Rayleigh–Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present a linearized theory for arbitrary three-dimensional (3D) initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, and compared and contrasted with the early-time linearized theory.

A new method, called Cloud of Points (COP) Reconstruction, is proposed in the present work to extend the meshfree method to simulate viscous flows. With the characters of viscous flows, the anisotropic COP structure is distributed in boundary layer. The proposed method can improve the anisotropic COP structure to isotropic COP structure and reduce the condition number of the least square coefficient matrix for conventional meshfree method. The values of the new reconstructed points are calculated by the Lagrange interpolation. The accuracy and the robustness of the presented meshfree solver are demonstrated on a number of standard test cases, including the functions with analytical gradients and the viscous flows past NACA0012 airfoil. The comparison of the simulation results with the experimental data and other numerical simulation data are also investigated.

The deformation behavior of Ti-based bulk metallic glass (BMG) and metallic glass matrix composite (MGMC), both having a multistep crystallization behavior upon heating, has been investigated in the supercooled liquid region. The BMG deforms homogeneously and exhibits moderate elongation to failure due to its multistep crystallization behavior, but shows a significant variation of the flow stress during deformation. For the MGMC containing an in situ β-phase, a stress-overshoot characteristic, observed in the BMG, is not presented, but elongation to failure is rather limited because the crystalline β-phase prevents the viscous flow of the amorphous phase. The different presence of the crystalline phases in the metallic glasses can differently affect the flow behavior of metallic glass in the supercooled liquid region.