Why Your CFD is Wrong – Part 2: Solving Mathematical Models
Last time, we saw how engineers construct differential equations to describe physical phenomena such as fluid flows, representing these real things in the language of mathematics . You may have found yourself wondering, “How do we solve these?” Generally, engineers can use one of two methods. First, we can attempt to solve the equations or systems like any other math problem, the way you’re probably used to doing since as far back as you can remember. This involves manipulating the equations and transforming them using mathematical operations to arrive at an answer. We call this the analytical approach. Implementing a number of simplifying assumptions (constant density, constant pressure, no viscosity, etc.) leads to a scalar equation derived from the Navier-Stokes equations that is solvable analytically. In class last spring, we used this “1-dimensional linear advection” equation to check the numerical solutions we developed later on. Analytical Solutions If we ...