Gradient Calculation Method Research Articles

Performance of numerical schemes in the simulation of two-phase free flows and wall bounded mini channel flows

In the present paper, simulations of two-phase flows using volume of fluid method are presented and analyzed. Two important problems in two-phase flow simulations are identified—dependence of the simulation on momentum discretization scheme and on the gradient calculation scheme. The dependence of the solution on the momentum discretization schemes is analyzed using bubble rise simulations, which does not involve the wall adhesion (contact angle), and compared with published results. Performance of the momentum discretization schemes with the inclusion of wall adhesion effect is analyzed using simulations in T-junctions of minichannels and validated against experimental results available in literature. Reasoning for the better performance of a few schemes over the others is provided. Sensitivity of the solution to the gradient calculation method is analyzed using T-junction simulations and flow maps are generated with different gradient calculation schemes. These flow maps are compared with experimental flow maps reported in literature and the gradient calculation scheme that generates a physically realizable flow map is reported. Unlike most of the work to date, which only explore small parts of the flow map containing a single regime, we study the capability of the commercial software FLUENT in simulating across several flow regimes observed in experiments.

A multi-direction GVF snake for the segmentation of skin cancer images

A multi-direction gradient vector flow (GVF) snake-based scheme is proposed in this paper for the segmentation of skin cancer images. Unlike the traditional anisotropic diffusion (AD) filter, which has many disadvantages such as sensitivity to noise, a new AD filter has been developed to remove the noise. The proposed AD filter uses adaptive threshold selection and a new gradient computation method, which is robust to noise and can effectively remove the hairs. After the noise is removed from the skin cancer image, the image is segmented using a multi-direction GVF snake. The multi-direction GVF snake extends the single direction GVF snake and traces the boundary of the skin cancer even if there are other objects near the skin cancer region. Experiments performed on 11 cancer images show the effectiveness of the proposed algorithm.

Environment Modelling for Robot Navigation Using VLSI-Efficient Logarithmic Approximation Method

One of the major drawbacks of the visibility graph-based environment modelling process is its high computational complexity, particularly when the number of obstacles is large. In this paper, a logarithmic approximation based gradient computation method has been proposed to efficiently identify the farthest front vertices. It has been shown that the half-plane methods can be employed by examining only these farthest front vertices to rapidly identify the links that are obstructed by other objects. Novel techniques have been incorporated to substantially reduce the size of the look-up table required to implement the logarithmic approximation method. VLSI efficient architecture was then developed to demonstrate the viability of incorporating the visibility graph-based approach into a high-speed environment modelling process, which is well suited to dynamic robot navigation.

Development of an on-board gradient data acquisition system

This report describes the development of an on-board gradient data acquisition system that adopts a gradient calculation method based on vehicle acceleration and velocity. Gradient data is critical in assessing the reliability and cooling performance of vehicles. The acquisition system has proven to be economical, compact, lightweight provides long- term measurement stability, and is capable of real-time calculations.

Intelligent gradient-based search of incompletely defined design spaces

AbstractGradient-based numerical optimization of complex engineering designs offers the promise of rapidly producing better designs. However, such methods generally assume that the objective function and constraint functions are continuous, smooth, and defined everywhere. Unfortunately, realistic simulators tend to violate these assumptions. We present a rule-based technique for intelligently computing gradients in the presence of such pathologies in the simulators, and show how this gradient computation method can be used as part of a gradient-based numerical optimization system. We tested the resulting system in the domain of conceptual design of supersonic transport aircraft, and found that using rule-based gradients can decrease the cost of design space search by one or more orders of magnitude.

Trajectory optimization by a direct descent process

The problem considered is that of trajectory optimization using step-by-step descent to minimum cost along the direction of the cost gradient with respect to the control. Using a hybrid computer, the gradient is computed di rectly as the response to nearly impulsive control perturba tions. A method is presented for computing the gradient when several terminal constraints are enforced. Examples of application of the method are presented. It is concluded that the direct gradient computation method has some significant advantages over other methods.