A CFD Tutorial in Julia: Introduction to Laminar Boundary-Layer Theory

Abstract

Numerical simulations of laminar boundary-layer equations are used to investigate the origins of skin-friction drag, flow separation, and aerodynamic heating concepts in advanced undergraduate- and graduate-level fluid dynamics/aerodynamics courses. A boundary-layer is a thin layer of fluid near a solid surface, and viscous effects dominate it. Students must understand the modeling of flow physics and implement numerical methods to conduct successful simulations. Writing computer codes to solve equations numerically is a critical part of the simulation process. Julia is a new programming language that is designed to combine performance and productivity. It is dynamic and fast. However, it is crucial to understand the capabilities of a new programming language before attempting to use it in a new project. In this paper, fundamental flow problems such as Blasius, Hiemenz, Homann, and Falkner-Skan flow equations are derived from scratch and numerically solved using the Julia language. We used the finite difference scheme to discretize the governing equations, employed the Thomas algorithm to solve the resulting linear system, and compared the results with the published data. In addition, we released the Julia codes in GitHub to shorten the learning curve for new users and discussed the advantages of Julia over other programming languages. We found that the Julia language has significant advantages in productivity over other coding languages. Interested readers may access the Julia codes on our GitHub page.

Controlling hypersonic boundary layer transition with localized cooling and metasurface treatments

“…In this study, the nose radius is selected to be small enough to diminish the stabilization effect of the entropy layer 17 , 57 , 59 , 60 . Additionally, the steady flow boundary layer velocity and temperature profiles are compared with the similarity solution 61 , 62 in Fig. 5 , and an excellent agreement is found.…”

A CFD Tutorial in Julia: Introduction to Compressible Laminar Boundary-Layer Flows

“…Incompressible Blasius solution is a similarity solution for a flat plate. The assumptions for the incompressible Blasius equations are given in our previous work [19]; interested readers can check the details from there. In the compressible region, the temperature effects must be taken into account for an accurate solution.…”

“…This makes Julia a great choice for researchers due to the ability to combine high-performance with productivity. Although there are some tutorial papers and modules developed in other languages [14][15][16][17], the current number of publications is not enough to gain a thorough understanding of the Julia language in CFD [18,19].…”

Contributions to the Teaching and Learning of Fluid Mechanics

“…The article [14] by Oz and Kara discuss computational methods relevant to 'Boundary Layer theory', a subject appropriate for introduction in an upper level undergraduate or graduate course. Relevant problems such as Blasius, Hiemenz, Homann, and Falkner-Skan flow equations are derived and numerically solved using the language, Julia.…”