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Kernel-Based Local Meshless Method for Solving Multi-DimensionalWave Equations in Irregular Domain
Get PDFThis work explores the application of kernel based local meshless method for solving multi-dimensional wave equations in irregular domain. The method is tested for various types of boundary conditions in irregular shaped domain. The method is capable of solving multi-dimension large scaled problems in complex shaped domain
Approximation of Unit-Hypercubic Infinite Noncooperative Game Via Dimension-Dependent Samplings and Reshaping the Player’s Payoffs into Line Array for the Finite Game Simplification
Get PDFThe problem of solving infinite noncooperative games approximately is considered. The game may either have solution or have no solution. The existing solution may be unknown as well. Therefore, an approach of obtaining the approximate solution of the infinite noncooperative game on the unit hypercube is suggested. The unit-hypercubic game isomorphism to compact infinite noncooperative games allows to disseminate the approximation approach on a pretty wide class of noncooperative games. The approximation intention is in converting the infinite game into a finite one, whose solution methods are easier rather than solving infinite games. The conversion starts with sampling the players’ payoff functions. Each dimension of the player’s pure strategies unit hypercube is sampled with its own sampling constant, being the number of equal-measure intervals between the selected points along the dimension. There are stated requirements for the sufficiently accurate sampling. Having got the finite game on hypercubic lattice after the sampling, every player’s payoff multidimensional matrix is reshaped to reduce number of its dimensions down to the number of players. Dimensionality reduction will commonly accelerate computations, connected with the approximate solution consistency. The introduced consistency mechanism rejects the finite game solution, pretended to being the initial game approximate solution, if the solution depends vastly on the sampling steps. If the solution is weakly consistent then, changing the sampling steps minimally, there are non-decreasing difference of the players’ payoffs and difference of the players’ equilibrium strategies and cardinalities of their supports. If the solution is consistent then the non-decreasing property holds stricter for cardinalities of the supports and their upper densities
Computation of Aerodynamic Noise Radiated From Open Propeller Using Boundary Element Method
No full textIn order to accurately predict the aerodynamic noise of the propeller, a hybrid method combining Computational Fluid Dynamics (CFD) method with Boundary Element Method (BEM) is developed in this paper. The calculation includes two steps: firstly, the unsteady viscous flow around the propeller is calculated using the CFD method to acquire the noise source information; secondly, the radiated sound pressure is calculated using BEM method in the frequency domain. In comparison with the experimental results from wind tunnel, the calculated results of aerodynamic performance are rather desirable. The simulation and experimental results of aerodynamic noise are well fitted. The directivity of sound pressure levels (SPLs) of propeller noise is shown in this paper. Simulation shows that the method can effectively calculate aerodynamic noise of the propeller. The acoustic analysis draws some meaningful conclusions
Solving a Class of PDEs by a Local Reproducing Kernel Method with An Adaptive Residual Subsampling Technique
Get PDFA local reproducing kernel method based on spatial trial space spanned by the Newton basis functions in the native Hilbert space of the reproducing kernel is proposed. It is a truly meshless approach which uses the local sub clusters of domain nodes for approximation of the arbitrary field. It leads to a system of ordinary differential equations (ODEs) for the time-dependent partial differential equations (PDEs). An adaptive algorithm, so-called adaptive residual subsampling, is used to adjust nodes in order to remove oscillations which are caused by a sharp gradient. The method is applied for solving the Allen-Cahn and Burgers’ equations. The numerical results show that the proposed method is efficient, accurate and be able to remove oscillations caused by sharp gradient
The Study of Thermal Stresses of a Two Phase FGM Hollow Sphere
Get PDFThis article focuses on the analytical solution for uniform heating of a FGM hollow sphere made of two phase of different materials. It is assumed that the volume fraction of one phase is a function f1=(rn-an)/(bn-an) varied in the radial direction. Based on the Voigt constant strain approximation, analytical solutions of stresses, displacements and the effective coefficient of thermal expansion are obtained. The effects of the volume fraction, Poisson’s ratio, Young’s moduli and coefficients of thermal expansion on the solutions are studied. Two special cases, constant elastic modulus and constant coefficient of thermal expansion, are finally discussed
Double Optimal Regularization Algorithms for Solving Ill-Posed Linear Problems under Large Noise
Get PDFA double optimal solution of an n-dimensional system of linear equations Ax = b has been derived in an affine m « n. We further develop a double optimal iterative algorithm (DOIA), with the descent direction z being solved from the residual equation Az = r0 by using its double optimal solution, to solve ill-posed linear problem under large noise. The DOIA is proven to be absolutely convergent step-by-step with the square residual error ||r||2 = ||b - Ax||2 being reduced by a positive quantity ||Azk||2 at each iteration step, which is found to be better than those algorithms based on the minimization of the square residual error in an m-dimensional Krylov subspace. In order to tackle the ill-posed linear problem under a large noise, we also propose a novel double optimal regularization algorithm (DORA) to solve it, which is an improvement of the Tikhonov regularization method. Some numerical tests reveal the high performance of DOIA and DORA against large noise. These methods are of use in the ill-posed problems of structural health-monitoring
Numerical Simulation of Bubble Formation at a Single Orifice in Gas-fluidized Beds with Smoothed Particle Hydrodynamics and Finite Volume Coupled Method
Get PDFA coupled method describing gas-solid two-phase flow has been proposed to numerically study the bubble formation at a single orifice in gas-fluidized beds. Solid particles are traced with smoothed particle hydrodynamics, whereas gas phase is discretized by finite volume method. Drag force, gas pressure gradient, and volume fraction are used to couple the two methods. The effect of injection velocities, particle sizes, and particle densities on bubble growth is analyzed using the coupled method. The simulation results, obtained for two-dimensional geometries, include the shape and diameter size of a bubble as a function of time; such results are compared with experimental data, previous numerical results, and other approximate model predictions reported in the literature. Moreover, the flow profiles of gas and particle phases and the temperature distribution by the heat transfer model around the forming bubble are also discussed. All results show that the coupled method efficiently describes of the bubble formation in fluidized beds. The proposed method is applicable for solving gas–solid two-phase flow in fluidization
Experimental and Numerical Investigation for Membrane Deployment using SPH and ALE Formulations
Get PDFSimulation of airbag and membrane deployment under pressurized gas problems becomes more and more the focus of computational engineering, where FEM (Finite element Methods) for structural mechanics and Finite Volume for CFD are dominant. New formulations have been developed for FSI applications using mesh free methods as SPH method, (Smooth Particle Hydrodynamic). Up to these days very little has been done to compare different methods and assess which one would be more suitable. For small deformation, FEM Lagrangian formulation can solve structure interface and material boundary accurately, the main limitation of the formulation is high mesh distortion for large deformation and moving structure. One of the commonly used approach to solve these problems is the ALE formulation which has been used with success in the simulation of FSI (Fluid Structure Interaction) with large structure motion such as sloshing fuel tank in automotive industry and bird impact in aeronautic industry. For some applications, including bird impact and high velocity impact problems, engineers have switched from ALE to SPH method to reduce CPU time and save memory allocation.
In this paper the mathematical and numerical implementation of the ALE and SPH formulations are described. From different simulation, it has been observed that for the SPH method to provide similar results as ALE or Lagrangian formulations, the SPH meshing, or SPH spacing particles needs to be finer than the ALE mesh.
To validate the statement, we perform a simulation of membrane deployment generated by high pressurized gas. For this simple problem, the particle spacing of SPH method needs to be at least two times finer than ALE mesh. A contact algorithm is performed at the FSI for both SPH and ALE formulations
An Improved WCSPH Method to Simulate the Non-Newtonian Power Law Fluid Flow Induced by Motion of a Square Cylinder
No full textIn this study, an improved weakly compressible Smoothed Particle Hydrodynamics method is introduced and applied for investigation of the non- Newtonian power-law fluid flow which is induced by motion of a square cylinder. The method is based on a predictor-corrector scheme and pressure velocity coupling to overcome the non-physical fluctuations of WCSPH. The numerical method is also supported by the corrective tensors and shifting algorithm. The results are validated against the well known test cases and benchmark data. The square motion is tested in various Reynolds numbers for various power law indices. The results show that the drag coefficient increases by increasing the power-law index although there are some irregular behaviors for the lower power-law indices at higher Reynolds numbers
RBFN stochastic coarse-grained simulation method: Part I - Dilute polymer solutions using Bead-Spring Chain models
Get PDFIn this paper, dynamic behaviours of dilute polymer solutions of various bead-spring chain models in shear flow are studied using a coarse-grained method based on the Integrated Radial Basis Function Networks (IRBFNs) and stochastic technique. The velocity field governed by the macroscopic conservation equations is determined by the IRBFN-based method, whereas the evolution of configurations of polymer chains governed by the diffusion stochastic differential equations are captured by the Brownian Configuration Field (BCF) approach. The system of micro-macro equations is closed by the Kramers’ expression, which allows for the determination of the polymer stresses in terms of BCF configurations. In this work, all nonlinear effects in a BSC model such as hydrodynamic interaction and excluded volume are considered. Since the simulation requires a considerable computational effort, parallel calculations are performed where possible. As an illustration of the method, the start-up planar Couette flow is examined, in which the evolution of viscometric functions such as shear stress, the first and the second normal stress differences is assessed with various BSC models