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Investigation of Tissue Thermal Damage Process with Application of Direct Sensitivity Method
Get PDFIn the paper the numerical analysis of thermal processes proceeding in the biological tissue is presented. The tissue is subjected to the external heat flux and 2D problem is taken into account. In order to determine the influence of variations of thermophysical parameters of tissue on the value of Arrhenius injury integral the direct approach of sensitivity analysis is applied. On the basis of tissue damage fraction the thermal injury formation process is analysed. At the stage of numerical realization the boundary element method is used. In the final part of the paper the example of numerical simulation is shown
A Hydrodynamic Assessment of a Remotely Operated Underwater Vehicle Based on Computational Fluid Dynamic – Part 1 – Numerical Simulation
No full textThe authors have developed a remote operate vehicle (ROV) that allow carried out highly risky task, in confined space such as inside of submerged sewers and pipes systems, areas were commercial ROV may not provide good performing. In addition, this ROV is low cost. This paper analyses based on the computational fluid dynamic the hydrodynamic performance of this ROV. The first part of the paper presents the theoretical approach and introduces the finite volume model developed in order to complete the study. Results of the model compare with published research shows good agreement. The second (forthcoming) part of the paper analyzes the hydrodynamic behavior of the ROV under different flow conditions
Local strong form meshless method on multiple Graphics Processing Units
No full textThis paper deals with the implementation of the local meshless numerical method (LMM) on general purpose graphics processing units (GPU) in solving partial differential equations (PDE). The local meshless solution procedure is formulated in a way suitable for parallel execution and has been implemented on multiple GPUs. The implementation is tested on a solution of diffusion equation in a 2D domain. Different setups of the meshless approach regarding the selection of basis functions are tested on an interval up to 2.5 million of computational points. It is shown that monomials are a good selection of the basis when working with a high number of nodes. The results are presented in terms of error analysis, convergence analysis and computational performance measurements
Wavelet operational matrix method for solving fractional integral and differential equations of Bratu-type
No full textIn this paper, a wavelet operational matrix method based on the second kind Chebyshev wavelet is proposed to solve the fractional integral and differential equations of Bratu-type. The second kind Chebyshev wavelet operational matrix of fractional order integration is derived. A truncated second kind Chebyshev wavelet series together with the wavelet operational matrix is utilized to reduce the fractional integral and differential equations of Bratu-type to a system of nonlinear algebraic equations. The convergence and the error analysis of the method are also given. Two examples are included to verify the validity and applicability of the proposed approach
Applications of the MLPG Method in Engineering & Sciences: A Review
No full textA review is presented for analysis of problems in engineering & the sciences, with the use of the meshless local Petrov-Galerkin (MLPG) method. The success of the meshless methods lie in the local nature, as well as higher order continuity, of the trial function approximations, high adaptivity and a low cost to prepare input data for numerical analyses, since the creation of a finite element mesh is not required. There is a broad variety of meshless methods available today; however the focus is placed on the MLPG method, in this paper. The MLPG method is a fundamental base for the derivation of many meshless formulations, since the trial and test functions can be chosen from different functional spaces. In the last decade, a broad community of researchers and scientists contributed to the development and implementation of the MLPG method in a wide range of scientific disciplines.
This paper first presents the basics and principles of the MLPG method, the meshless local approximation techniques for trial and test functions, applications to elasticity and elastodynamics, plasticity, fracture and crack analysis, heat transfer and fluid flow, coupled problems involving multiphase materials, and techniques for increasing the accuracy and computational effectiveness. Various applications to 2-D planar problems, axisymmetric problems, plates and shells or 3-D problems are included.
An increased number of published papers in literature in the recent years can be considered as a measure of the growing research activity in the general scope of the MLPG method, and thus, several trends and ideas for future research interest are also outlined
An alternating finite difference material point method for numerical simulation of high explosive explosion problems
No full textBased on the material point method (MPM), an alternating finite difference material point (AFDMP) method is proposed for modeling the 3D high explosive (HE) explosion and its interaction with structures nearby. The initiatory detonation and eventual fluid structure interaction (FSI) are simulated by the standard MPM. On the other hand, the finite difference method (FDM) is employed to simulate the dispersion of the detonation products into the surrounding air where the particles degenerate to marker points which track the moving interface between detonation products and air. The conversion between MPM and FDM is implemented by the projection between the particles variables in MPM and the cell centers variables in FDM. In several numerical tests, predictions of the proposed method tests are in good agreement with theoretical solutions or empirical formulae. They illustrate that the method can yield good prediction for the entire HE explosion process
Parameter Sensitivity and Probabilistic Analysis of the Elastic Homogenized Properties for Rubber Filled Polymers
Get PDFThe main aim in this paper is a computational study devoted to the sensitivity gradients and probabilistic moments of the effective elastic parameters for the rubber-filled polymers. The methodology is based on least squares recovery of the polynomial functions relating the effective tensor components and the given input design/random parameters. All numerical experiments are provided with respect to Young’s moduli of the elastomer constituents. Computational analysis is possible thanks to the application of the Response Function Method, which is enriched in our approach with the weighting procedures implemented according to the Dirac-type distributions. The homogenized elasticity tensor components are derived with the use of the variational upper and lower bounds for 2 D idealization of the composite and also thanks to the computational solution to the plane strain cell problem solved on the elastomer’s Representative Volume Element. Sensitivity analysis results in the first order gradients of the effective tensor, while probabilistic moments consist of up to the fourth order probabilistic moments and coefficients of the tensor; all numerical experiments are carried out in the FEM-oriented code MCCEFF and also using the symbolic computer algebra system MAPLE. This approach is straightforwardly applicable in deterministic and probabilistic optimization of polymers filled with rubber or carbon particles; it gives also the basis to further homogenization-based experiments with more advanced constitutive laws like Mullins theory
A Proposal of Nonlinear Formulation of Cell Method for Thermo-Elastostatic Problems
Get PDFThe growing necessity of accuracy in analyzing engineering problems requires more detailed and sophisticated models. Those models can include multiphysics interactions, that, sometimes, are highly nonlinear and the application of the superposition principle is then not possible. The cell method can be suitably used to study nonlinear multiphysics problems, because its theoretical framework for the physical laws is intrinsically multiphysics. In this way it is possible to take into account the mutual effects between different physics. Within the cell method framework, the coupling terms can be directly formulated in terms of the global variables used for the solution of the elementary problems. In this way it is possible to solve the coupled problem in a single solver run. In this paper a nonlinear procedure for elastostatic analysis with cell method is developed and the Fixed Point technique is applied to a 1D two-node cell and to a 3D four-node tetrahedral cell. The procedure is numerically and experimentally validated. After the theoretical part, a nonlinear thermo-mechanical analysis of an exhaust manifold is presented as case-study
ACA-accelerated Time Domain BEM for Dynamic Analysis of HTR-PM Nuclear Island Foundation
Get PDFThis paper presents the use of a three-dimensional time domain boundary element method (BEM) in conjunction with adaptive cross approximation method (ACA) for dynamic analyses of the HTR-PM nuclear island foundation. The advantage of this approach is that only foundation of the HTR-PM nuclear island and limited surfaces of the supporting half-space soil medium are modeled and analyzed in a direct time stepping scheme. In addition, the ACA can compress the BEM coefficient matrices at each time step efficiently, therefore allowing larger models to be analyzed compared with conventional BEMs. In order to discretize the boundary integral equation (BIE) we use collocation method and eight-node discontinuous quadratic element. In order to preserve the causality condition an element subdivision technique suggested by Marrero (Engineering Analysis with Boundary Elements 2003; 27: 39–48) is adopted. In the numerical tests, sensitivity analyses are carried out in order to study dynamic characteristics of the HTR-PM nuclear island foundation and to establish fixed base criteria of the supporting soil medium for the associated seismic design of the nuclear island
Vortex Patches
Get PDFA vortex patch is a bounded region of uniform vorticity in twodimensional, incompressible, inviscid fluid flow. The streamfunction satisfies the Poisson equation with the vorticity acting as a source term. The standard formulation is to write the streamfunction as a convolution of the vorticity with the twodimensional free-space Greens function. A simple application of Greens theorem converts the area integral to a boundary integral. Numerical methods must then account for the singular nature of the boundary integral, and high accuracy is difficult when filamentation takes place, that is, when long, very thin filaments of vorticity erupt from the main boundary. A new boundary integral is derived based on a different viewpoint. A particular solution is readily known which represents solid body rotation. To the particular solution must be added a homogeneous solution, and the combination must satisfy the boundary conditions. A standard boundary integral can be used to solve the Laplace equation with Dirichlet boundary conditions. This approach leads to a boundary integral without singularity and easily approximated by the trapezoidal rule that ensures spectral accuracy. Results indicate that high accuracy is possible with even modest resolution. The method is used to explore the mathematical properties of filamentation