4 Computational Fluid Dynamics
309
Fig. 4.14 Flow field calculated by vortex panel method
high-speed computer makes a breakthrough in the numerical solution of
this integral equation. Its main idea is to discretize the integral equation,
which represents the sum of singular points such as source and sink in
space. For example, if the airfoil and fuselage surface is divided into many
small elements, the singular point strength on each element is averaged
and the sum of the singular point strength is the total effect of the flow
field. Therefore, it uses the sum of finite terms instead of integral, and the
final solution is a set of algebraic equations. Because the basic solutions
are all functions with singularities, this method is also called the finite
singularities method or the scale method. In the aerodynamic calculation of aviation, the panel method is most commonly used (as shown in
Fig. 4.14). In this method, the characteristic surfaces such as the surface
of the object or the arc surface of the wing are discretized. After the mesh
is generated, a plane or surface is used to replace the original surface of the
object, which is called the surface element. The singular points such as
source, vortex, dipole, and their combination are arranged on the surface
element to solve the aerodynamic problem.
4.3.2 Numerical Solution of Transonic Flow
For the steady potential flow, the governing equation of subsonic flow is the
elliptic partial differential equation, while the governing equation of supersonic flow is the hyperbolic partial differential equation. The flow field of
309
Fig. 4.14 Flow field calculated by vortex panel method
high-speed computer makes a breakthrough in the numerical solution of
this integral equation. Its main idea is to discretize the integral equation,
which represents the sum of singular points such as source and sink in
space. For example, if the airfoil and fuselage surface is divided into many
small elements, the singular point strength on each element is averaged
and the sum of the singular point strength is the total effect of the flow
field. Therefore, it uses the sum of finite terms instead of integral, and the
final solution is a set of algebraic equations. Because the basic solutions
are all functions with singularities, this method is also called the finite
singularities method or the scale method. In the aerodynamic calculation of aviation, the panel method is most commonly used (as shown in
Fig. 4.14). In this method, the characteristic surfaces such as the surface
of the object or the arc surface of the wing are discretized. After the mesh
is generated, a plane or surface is used to replace the original surface of the
object, which is called the surface element. The singular points such as
source, vortex, dipole, and their combination are arranged on the surface
element to solve the aerodynamic problem.
4.3.2 Numerical Solution of Transonic Flow
For the steady potential flow, the governing equation of subsonic flow is the
elliptic partial differential equation, while the governing equation of supersonic flow is the hyperbolic partial differential equation. The flow field of