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Impact craters are the primary geomorphic features on the surfaces of celestial bodies such as the Moon, and their formation has significant implications for the evolutionary history of the celestial body. The study of the impact crater formation process relies mainly on numerical simulation methods, with two-dimensional simulations capable of reproducing general patterns of impact processes while conserving computational resources. However, to mitigate the artificial reflections of shock waves at numerical boundaries, a common approach involves expanding the computational domain, greatly reducing the efficiency of numerical simulations. In this study, we developed a novel two-dimensional code SALEc-2D that employs the perfect matched layer (PML) method to suppress artificial reflections at numerical boundaries. This method enhances computational efficiency while ensuring reliable results. Additionally, we implemented MPI parallel algorithms in the new code to further improve computational efficiency. Simulations that would take over ten hours using the conventional iSALE-2D code can now be completed in less than half an hour using our code, SALEc-2D, on a standard computer. We anticipate that our code will find widespread application in numerical simulations of impact craters in the future., Comment: 17 pages, 8 figures

Accurate estimation of cratering asymmetry on the Moon is crucial for understanding Moon evolution history. Early studies of cratering asymmetry have omitted the contributions of high lunar obliquity and inclination. Here, we include lunar obliquity and inclination as new controlling variables to derive the cratering rate spatial variation as a function of longitude and latitude. With examining the influence of lunar obliquity and inclination on the asteroids population encountered by the Moon, we then have derived general formulas of the cratering rate spatial variation based on the crater scaling law. Our formulas with addition of lunar obliquity and inclination can reproduce the lunar cratering rate asymmetry at the current Earth-Moon distance and predict the apex/ant-apex ratio and the pole/equator ratio of this lunar cratering rate to be 1.36 and 0.87, respectively. The apex/ant-apex ratio is decreasing as the obliquity and inclination increasing. Combining with the evolution of lunar obliquity and inclination, our model shows that the apex/ant-apex ratio does not monotonically decrease with Earth-Moon distance and hence the influences of obliquity and inclination are not negligible on evolution of apex/ant-apex ratio. This model is generalizable to other planets and moons, especially for different spin-orbit resonances., Comment: 18 pages, 7 figures

An Equilibrium Phase (EP) spray model has been recently proposed for modeling high-pressure diesel fuel injection, which is based on jet theory and a phase equilibrium assumption. In this approach, the non-equilibrium processes of drop breakup, collision and surface vaporization are neglected, assuming that spray vaporization is a mixing-controlled equilibrium process. A liquid-jet model and a gas-jet model are also intro-duced to improve grid-independency. In the current study, the EP model is applied in simulations of multi-hole gasoline direct injection (GDI). The model is validated at ambient densities from 3 to 9 kg/m3 and ambient temperatures from 400 K to 900 K, for two different GDI injectors, i.e. the Engine Combustion Network (ECN) Spray G injector and a GM injector. Iso-octane is used as the surrogate in consistency with available experi-ments. The results show good agreement in terms of liquid/vapor penetration, shape of the vapor envelope, and the velocity evolution along the injector centerline. Then, a 10-component gasoline surrogate fuel is used to demonstrate the capability of this model for multi-component spray simulations, which is essential for engine combustion and emission predictions.

This paper presents a CFD study of Engine Combustion Network (ECN) Spray G, focusing on the transient characteristics of spray at start of injection. The Large Eddy Simulation (LES) coupled with Volume of Fluid (VOF) method is used to model the turbulent two-phase flow. A moving needle boundary condition is applied to capture the internal flow condition accurately. The injector geometry was measured with micron-level resolution using full spectrum x-ray tomographic imaging at Advanced Photon Source (APS) at Argonne National Labora-tory, providing detailed machining error from manufacturer and realistic rough surface. For comparison, a nominal geometry is also used for the simulation. Spray characteristics such as Sauter Mean Diameter (SMD), droplet volume and surface area are extracted by post-processing the CFD outputs. It is seen that compared to the nominal geometry, the use of the high resolution real geometry predicts about 11% lower SMD. The rough surface along with manufacturing defects generate more unstable structures along the jet surface and accelerates the liquid de-formation and breakup processes, starting inside of the counter-bore. This result shows that the machining details of injector, which is usually ignored in the two-phase flow simulations, has considerable impact on the spray development process., Comment: 8 pages, 10 figures, ICLASS 2018, 14th Triennial International Conference on Liquid Atomization and Spray Systems, Chicago, IL, USA, July 22-26, 2018