The steady two-dimensional flow over a rectangular obstacle lying on the bottom

Abstract

We study a plane problem with mixed boundary conditions for a harmonic function in an unbounded Lipschitz domain contained in a strip. The problem is obtained by linearizing the hydrodynamic equations which describe the steady flow of a heavy ideal fluid over an obstacle lying on the flat bottom of a channel. In the case of obstacles of rectangular shape we prove unique solvability for all velocities of the (unperturbed) flow above a critical value depending on the obstacle depth. We also discuss regularity and asymptotic properties of the solutions.

Artificial Neural Networking (ANN) Model for Drag Coefficient Optimization for Various Obstacles

“…Some solution approaches in this regard can access in refs. [5][6][7][8][9][10]. Kenjere et al [11] published a paper on numerical simulations of vortical formations in transient flow regimes caused by the Lorentz force acting locally on an electrically conductive fluid.…”

Existence and Uniqueness in the Linearised One and Two-dimensional Problem of Partial Differential Equations With Variational Method

“…In that article, they analyzed weak solutions by functional analysis to prove the existence of a single solution of the linear boundary value problem that describes the motion of the equilibrium state of a half-submerged cylinder in an ideal, incompressible heavy fluid. We can also refer to the following articles: [53], [62], [17], [56], [44], [57], [16] to better understand the concept of variational method.…”