Numerical Simulation for Blood Flow - Microsurgery: Advances, Simulations, and Applications - page 160

5.1 Basic Equations of Flow Analysis

5.1.1 Introduction

Owing to rapid development in computer hardware in recent
years, numerical simulation has been highlighted as an approach
to solve problems in science and engineering. The numerical
calculation is widely accepted in the ield of engineering, because
it has several advantages in swiftness, safeness and cost compared
with experimental trial. As it has the potential to simulate complex
phenomena that are dificult to measure and analyze mathematically,
it is also the principal method in fundamental research. The solution
of phenomena in low by numerical calculation and the academic
ield of numerical calculation method itself are called numerical
luid dynamics and also computational luid dynamics. The
numerical calculation has a wide ield application such as low in
space, weather and ocean, and also airplanes, ships, trains and cars.
Moreover, biological lows in human vessel and organ are included.
As these low ields contain complex elements in boundary shape,
external force and luid property, it is dificult to express in analytical
formulation. In the area of numerical luid dynamics, basic equation
of low is numerically calculated and low ield is reconstructed
in calculator to predict and clarify various phenomena in low.
Basic equations for continuum luid have been established from
conservation law. They are law of conservation of mass, momentum
and energy, respectively. As necessary, gas equation and chemical re-
action equation is solved incrementally. The numerical simulation
of low means numerical calculation in the adequate initial and
boundary condition and simulation of actual low. To be more
precise, it is also said to be reproduction of low phenomena such
as momentarily, velocity, density and temperature in some points of
low ield.
Depending on the nature of low, we decide whether we solve the
Navier-Stokes equation or Euler's equation which is simpliied by
ignoring luid viscosity. We chose physics model such as turbulence
model and non-Newtonian constitutive equation if needed. As a
result, partial differential equation (PDE) for numerical calculation
is decided.
We discretize PDE with inite-difference method (FDM), inite-
element method (FEM), or inite-volume method (FVM) and then set