In this paper the propagation of detonation waves in high explosives as well as gaseous mixtures are studied by combining the DSD theory and the LEVEL SET METHOD. In first step, the D-k and D-D-k relations for high explosive materials and gaseous mixtures are obtained. Then, using LEVEL SET METHOD, the detonation front is tracked in different geometries. A good agreement between DSD results and direct numerical simulations is observed for high explosive materials, where the curvature has an important role in detonation dynamic. Nevertheless, for gaseous mixtures the agreement is not as good as high explosives. In order to study the critical diameter problem in gaseous mixtures, the problem of detonation wave diffracting from a channel into an unconfined space is investigated. In this problem, the detonation failure criterion, based on the critical curvature concept, is utilized. A considerable difference between critical diameters which had been predicted by DSD theory and the experimental results is observed. The results indicate that the critical diameter in gaseous compositions (where the unsteadiness and chemical kinetic are more crucial than the curvature) is often underestimated by the DSD theory.

Introduction: Breast cancer can be considered as the most common cancer among women in the world. Hence, finding appropriate diagnosis METHODs is a critical and sensitive challenge in the health of the human community. Various METHODs have been proposed for breast screening in women, and one of the safest METHODs is magnetic resonance imaging. Tumors do not have morphological features of their own. Therefore, differentiating between benign and malignant lesions is normally very time-consuming and difficult. In this study, a computer-aided autodiagnosis system is developed for diagnosis and classification of axial magnetic resonance images of the breast in two classes of benign and malignant. METHODs: Initially, suspected parts of the lesion were separated as a rectangular box around the lesion by an experienced radiologist. Then, we used, for the first time, a LEVEL SET– based algorithm to precisely separate the lesion considering the unevenness of the images and to remove false positive regions using morphological operations and removing veins. In the next stage, four groups of features expressing particular states of the lesion structure are extracted from the separated parts of the lesions. These four groups are textural, kinetic, frequency, and morphological features. Here a new group of features called the Gabor-Haralik features, which present a particular efficiency, was extracted for each lesion. Finally, MLP classification was used to classify the lesions. Results: The proposed METHOD was tested on 46 lesions. By utilizing Gabor-Haralik features, we achieved mean sensitivity, specificity, accuracy, and F-measure of 95. 41, 90. 70, 92. 76, and 92. 19%, respectively. Conclusion: The performance measures indicate the efficiency of the proposed diagnosis system for classification of benign and malignant breast lesions in magnetic resonance imaging.

This paper proposes an effective algorithm based on the LEVEL SET METHOD (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary LEVEL SET METHOD (BLSM) is used instead. In the BLSM, the LEVEL SET function can only take 1 and -1 values at convergence. Thus, it is related to phase-field METHODs. We don’t need to solve the Hamilton-Jacobi equation, so it is free of the CFL condition and the reinitialization scheme. This favorable properties lead to a great time advantage in this METHOD. In this paper, the BLSM is implemented with the additive operator splitting (AOS) scheme and several numerical issues of the implementation are discussed.The proposed scheme is much more efficient than the conventional LEVEL SET METHOD. Several 2D examples are presented which demonstrate the effectiveness and robustness of the proposed METHOD.

In the present paper, an approach is proposed for structural topology optimization based on combination of Radial Basis Function (RBF) LEVEL SET METHOD (LSM) with Isogeometric Analysis (IGA). The corresponding combined algorithm is detailed. First, in this approach, the discrete problem is formulated in Isogeometric Analysis framework. The objective function based on compliance of particular locations of materials in the structure is used and find the optimal distribution of material in the domain to minimize the compliance of the system under a volume constraint. The refinement is employed for construction of the physical mesh to be consistent with the mesh is used for LEVEL SET function. Then a parameterized LEVEL SET METHOD with radial basis functions (RBFs) is used for structural topology optimization. Finally, several numerical examples are provided to confirm the validity of the METHOD.

This study focuses on the topology optimization of structures using a hybrid of LEVEL SET METHOD (LSM) incorporating sensitivity analysis and isogeometric analysis (IGA). First, the topology optimization problem is formulated using the LSM based on the shape gradient. The shape gradient easily handles boundary propagation with topological changes. In the LSM, the topological gradient METHOD as sensitivity analysis is also utilized to precisely design new holes in the interior domain. The hybrid of these gradients can yield an efficient algorithm which has more flexibility in changing topology of structure and escape from local optimal in the optimization process. Finally, instead of the conventional finite element METHOD (FEM) a Non–Uniform Rational B–Splines (NURBS) –based IGA is applied to describe the field variables as the geometry of the domain. In IGA approach, control points play the same role with nodes in FEM, and B–Spline functions are utilized as shape functions of FEM for analysis of structure. To demonstrate the performance of the proposed METHOD, three benchmark examples widely used in topology optimization are presented. Numerical results show that the proposed METHOD outperform other LSMs.

In this paper, we propose an adaptive mesh approach for time dependent parial differential equations, based on a so-called moving mesh PDE (MMPDE) and LEVEL SET METHOD. It means that the velocity of mesh nodes is calculated by MMPDE and is employed as veocity in the LEVEL SET equation. Then, at each time LEVEL, the mesh points are considered as the LEVEL contours of the LEVEL SET function. Finally the METHOD is merged with local time step technique.

In this research, second order LEVEL SET METHOD for simulation of grain burn-back analysis is presented and compared with the first order LEVEL SET according to discretisation technique, accuracy, and CPU time. In this manner and at the first step, we describe total necessities of LEVEL SET METHOD that are grid generation, minimum distance function calculation, relative condition estimation, ballistic characteristics calculation, and obtaining results. Then, at the second step, we improve forth necessity of LEVEL SET METHOD by second order model. For validation of presented model, we consider many type of simple and complex grains and evaluate grain burn- back analysis. The obtained results indicate that second order model is more accurate than the first order model for simulation of complex grains. But, at the simple grains with more CPU time related to second order model, accuracy of two models are similar. A compromise between accuracy and CPU time suggest that one can use second order model for simulation of complex grains and first order model for simulation of simple grains.

In this research, interaction and oblique coalescence of bubbles under buoyancy force was simulated, numerically. The governing equations are continuity and momentum equations which have been discretized using the finite volume METHOD and the SIMPLE algorithm. For simulating the interface of two phases, the LEVEL SET METHOD has been incorporated. LEVEL SET METHOD suffers from poor mass conservation of dispersed phase especially in the case of severe deformation of interface. In order to control of mass conservation of the LEVEL SET METHOD, re-initialization equations and a geometric mass control loop are used which this loop is implemented in the LEVEL SET METHOD for the first time in this research. Using proposed geometric mass control loop, mass dissipation drawback of the LEVEL SET METHOD is handled in simulation of bubbles’ coalescence. The results outlined in the present study well agree with the existing experimental results. Also results of investigation of mass dissipation of the proposed scheme to simulation of oblique coalescence problem show that the maximum amount of this mass dissipation was less than 4%. Therefore, the LEVEL SET METHOD with proposed geometric mass control loop could be used properly for simulation of oblique interactions and coalescence of bubbles in multiphase flows.

The structural design must ensure suitable working conditions by attending for safe and economic criteria. However, the optimal solution is not easily available, because these conditions depend on the bodies’dimensions, materials strength and structural system configuration.In this regard, topology optimization aims for achieving the optimal structural geometry, i.e. the shape that leads to the minimum requirement of material, respecting constraints related to the stress state at each material point. The present study applies an evolutionary approach for determining the optimal geometry of 2D structures using the coupling of the boundary element METHOD (BEM) and the LEVEL SET METHOD (LSM). The proposed algorithm consists of mechanical modelling, topology optimization approach and structural reconstruction.The mechanical model is composed of singular and hypersingular BEM algebraic equations. The topology optimization is performed through the LSM. Internal and external geometries are evolved by the LS function evaluated at its zero LEVEL. The reconstruction process concerns the remeshing. Because the structural boundary moves at each iteration, the body’s geometry change and, consequently, a new mesh has to be defined. The proposed algorithm, which is based on the direct coupling of such approaches, introduces internal cavities automatically during the optimization process, according to the intensity of Von Mises stress. The developed optimization model was applied in two benchmarks available in the literature.Good agreement was observed among the results, which demonstrates its efficiency and accuracy.