Stable and high order accurate finite difference method for the incompressible laminar boundary layer equations - Nchupang, Mojalefa Prince (Department of Mechanical Engineering, 2021)
Numerical simulations of incompressible flows are unequivocally important due to their numerous industrial applications. These applications ranges from the large-scale fluid's flow modelling such as aerodynamics [1], atmospheric-ocean modelling [2] to a simple pipe flows in the petroleum industry [3]. This study is devoted to develop a provably stable and high order approximation for the incompressible laminar boundary layer equations. A new set of energystable boundary conditions are derived using the energy method. It is shown that both the weak and strong implementation of these boundary conditions yields an energy estimate. The semidiscrete problem is formulated by discretizing the continuous spatial derivatives using high order finite difference approximations on summation-by-parts form. The boundary conditions are implemented weakly using the simultaneous approximation terms methods. The discrete energy estimate is derived by mimicking the continuous analysis and hence, the numerical approximation is proved to be stable. The accuracy and linear stability of the developed scheme is also validated by solving the celebrated laminar flat plate flow problem. This is done by injecting the Blasius solution into the coefficient matrix as well as weak boundary conditions