Abstract
A boundary-layer is a thin fluid layer near a solid surface, and viscous effects dominate it. The laminar boundary-layer calculations appear in many aerodynamics problems, including skin friction drag, flow separation, and aerodynamic heating. A student must understand the flow physics and the numerical implementation to conduct successful simulations in advanced undergraduate- and graduate-level fluid dynamics/aerodynamics courses. Numerical simulations require writing computer codes. Therefore, choosing a fast and user-friendly programming language is essential to reduce code development and simulation times. Julia is a new programming language that combines performance and productivity. The present study derived the compressible Blasius equations from Navier–Stokes equations and numerically solved the resulting equations using the Julia programming language. The fourth-order Runge–Kutta method is used for the numerical discretization, and Newton’s iteration method is employed to calculate the missing boundary condition. In addition, Burgers’, heat, and compressible Blasius equations are solved both in Julia and MATLAB. The runtime comparison showed that Julia with for loops is 2.5 to 120 times faster than MATLAB. We also released the Julia codes on our GitHub page to shorten the learning curve for interested readers.
Highlights
Introduction to Compressible LaminarBoundary-Layer Flows Furkan Oz * and Kursat KaraSchool of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA; Citation: Oz, F.; Kara, K
The fluid flow over a surface is divided into two regions by the boundary-layer edge: an area between the surface and the boundary-layer edge dominated by the viscous effects and a region outside the boundary-layer edge where the viscous effects can be neglected
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 computational fluid dynamics (CFD) [18,19]
Summary
Until the 19th century, scientists neglected the effects of viscosity in their hydrodynamic and aerodynamic calculations using potential flow theory. Students tend to use user-friendly languages for their coursework and simple problems; in the industry, it is crucial to have a fast solver In this gap, Julia provides easy syntax, as Python and MATLAB, and a fast performance, as Fortran and. 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] In this tutorial paper, compressible Blasius equation and energy equation are derived from scratch and implemented in the Julia environment. Burger’s, heat, and compressible Blasius equations solution times obtained by Julia and MATLAB solvers are compared with each other. We make all these codes available on GitHub to shorten the learning curve. The other research studies where boundary-layer flow is involved are presented in the references [38,39,40,41,42,43]
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