A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation

We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier- Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation. We show that the scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, we prove that the scheme is uncondition- ally uniquely solvable at each time step by exploring the monotonicity associated with the scheme. Thanks to the weak coupling of the scheme, we design an efficient Picard iteration procedure to further decouple the computation of Cahn-Hilliard equation and Navier-Stokes equation. We implement the scheme by the mixed finite element method. Ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme

Existence and uniqueness of global weak solutions to a Cahn-Hilliard-Stokes-Darcy system for two phase incompressible flows in karstic geometry

We study the well-posedness of a coupled Cahn-Hilliard-Stokes-Darcy system which is a diffuse-interface model for essentially immiscible two phase incompressible flows with matched density in a karstic geometry. Existence of finite energy weak solution that is global in time is established in both 2D and 3D. Weak-strong uniqueness property of the weak solutions is provided as well

An Analytical Model of Residual Stress for Flank Milling of Ti-6Al-4V

AbstractResidual stress is one of the most critical parameters in surface integrity, which has a great impact on fatigue life of the machined components. While the flank milling of titanium alloy Ti-6Al-4V has been widely applied to the manufacture of jet engine for its high productivity in aerospace industry, prediction of residual stress induced by this process is seldom reported. In this paper, an analytical model of residual stress is proposed, based on comprehensive analysis of the mechanical loading during flank milling. For the first time, the sequential discontinuous variable loading feature of flank milling is taken into consideration. An incremental elasto-plastic method followed by a relaxation procedure is used to get the stress-strain history of an arbitrary point in the subsurface so as to predict the residual stress retained in the workpiece after several loading cycles. We find that during the last phase in which the machined surface is generated, the main load comes from the plough effect of cutting edge as the uncut depth approaches zero. The simulation results indicate that the flank milled surface shows more compressive residual stress in the axial direction than in the feed direction. To validate the prediction, a series of cutting tests are conducted on Ti-6Al-4V using finish parameters and X-ray diffraction is utilized to obtain the residual stress

Dadu-RBD: Robot Rigid Body Dynamics Accelerator with Multifunctional Pipelines

Rigid body dynamics is a key technology in the robotics field. In trajectory optimization and model predictive control algorithms, there are usually a large number of rigid body dynamics computing tasks. Using CPUs to process these tasks consumes a lot of time, which will affect the real-time performance of robots. To this end, we propose a multifunctional robot rigid body dynamics accelerator, named RBDCore, to address the performance bottleneck. By analyzing different functions commonly used in robot dynamics calculations, we summarize their reuse relationship and optimize them according to the hardware. Based on this, RBDCore can fully reuse common hardware modules when processing different computing tasks. By dynamically switching the dataflow path, RBDCore can accelerate various dynamics functions without reconfiguring the hardware. We design Structure-Adaptive Pipelines for RBDCore, which can greatly improve the throughput of the accelerator. Robots with different structures and parameters can be optimized specifically. Compared with the state-of-the-art CPU, GPU dynamics libraries and FPGA accelerator, RBDCore can significantly improve the performance

Kinetic Particle Simulations Of Plasma Charging At Lunar Craters Under Severe Conditions

This paper presents fully kinetic particle simulations of plasma charging at lunar craters with the presence of lunar lander modules using the recently developed Parallel Immersed-Finite-Element Particle-in-Cell (PIFE-PIC) code. The computation model explicitly includes the lunar regolith layer on top of the lunar bedrock, taking into account the regolith layer thickness and permittivity as well as the lunar lander module in the simulation domain, resolving a nontrivial surface terrain or lunar lander configuration. Simulations were carried out to study the lunar surface and lunar lander module charging near craters at the lunar terminator region under mean and severe plasma environments. The lunar module\u27s position is also investigated to see its effect on the plasma charging relative to the craters. Differential surface charging was clearly resolved by the simulations. For the charging of a lunar lander module made of conducting materials, the results show a near-uniform potential close to that of its surrounding environment and moderate levels of local electric fields. Additionally, the risks associated with charging and discharging increase significantly under a more severe plasma charging environment as shown in the severe plasma environment cases