312
P. Liu
The Shock-Capture method does not need any special treatment for the
shock itself, but directly or indirectly introduces the “viscosity” term in the
calculation formula, and automatically calculates the position and strength
of the shock to “capture” the shock. There are so-called artificial viscosity
and format viscosity. The artificial viscosity method was first proposed by the
American scientists J. von Neumann and R. D. Richtmall in 1950. It is an
automatic shock wave approximation method based on the physical theory
of real viscous fluid. In this method, a viscous term is added artificially in
the shock layer to make the shock discontinuity become a smooth transition region. In recent years, it has been widely used in supersonic flow. The
scheme viscosity is a kind of difference scheme which indirectly introduces
the viscosity term Lax scheme. The Shock-Fitting method treats the shock
wave as a discontinuity and satisfies the condition of shock jump before and
after the shock wave. But it is very difficult to realize in common coordinates.
Generally, the coordinate transformation is used to make the shock position
(unknown at this time) coincide with a coordinate axis, and then the shock
is regarded as the inner boundary. This kind of processing is more accurate,
but also very troublesome and inconvenient. The best way is to combine the
Shock-Capturing method with the Shock-Fitting method. For example, the
Shock-Fitting method is used for the shock wave in the outer of the flow
field, and the Shock-Capture method is used for the shock wave in the inner
of the flow field. The successive development of shock wave capture formats
are TVD (Total Variation Diminishing) format (Harten 1983); NND (NonOscillatory Containing No Free Parameter and Dissipative Scheme) format
(Zhang Hanxin 1984); ENO (Essential Non-Oscillatory Scheme) format
(Harten et al. 1987); WENO (Weighted Essential Non Oscillatory Scheme)
format (Liu et al. 1994), as shown in Figs. 4.16 and 4.17.
4.4 Commercial Software for Computational
Fluid Dynamics
CFD commercial software generally includes a variety of physical models,
such as steady and unsteady flows, laminar and turbulent flows, incompressible and compressible flows, heat transfer and chemical reaction, etc.
For each kind of physical problem, there are suitable numerical solutions
for users. Users can choose explicit or implicit difference schemes in order
to achieve the best calculation speed, stability, and accuracy. CFD software
can easily exchange numerical values and adopt unified pre-processing and
post-processing tools, which saves researchers’ repeated and inefficient work
P. Liu
The Shock-Capture method does not need any special treatment for the
shock itself, but directly or indirectly introduces the “viscosity” term in the
calculation formula, and automatically calculates the position and strength
of the shock to “capture” the shock. There are so-called artificial viscosity
and format viscosity. The artificial viscosity method was first proposed by the
American scientists J. von Neumann and R. D. Richtmall in 1950. It is an
automatic shock wave approximation method based on the physical theory
of real viscous fluid. In this method, a viscous term is added artificially in
the shock layer to make the shock discontinuity become a smooth transition region. In recent years, it has been widely used in supersonic flow. The
scheme viscosity is a kind of difference scheme which indirectly introduces
the viscosity term Lax scheme. The Shock-Fitting method treats the shock
wave as a discontinuity and satisfies the condition of shock jump before and
after the shock wave. But it is very difficult to realize in common coordinates.
Generally, the coordinate transformation is used to make the shock position
(unknown at this time) coincide with a coordinate axis, and then the shock
is regarded as the inner boundary. This kind of processing is more accurate,
but also very troublesome and inconvenient. The best way is to combine the
Shock-Capturing method with the Shock-Fitting method. For example, the
Shock-Fitting method is used for the shock wave in the outer of the flow
field, and the Shock-Capture method is used for the shock wave in the inner
of the flow field. The successive development of shock wave capture formats
are TVD (Total Variation Diminishing) format (Harten 1983); NND (NonOscillatory Containing No Free Parameter and Dissipative Scheme) format
(Zhang Hanxin 1984); ENO (Essential Non-Oscillatory Scheme) format
(Harten et al. 1987); WENO (Weighted Essential Non Oscillatory Scheme)
format (Liu et al. 1994), as shown in Figs. 4.16 and 4.17.
4.4 Commercial Software for Computational
Fluid Dynamics
CFD commercial software generally includes a variety of physical models,
such as steady and unsteady flows, laminar and turbulent flows, incompressible and compressible flows, heat transfer and chemical reaction, etc.
For each kind of physical problem, there are suitable numerical solutions
for users. Users can choose explicit or implicit difference schemes in order
to achieve the best calculation speed, stability, and accuracy. CFD software
can easily exchange numerical values and adopt unified pre-processing and
post-processing tools, which saves researchers’ repeated and inefficient work