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Laser cladding has been widely used in direct laser fabrication and laser refabrication for metal parts. It is a high precision and complicated process due to multiple process parameters involved. These parameters are strongly tied to each other and their effects are still far from being completely understood. In order to make the optimal choice, a feasible mathematical model is established to describe the interaction between laser and powder particles and to predict and control the cross sectional area. Additionally, analysis concentrating on the effect of the various parameters on the cross sectional area is made. Results show that laser power, powder feed rate, scan speed and radius of focused powder stream are the main factors. Correlations between main process parameters and cross sectional area of an individual clad track have been found. The model also provides predictions of range of process parameters for melting powder to form specific cross sectional area, which will guide the experiment and greatly reduce the cost of the experimental investigations.

A new formulation, a gauge formulation of the incompressible Navier-Stokes equations in terms of an auxiliary field $\mathbf{a}$ and a gauge variable $\phi$, $\mathbf{u} =\mathbf{a}+\nabla\phi$, was proposed recently by E and Liu. This paper provides a theoretical analysis of their formulation and verifies the computational advantages. We discuss the implicit gauge method, which uses backward Euler or Crank-Nicolson in time discretization. However, the boundary conditions for the auxiliary field $\mathbf{a}$ are implemented explicitly (vertical extrapolation). The resulting momentum equation is decoupled from the kinematic equation, and the computational cost is reduced to solving a standard heat and Poisson equation. Moreover, such explicit boundary conditions for the auxiliary field $\mathbf{a}$ will be shown to be unconditionally stable for Stokes equations. For the full nonlinear Navier-Stokes equations the time stepping constraint is reduced to the standard CFL constraint ${\triangle t} / {\triangle x} \le C$. We also prove first order convergence of the gauge method when we use MAC grids as our spatial discretization. The optimal error estimate for the velocity field is also obtained.

The accurate control of process parameters is particularly important for the growth of high quality structures during laser cladding. Melt pool size and cross sectional area are key process characteristics that can be controlled to allow the precise deposition of complex features. A feasible mathematical model is established to describe the interaction between laser and powder particles and to predict and control the cross sectional area. Also, a vision-based sensing system is proposed to detect the transient shape and size of the melt pool. The system focuses on the measuring of the geometric parameters of the melt pool by using a digital image processing method and thus giving researchers the parameters on-line, which gives us a necessary tool to gain insight into the cladding process and to optimize the material quality

This paper is devoted to developing and analysing a highly accurate conservative method for solving the quantum Zakharov system. The scheme is based on a linearly-implicit compact finite difference discretization and conserve the mass as well as energy in discrete level. Detailed numerical analysis is presented which shows the method is fourth-order accurate in space and second-order accurate in time. Several numerical examples are reported to confirm the conservation properties and high accuracy of the proposed scheme. Finally the compact scheme is applied to study the convergence rate of the quantum Zakharov system to its limiting model in the semi-classical limit.