Hybrid Cartesian Grid/Gridless Algorithm for Store Separation Prediction

The DNSs of the incompressible flows around a sphere are performed by using the Cartesian grid approach with virtual boundary method. In the virtual boundary method, the body surface is expressed by a set of plural points, and the velocity components on virtual boundary are feedbacked to the momentum equations as the additional forcing terms. The DNSs are carried out in the range from Re = 10 to Re = 1000. In the steady flows up to Re = 240 in order to validate the present method, the flow characteristics are in good agreement with the other results. In the unsteady flows, it is clearly observed that the hairpin vortex ring is released and the flow transits from laminar to turbulence. Consequently, the present method is very promising for the DNSs of the incompressible complicated flow.

An automatic adaptive hybrid Cartesian grid generation and solution system is presented together with applications for turbulent flows around complicated three-dimensional geometries. The primary computational grid is an octree Cartesian grid with a cut-cell approach. A quasi-prismatic grid may be added for resolving the boundary layer region of viscous flow around the solid body. For external flow simulations the flow solver TAU from the Deutsches Zentrum fiir Luftund Raumfahrt is integrated in the simulation system. Coarse grids are generated automatically, which are required for multilevel smoothing. The initial hybrid Cartesian grid is improved with help of several adaptation features, which are optimized in order to avoid any user interaction. Therefore, the final grid depends only on the particular geometry and flow structure (selforganized grid).

In this work, a novel technique called normal ray refinement (NRR) is developed, implemented and investigated. Normal ray refinement is designed to allow for the viscous fluid flow simulations using an unstructured Cartesian grid framework in a computationally efficient manner. A key benefit of using a Cartesian grid method is that the grid can be automatically generated, thereby saving a vast amount of time and effort for complex geometries. The main drawback of using the Cartesian grid method is the large number of cells required to resolve viscous boundary layers, and it is this problem that the NRR approach addresses. The NRR approach relies on the use of refined normal rays of cells emanating from the body surface and spanning the boundary layer. Separating these rays along the body surface are relatively large cells too coarse to accurately capture viscous gradients. The heart of the NRR approach lies in the inter-ray communication strategies used between the normal rays that allow the accurate simulation of boundary layers even though the cells separating the rays are large. This yields a large reduction in the number of cells in the grid, which reduces the computational cost of simulation. This paper provides a background on different viscous Cartesian grid-based methods, followed by an explanation of the NRR approach, then some initial 2D results obtained using NRR for Reynolds numbers up to 1 million. It is shown that NRR can yield substantial reduction in computational cost relative to the standard Cartesian approach.

The trajectory of a store released from an aircraft is subject to the uncertainty in parameters such as inertial properties, aerodynamic coefficients and external factors. Extensive Monte-Carlo simulations are conducted by store separation engineers for certifying the safety of store separation. An enormous amount of data is generated in this process demanding specific tools for further analysis. The objective of this work is to develop tools to address questions such as (i) what parameters cause un-safe store trajectories (ii) what are the worst-case combinations of parameters (iii) how can un-safe trajectories be avoided and (iv) what level of parameter uncertainty is acceptable for store certification. Techniques from data mining and machine learning tools such as recursive least squares, principal component analysis, K-means clustering, and probability binning are employed in this work to address these questions.

In this study, the Building-Cube method (BCM) devised for calculating large-scale flows and getting rid of the grid dependencies of computational results is extended to perform 3D inviscid compressible fluid flow simulations. The proposed scheme divides a computational domain into a large number of cubes with different sizes, and each individual cube is a sub-flow field simulated with a Cartesian grid of uniform spacing and an equal number of cells and nodes. Through the proposed scheme, we determine the geometric size of individual cube by Adapting the flow characteristics and geometrical shapes using an adaptively refining Cartesian grid approaches. The uniform spacing and equal number of cells and nodes in the Cartesian grid of individual cubes ensure a good performance for parallel computations; large result data can be handled efficiently. Further, an algorithm to solve the inviscid flow equations on the Building-Cube mesh for three-dimensional (3D) geometries is presented. The validation and performance of the proposed 3D BCM are demonstrated through comparisons of the computed results with the experimental data for the ONERA M6 wing and ONERA M5 wing-fuselage configurations.

DSMC [1] can become increasingly expensive when extended to the near‐continuum regime. Because of the statistical nature of the results, long run times are required to build up samples of simulator particles large enough to reduce the statistical scatter to acceptable levels. Here we adapt a kinetic theory based flux method to produce a quick approximate solver for transition and near‐continuum flows. The results have no statistical scatter. The CPU times are similar to those of traditional continuum (Navier‐Stokes or Euler) solvers. The True Direction Equilibrium Flux Method (TDEFM) [2, 3] is a generalisation of Pullin’s kinetic theory based EFM [4]. TDEFM can transfer fluxes of mass, momentum and energy in physically realistic directions from any source cell to any destination cell, even if the cells do not share an interface. TDEFM, as an Euler solver, has been shown to provide good results on a Cartesian grid for flows where standard continuum methods produce unphysical asymmetries apparently because the continuum fluxes are constrained (in one time step) to flow in the grid coordinate directions rather than the correct physical direction. [2, 3] The new method for rarefied flow does not try to produce the correct velocity distribution function, but does ensure that mass, momentum and energy are transported within the flow over the physically correct distances between “pseudo‐collisions.” To ensure this, (1) the time step is restricted so that mass, momentum and energy are exchanged between contiguous cells only in one time step, and (2) the cells sizes are adapted, as steady state is approached, to be approximately equal to the local mean free path. The results for Mach 5 flow over a flat plate for varying Knudsen numbers show an average difference (compared to DSMC) in the X‐velocity profile near the surface of the plate of less than 6 percent. TDEFM, employing adaptive mesh refinement, required less than 9 percent of the computational time required by DSMC for the same flow. Thus the approximate method could be useful for quick “first‐estimate” solutions of otherwise time consuming design problems.

Shock waves interacting with multi-material interfaces in compressible flows result in complex shock diffraction patterns involving total or partial reflection, refraction and transmission of the impinging shock wave. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with level set interface tracking is attractive. In this regard, a unified Riemann solver based Ghost Fluid Method (GFM) was developed to accurately resolve and represent the embedded solid and fluid object(s) in high speed compressible multiphase flows. While the GFM-based Cartesian grid approach significantly alleviates the complexity associated with mesh management, the method lacks flexibility in effective grid point placement in regions with rich structures in the flow field. Thus for higher-order and highly accurate sharp interface Cartesian grid based calculations with optimal computational effort, it is imperative to supplement the solution with adaptive mesh refinement technique. Hence in this work, a simple procedure is presented to complement the Riemann solver based GFM approach with quadtree (octree in three dimensions) based Local Mesh Refinement (LMR) technique for efficient and high fidelity computations involving strong shock interactions in multiphase compressible flows. The paper reports on a simple, conservative formulation for accurate calculation of ENO-based numerical fluxes at the fine-coarse mesh boundary. The numerical examples displayed in this paper clearly demonstrate that the methodology is consistent in generating satisfactory solutions, and effectively capturing fine structures in the flow.

Worldwide, clinicians, dentists, nurses, researchers, and other health professionals need to monitor the wound healing progress and to quantify the rate of wound closure. The aim of this study is to demonstrate, step by step, a fully automated numerical method to estimate the size of the wound and the percentage damaged relative to the body surface area (BSA) in images, without the requirement for human intervention. We included the formula for BSA in rats in the algorithm. The methodology was validated in experimental wounds and human ulcers and was compared with the analysis of an experienced pathologist, with good agreement. Therefore, this algorithm is suitable for experimental wounds and burns and human ulcers, as they have a high contrast with adjacent normal skin.

The pulsed Doppler method theoretically enables human arterial blood flow (BF) to be determined in all of the abdominal-pelvic organs (BFAP) by subtracting the bilateral proximal femoral arterial BF from the upper abdominal aorta BF above the coeliac trunk. Evaluation of BFAP is a potentially useful indicator of exercise or food intake related flow distribution to organs; however, there is a lack of information regarding the physiological significance of BFAP, and the measurements are yet to be validated. The aims of the present study are to examine the range in BFAP among subjects, monitor physiological day-to-day variability in BFAP over three different days and then determine whether mean BFAP (averaged over the three different measurement days) is related to body surface area (BSA). Forty healthy males (19–39 years) with a wide range of body weights (51–89 kg) were evaluated in a sitting position following a 12 h fast. The above-mentioned three conduit arteries were measured to determine BFAP using pulsed Doppler with spectral analysis. The mean BFAP was 2078 ± 495 ml min−1 (mean ± SD) (range, 1153–3285 ml min−1), which is in agreement with a previous study that measured the sum of BF in the major part of the coeliac, mesenteric and renal arteries. The physiological day-to-day variability (mean coefficient of variation) was 14.5 ± 10.0%. Significant (p < 0.05) positive linear relationships were observed between BFAP and BSA as well as body weight, which is in good agreement with the results of a previous study. The present data suggest that BFAP determined by three-conduit arterial hemodynamics may be a valid measurement that encompasses physiologic flow to multiple abdominal-pelvic organ systems.

Analytical Measurement

A Three-Dimensional Desingularized High Order Panel Method Based on Nurbs

Coupled computational fluid dynamics with six-degree-of-freedom trajectory predictions using an automated Cartesian method are demonstrated by simulating a GBU-31/Joint Direct Attack Munition store separating from an F/A-18C aircraft. Numerical simulations are performed at two Mach numbers near the sonic speed and compared with flight-test telemetry and photographic-derived data. For both Mach numbers, simulation results using a sequential-static series of flow solutions are contrasted with results using a time-dependent approach. Both numerical approaches show good agreement with the flight-test data through the first 0.25 s of the trajectory. At later times the sequential-static and time-dependent methods diverge, after the store produces peak angular rates; however, both remain close to the flight-test trajectory

With the rapid increasing of car usage, congestion is becoming more and more severe in metropolitans. To tackle this problem, the classification and prediction of traffic states are vital for the authority to quickly react. This study proposes a machine learning method to identify and predict traffic states at small region levels. In this paper, we compare two different spatial division methods, namely rectangular grids and hexagonal grids and measure the traffic characteristics through aggregating floating car trajectory data. Then a dimensionality reduction technique is applied to the traffic parameter, followed by a clustering model for traffic state recognition and labeling. From the analysis in this study, speed is found to be an important feature for classifying the traffic state. Therefore, two Convolutional Neural Network (CNN) models using different architecture were used for both speed and traffic state prediction, which could consider the spatial and temporal features simultaneously. Random forest regression, Gradient boosting decision tree and Long-short term memory neural network model are used as baseline models. The case study performed in Chengdu demonstrates that the proposed model outperforms the baseline models.

A VOS based Immersed Boundary-Lattice Boltzmann method for incompressible fluid flows with complex and moving boundaries

Numerical simulations of the unsteady flowfield of helicopter rotors on moving embedded grids