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.
Highlights
Introduction to Laminar BoundaryLayer TheoryFurkan Oz * and Kursat KaraCitation: Oz, F.; Kara, K
In the computational fluid dynamics industry, it is crucial to have some predictions about the flow that will be simulated
Fundamental knowledge about canonical flows is crucial in this point because most of the complex flow consists of a combination of a couple of canonical flows
Summary
Computational fluid dynamics (CFD) simulation is one of the vital steps of the design of a product that includes fluid motion. Blasius [2] worked on the same problem as Prandtl did He aimed to overcome the enigma of turbulence by considering the phenomenon of boundary-layer flow explained by Hager [3]. Understanding the aforementioned fundamental flows are crucial for a senior undergraduate student or a graduate student in order to simulate more complex flows Modeling these equations in a computer environment requires more than knowledge about canonical flows instead it requires knowledge about programming languages as well. The computer codes and the implementation instructions will help students to understand the fundamental flows which will provide insight for student’s course work and researches. Using these examples, they can solve more complex flow types and develop their own codes. The GitHub link of the codes can be found in Appendix A
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