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In this work, we report the development of a spatially fourth order temporally second order compact scheme for incompressible Navier-Stokes (N-S) equations in time-varying domain. Sen [J. Comput. Phys. 251 (2013) 251-271] put forward an implicit compact finite difference scheme for the unsteady convection-diffusion equation. It is now further extended to simulate fluid flow problems on deformable surfaces using curvilinear moving grids. The formulation is conceptualized in conjunction with recent advances in numerical grid deformations techniques such as inverse distance weighting (IDW) interpolation and its hybrid implementation. Adequate emphasis is provided to approximate grid metrics up to the desired level of accuracy and freestream preserving property has been numerically examined. As we discretize the non-conservative form of the N-S equation, the importance of accurate satisfaction of geometric conservation law (GCL) is investigated. To the best of our knowledge, this is the first higher order compact method that can directly tackle non-conservative form of N-S equation in single and multi-block time dependent complex regions. Several numerical verification and validation studies are carried out to illustrate the flexibility of the approach to handle high-order approximations on evolving geometries., Comment: 43 pages in all including 5 tables and 19 figures

Image segmentation plays an important role in computer vision, object detection, traffic control, and video surveillance. Typically, it is a critical step in the 3D reconstruction of a specific organ in medical image processing which unveils the detailed tomography of organ, tumor, and nerve, and thus helping to improve the quality of surgical pathology. However, there may be high computational requirements in it. With the advent of GPUs, more complex and realistic models can be simulated, but the deployment of these facilities also requires a huge amount of capital. As a consequence, how to make good use of these computational resource is essential to GPU computing. This study discusses the image segmentation of 3D airway reconstruction, identifies the computing-intensive task, and parallelizes the algorithm of image segmentation in order to obtain theoretical maximum speedup in terms of the benchmark ratio of GPU to CPU. There are five steps involved, which are the image acquisition, pre-processing, segmentation, reconstruction, and object recognition. It is worth to note that it takes 85\% of time on segmentation. This study successfully accelerates the image segmentation of 3D airway reconstruction by optimizing the memory usage, grid and block setting and multiple GPUs communication, thereby gaining a total speedup of 61.8 on two GPUs (Nvidia K40)., Comment: 7 pages, 8 figures, and 5 tables

The aim of this paper is to introduce a finite element formulation within Arbitrary Lagrangian Eulerian framework with vanishing discrete {\it Space Conservation Law} (SCL) for differential equations on time dependent domains. The novelty of the formulation is the method for temporal integration which results in preserving the SCL property and retaining the higher order accuracy at the same time. Once the time derivative is discretized (based on integration or differentiation formula), the common approach for terms in differential equation which do not involve temporal derivative is classified to be a kind of "time averaging" between time steps. In the spirit of classical approaches, this involves evaluating these terms in several points in time between the current and the previous time step ($[t_n,t_{n+1}]$), and then averaging them in order to provide the satisfaction of discrete SCL. Here, we fully use the polynomial in time form of mapping through which evolution of domain is realized -- the so called ALE map -- in order to avoid the problematics arising due to the moving grids. We give a general recipe on temporal schemes that have to be employed once the discretization for the temporal derivative is chosen. Numerical investigations on stability, accuracy and convergence are performed and the simulated results are compared with benchmark problems set up by other authors., Comment: 21 pages, 10 figures

A chemotaxis-diffusion-convection coupling system for describing a form of buoyant convection in which the fluid develops convection cells and plume patterns will be investigated numerically in this study. Based on the two-dimensional convective chemotaxis-fluid model proposed in the literature, we developed an upwind finite element method to investigate the pattern formation and the hydrodynamical stability of the system. The numerical simulations illustrate different predicted physical regimes in the system. In the convective regime, the predicted plumes resemble B\'enard instabilities. Our numerical results show how structured layers of bacteria are formed before bacterium rich plumes fall in the fluid. The plumes have a well defined spectrum of wavelengths and have an exponential growth rate, yet their position can only be predicted in very simple examples. In the chemotactic and diffusive regimes, the effects of chemotaxis are investigated. Our results indicate that the chemotaxis can stabilize the overall system. A time scale analysis has been performed to demonstrate that the critical taxis Rayleigh number for which instabilities set in depends on the chemotaxis head and sensitivity. In addition, the comparison of the differential systems of chemotaxis-diffusion-convection, double diffusive convection, and Rayleigh-B\'enard convection establishes a set of evidences that even if the physical mechanisms are different at the same time the dimensionless systems are strongly related to each other., Comment: 29 pages, 18 figures, 9 tables

High intensity focused ultrasound (HIFU) has many applications ranging from thermal ablation of cancer to hemostasis. Although focused ultrasound can seal a bleeding site, physical mechanisms of acoustic hemostasis are not fully understood yet. To understand better the interaction between different physical mechanisms involved in hemostasis a mathematical model of acoustic hemostasis is developed. This model comprises the nonlinear Westervelt equation and the bioheat equations in tissue and blood vessel. In the three dimensional domain, the nonlinear hemodynamic equations are coupled with the acoustic and thermal equations. Convected cooling and acoustic streaming effects are incorporated in the modeling study. Several sonication angles and two wound shapes have been studied. The optimal focal point location is at the rear of the wound and the optimal angle is 45$^0$., Comment: 21 pages, 14 figures

The influences of blood vessels and focused location on temperature distribution during high-intensity focused ultrasound (HIFU) ablation of liver tumors is studied. A three-dimensional acoustics-thermal-fluid coupling model is employed to compute the temperature field in the hepatic cancerous region. The model is based on the linear Westervelt and bioheat equations as well as the nonlinear Navier-Stokes equations for the liver parenchyma and blood vessels. The effect of acoustic streaming is also taken into account in the present HIFU simulation study. Different blood vessel diameters and focal point locations were investigated. We found from this three-dimensional numerical study that in large blood vessels both the convective cooling and acoustic streaming can change considerably the temperature field and the thermal lesion near blood vessels. If the blood vessel is located within the beam width, both acoustic streaming and blood flow cooling effects should be taken into account. The predicted temperature difference for the cases considered with and without acoustic streaming effect is 54 % in regions close to the vessel wall. The necrosed volume can be reduced about 30 %, when taking into account acoustic streaming effect., Comment: 19 pages, 16 figures

A modified Mott-Smith method for predicting the one-dimensional shock wave solution at very high Mach numbers is constructed by developing a system of fluid dynamic equations. The predicted shock solutions in a gas of Maxwell molecules, a hard sphere gas and in argon using the newly proposed formalism are compared with the experimental data, direct-simulation Monte Carlo (DSMC) solution and other solutions computed from some existing theories for Mach numbers M<50. In the limit of an infinitely large Mach number, the predicted shock profiles are also compared with the DSMC solution. The density, temperature and heat flux profiles calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutions, Comment: 22 pages, 9 figures, Accepted for publication in Physical Review E

A modification of Mott-Smith method for predicting the one-dimensional shock wave solution is presented. Mott-Smith distribution function is used to construct the system of moment equations to study the steady-state structure of shock wave in a gas of Maxwell molecules and in argon. The predicted shock solutions using the newly proposed formalism are compared with the experimental data, direct-simulation Monte Carlo (DSMC) solution and the solutions predicted by other existing theories for Mach numbers M<11. The density, temperature, heat flux profiles and shock thickness calculated at different Mach numbers have been shown to have good agreement with the experimental and DSMC solutions. In addition, the predicted shock thickness is in good agreement with the DSMC simulation result at low Mach numbers.