A space-time generalized finite difference method for solving unsteady double-diffusive natural convection in fluid-saturated porous media

Research and application of surface heat treatment for CO2 continuous laser ablation of polymeric methyl methacrylate materials

“…The initial condition was set to approximately 300 K at room temperature, the heat energy transmission at the surface of PMMA plate was the absorption of laser energy by the material surface, and there was no further heat energy transmission at the maximum ablation depth of the sheet. [21][22][23] The nite-difference time-domain method was used to study the heat transfer physical model and boundary conditions, 24,25 and establishing a grid Fourier number, the heat transfer physical model of CO 2 continuous laser ablation of PMMA material was established as follows: 26,27 (see Appendix A)…”

“…After establishing the grid Fourier number , eqn (28) could be transformed into the following form: 25,26 …”

“…T(l,t) = T 0 , t = 0 The nite-difference time-domain method is a numerical method for solving differential equations, which can be used to solve ordinary differential equation and partial differential eqn (24) and (25). Therefore, the nite difference equations for the heat transfer physical model (20) and boundary conditions ( 17)- (19) were established as follows:…”

“…Aer organizing eqn (24), we could obtain: Aer establishing the grid Fourier number F0 1 ¼ kDt rcðDlÞ 2 , eqn (28) could be transformed into the following form: 25,26 Experiment for ultrasonic cleaning. In order to reduce the inuence of impurities such as droplets and dust on the observation results, the experimental acrylic sheets were placed in the ultrasonic cleaner and cleaned with puried water before laser ablation of PMMA materials and surface topography detection.…”

A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems

“…In transient applications, the implicit Crank-Nicolson method is the most common method and has been improved over time. Additionally, the ST [9,21], and the ST marching [22] methods have also been proposed. However, these two methods may exhibit error accumulation for simulations over a long period of time.…”