The absorbing boundary conditions of Newtonian fluid flowing across a semi-infinite plate with different velocities and pressures

Abstract

Abstract The Newtonian fluid flowing across a semi-infinite plate with variable velocity and pressure is considered in this work. The dimensionless governing equation is obtained by introducing the dimensionless quantities. For infinite region, the artificial boundary approach by using the Laplace transform is applied to gain the absorbing boundary condition (ABC) in a finite region which we call the inner region. The approach differs from the traditional approximation method for infinite boundaries with large values and is first applied to the research. And the stability of the ABC is verified by considering the same point of the outer region and inner region. The numerical difference scheme by using the L1-scheme to approximate the fractional derivative is used to get solutions, and the feasibility assessments, such as stability and convergence, are developed. Three numerical examples are given. In the first example, the exact solution is gained by importing a source term. Through the comparison of numerical solution with exact solution verifies the accuracy of difference method. A comparison between the velocity distribution of the ABC and the infinite boundary approximated by a large value is also discussed and graphically analyzed. In the following two examples, by analyzing the fluid flow over the plate with assorted speeds or pressure gradient, the impact of correlative parameters on the velocity distribution and the flow mechanism are thoroughly analyzed.