In Silico Biofluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 334

CHAPTER
13

In Sil ico Biofluid Mech anics

LEARNING OUTCOMES

1. Use computational methods to describe the

flow through various physiological
geometries

4. Use the Buckingham Pi Theorem to develop

dimensionless numbers

5. Analyze conditions for dynamic similarity

2. Describe the mathematics behind

computational fluid dynamics

6. Evaluate salient dimensionless numbers

3. Explain the need for fluid structure

interaction modeling

13.1 COMPUTATIONAL FLUID DYNAMICS

In earlier chapters, we were able to solve the fluid mechanics governing equations for
various fluid properties of interest by making assumptions that significantly simplify the
Navier-Stokes equations, the Conservation of Momentum equations, the Conservation of
Energy, and the Conservation of Mass governing equations. An exact solution could only
be reached if these assumptions were made and the boundary conditions as well as the
initial conditions were known. Note that this does not touch on the accuracy of any of
those conditions, only that they can be defined. However, in many situations, the Navier-
Stokes equations cannot be simplified such as when the flow is not steady, certain complex
body forces need to be considered, or when the flow is truly three dimensional. Thus, it
becomes very difficult to solve the Navier-Stokes equations as a set of partial differential
equations analytically along with the conservation laws. Computational fluid dynamics is
a tool often used to solve the coupled Navier-Stokes equations simultaneously with the
conservation equations, omitting many but not all of the previous assumptions made in
earlier chapters.