An Iterative Transformation Method for a Similarity Boundary Layer Model

2020/11/13 by Riccardo Fazio, Fazio, Riccardo
Engineering · Mathematics · #34B15 #65L08 #65L10 #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2011.09661

openalex publication_date 2020/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is defined on a semi-infinite interval. Using our transformation method we are able to solve the problem in point for a large range of the parameter involved. As far as the accuracy of our numerical method is concerned, for two specific values of the involved parameter, we are able to compare favorably the obtained numerical result for the so-called missing initial condition to the exact solution reported by Crane [Z. Angew. Math. Phys., 21:645-647, 1970].

Citations

• Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow

Related

• The Iterative Transformation Method
• A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations
• A Non-Iterative Transformation Method Applied to Boundary-Layer Flows of Non-Newtonian Fluids Past a Flat Plate
• On a general similarity boundary layer equation
• The Prandtl Plus Scaling Approximation for Turbulent Boundary Layer\n Flows