Abstract
CFD Julia is a programming module developed for senior undergraduate or graduate-level coursework which teaches the foundations of computational fluid dynamics (CFD). The module comprises several programs written in general-purpose programming language Julia designed for high-performance numerical analysis and computational science. The paper explains various concepts related to spatial and temporal discretization, explicit and implicit numerical schemes, multi-step numerical schemes, higher-order shock-capturing numerical methods, and iterative solvers in CFD. These concepts are illustrated using the linear convection equation, the inviscid Burgers equation, and the two-dimensional Poisson equation. The paper covers finite difference implementation for equations in both conservative and non-conservative form. The paper also includes the development of one-dimensional solver for Euler equations and demonstrate it for the Sod shock tube problem. We show the application of finite difference schemes for developing two-dimensional incompressible Navier-Stokes solvers with different boundary conditions applied to the lid-driven cavity and vortex-merger problems. At the end of this paper, we develop hybrid Arakawa-spectral solver and pseudo-spectral solver for two-dimensional incompressible Navier-Stokes equations. Additionally, we compare the computational performance of these minimalist fashion Navier-Stokes solvers written in Julia and Python.
Highlights
Coursework in computational fluid dynamics (CFD) usually starts with an introduction to discretization techniques of partial differential equations (PDEs), stability analysis of numerical methods, the order of convergence, iterative methods for elliptic equations, shock-capturing methods for compressible flows, and development of incompressible flow solver
CFD Julia is a programming module that contains several codes for problems ranging from one-dimensional heat equation to two-dimensional Navier-Stokes incompressible flow solver
We provide the main script in Julia so that reader will get familiar with the Julia syntax
Summary
Coursework in computational fluid dynamics (CFD) usually starts with an introduction to discretization techniques of partial differential equations (PDEs), stability analysis of numerical methods, the order of convergence, iterative methods for elliptic equations, shock-capturing methods for compressible flows, and development of incompressible flow solver. A lot of emphases is put on the theory of discretization, stability analysis, and different formulations of governing equations for compressible and incompressible flows. CFD Julia is a programming module that contains several codes for problems ranging from one-dimensional heat equation to two-dimensional Navier-Stokes incompressible flow solver. Some of these problems can be included as part of programming assignments or coursework projects.
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