Chapter 28

Numerical Solutions to the Navier-Stokes Equation

28.1 Introduction

At this point, we will turn to solving the most relevant partial differential equation in fluid mechanics, i.e., the Navier-Stokes equation, using some of the numerical methods we have studied in the previous sections. For this, we will turn to the pressure-driven Poiseuille flow which we have already studied analytically in section 16. As we will see, we can apply some of the methods we have studied pretty much directly to the simplified Navier-Stokes equation for the Poiseuille flow. Comparing the results obtained with the analytical solutions we have found previously, will give us a good understanding of the usefulness of these methods.

28.2 Solution to the Poisson ...

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