet flows [21,23], The methods of calculating the boundary-layer equations were considered in a sufficiently large number of works [4][5][6]11,12,[15][16][17][19][20][21]23,26,27] (a more complete bibliography can be found therein). Analysing the works on the numerical integration of the boundarylayer equations, we can emphasize the trend associated with the use of adaptive grids [15,18,21,23,27].…”

“…The finite difference method and the collocation grid method with the use of adaptive grids were developed in [15,27], respectively. The flows in the boundary layer itself were considered in [15,27]. Both laminar and turbulent flows were studied in the above works.…”