An Efficient Strategy to Deliver Understanding of Both Numerical and Practical Aspects When Using Navier-Stokes Equations to Solve Fluid Mechanics Problems

Abstract

An efficient and thorough strategy to introduce undergraduate students to a numerical approach of calculating flow is outlined. First, the basic steps, especially discretization, involved when solving Navier-Stokes equations using a finite-volume method for incompressible steady-state flow are developed with the main aim being for the students to follow through from the mathematical description of a given problem to the final solution of the governing equations in a transparent way. The well-known ‘driven-cavity’ problem is used as the problem for testing coding written by the students, and the Navier-Stokes equations are initially cast in the vorticity-streamfunction form. This is followed by moving on to a solution method using the primitive variables and discussion of details such as, closure of the Navier-Stokes equations using turbulence modelling, appropriate meshing within the computation domain, various boundary conditions, properties of fluids, and the important methods for determining that a convergence solution has been reached. Such a course is found to be an efficient and transparent approach for introducing students to computational fluid dynamics.

Nzubechukwu Chukwudum Ohalete

“…For example, in cardiovascular device design, these equations enable the simulation of blood flow, providing insights into pressure gradients and shear stresses. This is vital for assessing the performance and safety of devices like stents and artificial heart valves (Adair & Jaeger, 2019). The equations facilitate the understanding of hemodynamics, which is essential in ensuring that these devices do not adversely affect blood flow or cause damage to blood cells.…”

Teaching and Learning of Fluid Mechanics

“…Several collections in this issue deal with the development of computational tools to resolve important problems in fluid mechanics [12][13][14]. Addair and Jaeger [12] consider efficient and effective strategies to convey fundamental concepts in Computational Fluids Dynamics (CFD) to undergraduate students, such as the implementation of the finite volume method to solve Navier-Stokes equations. The paper by Battista [13] provides an open repository of several useful two-dimensional solvers written in MATLAB and Python 3.…”

Simulation Project to Promote Learner Autonomy in an Introductory Fluid Mechanics Course

“…A first course in Fluid Mechanics covers a wide range of applied principles and CFD can be used to enhance the underlying concepts relating pressure and flow [1] . While modern engineering tools can add legitimacy to course content students may perceive as old-school approaches, a solid foundation in these are needed to knowledgably apply simulation software [2]. To truly master CFD, students would need much more instruction than is possible in a junior-year one semester course, but simulation can be used to supplement theoretical topics like Potential Flow and Navier-Stokes [3].…”