102
3 Coupling Model and Numerical Computation Method of Keyhole and Weld Pool
3.5.3.3 Solution for the Velocity Boundary Conditions of the Free
Surface of Pores
In general, to deal with the velocity boundary conditions of a free interface is the
most difficult step in solving the problem of free interface flow. The purpose of
dealing with the velocity boundary conditions of a free interface is to make the free
interface grid close to the pore meet the continuity equation. For the problem of the
free interface flow in tracking the interface motion using Level Set and Particle Level
Set methods, processing of this velocity boundary conditions can be equivalent to
solving the partial differential equation.
∇
− →
U ext · ∇φ = 0
(3.104)
Equation (3.104) is a typical time-independent Hamilton–Jacobi equation that can
be quickly solved by using the Fast Sweeping Method. It is found that the first-order
upwind scheme is generally used to implicitly discretize and solve Eq. (3.104), to
achieve the condition that the velocity divergence of the free boundary is zero, i.e.,
the continuity equation condition.
3.5.4 Numerical Calculation Process
In the laser welding process, laser energy distribution can be represented by the
schematic diagram Fig. 3.12. Only Fresnel absorption is initially considered during
the calculation process of the numerical solution, and the preliminary depth and shape
of the pore can be obtained. Then, based on the first step, the multi-reflection Fresnel
absorption and the inverse bremsstrahlung absorption of the plasma are comprehensively considered to calculate the cross-sectional shape of the pore and the weld
pool.
Based on the mathematical model and numerical method of this paper, the numerical simulation system for the corresponding laser welding transient pore and motion
weld pool is programmed in C++ language. In order to speed up the calculation, the
corresponding code is parallelized in OpenMP language. The calculation process of
the software system is shown in Fig. 3.13.
3.6 Summary
In this chapter, the energy interaction mechanism between material and laser during
deep penetration laser welding and the related factors affecting the dynamics of pores
and weld pool are systematically analyzed. With consideration of physical factors
such as Fresnel absorption, evaporation, solidification, fusion and coupled convection
3 Coupling Model and Numerical Computation Method of Keyhole and Weld Pool
3.5.3.3 Solution for the Velocity Boundary Conditions of the Free
Surface of Pores
In general, to deal with the velocity boundary conditions of a free interface is the
most difficult step in solving the problem of free interface flow. The purpose of
dealing with the velocity boundary conditions of a free interface is to make the free
interface grid close to the pore meet the continuity equation. For the problem of the
free interface flow in tracking the interface motion using Level Set and Particle Level
Set methods, processing of this velocity boundary conditions can be equivalent to
solving the partial differential equation.
∇
− →
U ext · ∇φ = 0
(3.104)
Equation (3.104) is a typical time-independent Hamilton–Jacobi equation that can
be quickly solved by using the Fast Sweeping Method. It is found that the first-order
upwind scheme is generally used to implicitly discretize and solve Eq. (3.104), to
achieve the condition that the velocity divergence of the free boundary is zero, i.e.,
the continuity equation condition.
3.5.4 Numerical Calculation Process
In the laser welding process, laser energy distribution can be represented by the
schematic diagram Fig. 3.12. Only Fresnel absorption is initially considered during
the calculation process of the numerical solution, and the preliminary depth and shape
of the pore can be obtained. Then, based on the first step, the multi-reflection Fresnel
absorption and the inverse bremsstrahlung absorption of the plasma are comprehensively considered to calculate the cross-sectional shape of the pore and the weld
pool.
Based on the mathematical model and numerical method of this paper, the numerical simulation system for the corresponding laser welding transient pore and motion
weld pool is programmed in C++ language. In order to speed up the calculation, the
corresponding code is parallelized in OpenMP language. The calculation process of
the software system is shown in Fig. 3.13.
3.6 Summary
In this chapter, the energy interaction mechanism between material and laser during
deep penetration laser welding and the related factors affecting the dynamics of pores
and weld pool are systematically analyzed. With consideration of physical factors
such as Fresnel absorption, evaporation, solidification, fusion and coupled convection