摘要 :
A high-order accurate CFD solver, based on the Discontinuous Galerkin (DG) finite element method, is here employed to compute the heat transfer, with and without film coolant injection, around a turbine vane extensively tested in ...
展开
A high-order accurate CFD solver, based on the Discontinuous Galerkin (DG) finite element method, is here employed to compute the heat transfer, with and without film coolant injection, around a turbine vane extensively tested in a wind tunnel. The numerical solution makes also use of a high-order polynomial representation of the airfoil curved boundary in order to minimize the numerical sources of error, leaving possibly only those related to the physical model adopted. The objective of the work is therefore twofold: on the one hand to provide a detailed investigation, often beyond the reach of the experiments, of the complex flow field arising in a film-cooled gas turbine cascade, on the other hand to ascertain the limits of the Reynolds-averaged Navier-Stokes (RANS) approach and its associated turbulence model when using high-order accurate methods. The DG formulation is briefly reviewed, as well as the experimental apparatus and the measuring technique, and then the code is applied to the computation of various test cases characterized by different reference Reynolds and Mach numbers. Two-dimensional results (up to seventh-order accurate) obtained both with the high- and low-Reynolds version of the k-co model employed are presented. Reasonably good agreement between experimental and numerical results is obtained, even though the outcomes are far from being completely satisfactory especially for flow regimes in the low Reynolds number range. This is due to the lack of suitable modeling of the laminar-turbulent transition process taking place around the blade leading edge. Such a complex phenomenon is out of reach of the modeling capabilities of the high-Re k-co model, while can be roughly mimicked by the low Re version of the model, which is able to provide a delayed onset of the turbulence quantities along the blade surface.
收起
摘要 :
The paper is concerned with the numerical treatment of the uniformly heated inelastic Boltzmann equation by the direct simulation Monte Carlo (DSMC) method. This technique is presently the most widely used numerical method in kine...
展开
The paper is concerned with the numerical treatment of the uniformly heated inelastic Boltzmann equation by the direct simulation Monte Carlo (DSMC) method. This technique is presently the most widely used numerical method in kinetic theory. We consider three modi. cations of the DSMC method and study them with respect to their efficiency and convergence properties. Convergence is investigated with respect to both the number of particles and the time step. The main issue of interest is the time step discretization error due to various splitting strategies. A scheme based on the Strang-splitting strategy is shown to be of second order with respect to time step, while there is only first order for the commonly used Euler-splitting scheme. On the other hand, a no-splitting scheme based on appropriate Markov jump processes does not produce any time step error. It is established in numerical examples that the no-splitting scheme is about two orders of magnitude more efficient than the Euler-splitting scheme. The Strang-splitting scheme reaches almost the same level of efficiency as that of the no-splitting scheme, since the deterministic time step error vanishes sufficiently fast.
收起
摘要 :
In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. W...
展开
In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.
收起
摘要 :
A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with a weakly singular kernel is of concern in this paper. The scheme is targeted to reduce the computation time and ...
展开
A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with a weakly singular kernel is of concern in this paper. The scheme is targeted to reduce the computation time and to improve the accuracy of the scheme developed by Xu et al. The constructed scheme is armed by three steps: First, a small nonlinear system is solved on the coarse grid using a fix-point iteration. Second, Lagrange's linear interpolation formula is used to arrive at some auxiliary values for the analysis of the fine grid. Finally, a linearized Crank-Nicolson finite difference system is solved on the fine grid. Moreover, the algorithm uses a central difference approximation for the spatial derivatives. In the time direction, the time derivative and integral term are approximated by the Crank-Nicolson technique and product integral rule, respectively. By means of the discrete energy method, stability and space-time second-order convergence of the proposed approach are obtained in L-2-norm. Finally, the numerical verification is fulfilled as the numerical results of the given numerical experiments agree with the theoretical analysis and verify the effectiveness of the algorithm.
收起
摘要 :
The paper presents a new numerical wave flume packaged as PARISPHERE code based on the Incompressible Smoothed Particle Hydrodynamics (ISPH) method with an improved framework for enhancement of the numerical accuracy and stability...
展开
The paper presents a new numerical wave flume packaged as PARISPHERE code based on the Incompressible Smoothed Particle Hydrodynamics (ISPH) method with an improved framework for enhancement of the numerical accuracy and stability. PARISPHERE includes a new pressure gradient model for more enhancement and a new coupling model with Discrete Element Method (DEM)-ISPH to achieve flexible application of the spatial resolution between the solid and liquid targets. In addition, the existing porous model and scour model are introduced into the framework. Its enhancement is shown by comparing with the existing schemes through benchmarks with targeting a standing wave test, a wave propagation test, a breaking wave test, a dam break problem with a porous media, a drafting, kissing, and tumbling (DKT) problem, a two-phase flow, and a scour process by an overflowing tsunami.
收起
摘要 :
The study of the development of perturbations under the influence of various hydrodynamic instabilities, as well as the transition to turbulent mixing and turbulence, has been a subject of considerable interest over the past decad...
展开
The study of the development of perturbations under the influence of various hydrodynamic instabilities, as well as the transition to turbulent mixing and turbulence, has been a subject of considerable interest over the past decades. This is primarily due to the importance of these phenomena in various fields of science and engineering. In addition, it should be noted that studies of the characteristics of turbulent flows, for example, have still not been completed. This is inspiring a great deal of interest in this topic, both in the sense of physical theory and in the sense of developing new approaches to the mathematical modeling of the corresponding problems. The capabilities of modern computer technology make it possible to carry out numerical experiments in two-dimensional and three-dimensional setups and analyze the features of the new numerical methods. Presently, numerous methods with many modifications are used in practice. This review focuses on the most promising among them.
收起
摘要 :
The Jacobi-Fourier moments (JFMs) which are useful for many image processing, pattern recognition and computer vision applications provide a wide class of orthogonal rotation invariant moments (ORIMs). The accuracy of JFMs suffers...
展开
The Jacobi-Fourier moments (JFMs) which are useful for many image processing, pattern recognition and computer vision applications provide a wide class of orthogonal rotation invariant moments (ORIMs). The accuracy of JFMs suffers from various errors, such as the geometric error, numerical integration error, and discretization error. Moreover, the high order moments are vulnerable to numerical instability. In this paper, we present a fast method for the accurate calculation of JFMs which not only removes the geometric error and numerical integration error, but also provides numerical stability to JFMs of high orders. (C) 2016 Elsevier GmbH. All rights reserved.
收起
摘要 :
The performance of interFoam (a widely used solver within OpenFOAM package) in simulating the propagation of water waves has been reported to be sensitive to the temporal and spatial resolution. To facilitate more accurate simulat...
展开
The performance of interFoam (a widely used solver within OpenFOAM package) in simulating the propagation of water waves has been reported to be sensitive to the temporal and spatial resolution. To facilitate more accurate simulations, a numerical wave tank is built based on a Navier-Stokes model, which employs the VPM (volume-average/point-value multi-moment) scheme as the fluid solver and the TH1NC/QQ method (THINC method with quadratic surface representation and Gaussian quadrature) for the free-surface capturing. Simulations of regular waves in an intermediate water depth are conducted and the results are assessed via comparing with the analytical solutions. The performance of the present model and interFoam solver in simulating the wave propagation is systematically compared in this work. The results clearly demonstrate that compared with interFoam solver, the present model significantly improves the dissipation properties of the propagating wave, where the waveforms as well as the velocity distribution can be substantially maintained while the waves propagating over long distances even with large time steps and coarse grids. It is also shown that the present model requires much less computation time to reach a given error level in comparison with interFoam solver.
收起
摘要 :
Two new higher-order accurate ?nite-di?erence schemes for the numerical solution of boundary-value problem of the Burgers’ equation are suggested. Burgers equation is a one-dimensional analogue of the Navier-Stokes equations desc...
展开
Two new higher-order accurate ?nite-di?erence schemes for the numerical solution of boundary-value problem of the Burgers’ equation are suggested. Burgers equation is a one-dimensional analogue of the Navier-Stokes equations describing the dynamics of ?uids and it possesses all of its mathematical properties. Besides the Burgers’ equation, one of the few nonlinear partial di?erential equations which has the exact solution, and it can be used as a test model to compare the properties of di?erent numerical methods. A ?rst scheme is purposed for the numerical solution of the heat equation. It has a sixth-order approximation in the space variable, and a third-order one in the time variable. A second scheme is used for ?nding a numerical solution for the Burgers’s equation using the relationship between the heat and Burgers’ equations. This scheme also has a sixth-order approximation in the space variable. The numerical results of test examples are found in good agreement with exact solutions and con?rm the approximation orders of the schemes proposed.
收起
摘要 :
A new accurate finite-difference (AFD) numerical method is developed specifically for solving high-order Boussinesq (HOB) equations. The method solves the water-wave flow with much higher accuracy compared to the standard finite-d...
展开
A new accurate finite-difference (AFD) numerical method is developed specifically for solving high-order Boussinesq (HOB) equations. The method solves the water-wave flow with much higher accuracy compared to the standard finite-difference (SFD) method for the same computer resources. It is first developed for linear water waves and then for the nonlinear problem. It is presented for a horizontal bottom, but can be used for variable depth as well. The method can be developed for other equations as long as they use Pade approximation, for example extensions of the parabolic equation for acoustic wave problems. Finally, the results of the new method and the SFD method are compared with the accurate solution for nonlinear progressive waves over a horizontal bottom that is found using the stream function theory. The agreement of the AFD to the accurate Solution is found to be excellent compared to the SFD solution. Copyright (c) 2005 John Wiley & Sons, Ltd.
收起
原文获取