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提高变型标准遗传算法收敛速率的混合法及其推广

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随机抓取VGA／TVGA图像的技术

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On the Use of Compact Streamfunction-Velocity Formulation of Steady Navier-Stokes Equations on Geometries beyond Rectangular

In this paper, a new methodology has been proposed to solve two-dimensional (2D) Navier-Stokes (N-S) equations representing incompressible viscous fluid flows on irregular geometries. It is based on second order compact finite difference discretization of the fourth order streamfunction equation on computational plane. The important advantage of this formulation is not only to overcome the difficulties existing in the velocity-pressure and streamfunction-vorticity formulations, but also for being applicable to complex geometries beyond rectangular. We first apply the proposed scheme to a problem having analytical solution and then to the well-studied benchmark problem (problem of lid-driven cavity flow) in viscous fluid flow. Finally, we demonstrate the robustness of our proposed scheme on flow in a complex domain (e.g. constricted channel and dilated channel). It is seen to efficiently capture steady state solutions of the N-S equations with Dirichlet as well as Neumann boundary conditions. In addition to this, it captures viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variations. Estimates of the error incurred show that the results are very accurate on a coarser grid. The results obtained using this scheme are in excellent agreement with analytical and numerical results whenever available and they clearly demonstrate the superior scale resolution of the proposed scheme.     

Coupling of a nonlinear finite element structural method with a Navier-Stokes solver

A new three-dimensional viscous aeroelastic solver is developed in the present work. A well validated full Navier-Stokes code is coupled with a nonlinear finite element plate model. Implicit coupling between the computational fluid dynamics and structural solvers is achieved using a subiteration approach. Computations of several benchmark static and dynamic plate problems are used to validate the finite element portion of the code. This coupled aeroelastic scheme is then applied to the problem of three-dimensional panel flutter. Inviscid and viscous supersonic results match previous computations using the same aerodynamic method coupled with a finite difference structural solver. For the case of subsonic flow, multiple solutions consisting of static, upward and downward deflections of the panel are discussed. The particular solution obtained is shown to be sensitive to the cavity pressure specified underneath the panel.     

On the solution of the unsteady Navier- Stokes equations including multicomponent finite rate chemistry

An explicit-implicit time-dependent finite difference technique is presented which has been successfully implemented for the solution of the unsteady Navier-Stokes equations including multicomponent finite rate chemistry. Stability restrictions encountered in explicit schemes due to the variable relaxation times associated with the finite rate chemical reactions are eliminated. As a result, the stability of the coupled Navier-Stokes and species conservatiion finite difference equations is shown to be governed only by the hydrodynamic stability cri- terion. The viscous nonequilibrium flow about a blunt axisymmetric nosetip at high Mach number and low Reynolds number, where the viscous shock layer and shock transition zone are merged, was computed using this time-dependent numerical scheme. Solutions along the stagnation streamline are compared with corresponding solutions obtained by Dellinger using the thin layer approximation of the Navier-Stokes equations.     

A p-multigrid spectral difference method for two-dimensional unsteady incompressible Navier-Stokes equations

This paper presents the development of a 2D high-order solver with spectral difference method for unsteady incompressible Navier-Stokes equations accelerated by a p-multigrid method. This solver is designed for unstructured quadrilateral elements. Time-marching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. An artificial compressibility method (ACM) is employed in order to treat the inviscid fluxes using the traditional characteristics-based schemes. The viscous fluxes are computed using the averaging approach (Sun et al., 2007; Kopriva, 1998) [29] and [12]. A dual time stepping scheme is implemented to deal with physical time marching. A p-multigrid method is implemented (Liang et al., 2009) [16] in conjunction with the dual time stepping method for convergence acceleration. The incompressible SD (ISD) method added with the ACM (SD-ACM) is able to accurately simulate 2D steady and unsteady viscous flows.     

A residual-based scheme for computing compressible flows on unstructured grids

A second-order residual-based compact scheme, initially developed for computing flows on Cartesian and curvilinear grids, is extended to general unstructured grids in a finite-volume framework. The scheme is applied to the computation of several inviscid and viscous compressible flows governed by the Euler and Navier-Stokes equations. Its efficiency and accuracy properties are compared with those of conventional second-order upwind schemes based on variable reconstruction.     

Control of flow using genetic algorithm for a circular cylinder executing rotary oscillation

We propose here a new approach to optimally control incompressible viscous flow past a circular cylinder for drag minimization by rotary oscillation. The flow at Re = 15000 is simulated by solving 2D Navier-Stokes equations in stream function-vorticity formulation. High accuracy compact scheme for space discretization and four stage Runge-Kutta scheme for time integration makes such simulation possible. While numerical solution for this flow field has been reported using a fast viscous-vortex method, to our knowledge, this has not been done at such a high Reynolds number by computing the Navier-Stokes equation before. The importance of scale resolution, aliasing problem and preservation of physical dispersion relation for such vortical flows of the used high accuracy schemes [Sengupta TK. Fundamentals of computational fluid dynamics. Hyderabad, India: University Press; 2004] is highlighted.For the dynamic problem, a novel genetic algorithm (GA) based optimization technique has been adopted, where solutions of Navier-Stokes equations are obtained using small time-horizons at every step of the optimization process, called a GA generation. Then the objective functions is evaluated that is followed by GA determined improvement of the decision variables. This procedure of time advancement can also be adopted to control such flows experimentally, as one obtains time-accurate solution of the Navier-Stokes equation subject to discrete changes of decision variables. The objective function - the time-averaged drag - is optimized using a real-coded genetic algorithm [Deb K. Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley; 2001] for the two decision variables, the maximum rotation rate and the forcing frequency of the rotary oscillation. Various approaches to optimal decision variables have been explored for the purpose of drag reduction and the collection of results are self-consistent and furthermore match well with the experimental values reported in [Tokumaru PT, Dimotakis PE. Rotary oscillation control of a cylinder wake. J Fluid Mech 1991;224:77].     

Navier-Stokes Solution by New Compact Scheme for Incompressible Flows

A new high spectral accuracy compact difference scheme is proposed here. This has been obtained by constrained optimization of error in spectral space for discretizing first derivative for problems with non-periodic boundary condition. This produces a scheme with the highest spectral accuracy among all known compact schemes, although this is formally only second-order accurate. Solution of Navier-Stokes equation for incompressible flows are reported here using this scheme to solve two fluid flow instability problems that are difficult to solve using explicit schemes. The first problem investigates the effect of wind-shear past bluff-body and the second problem involves predicting a vortex-induced instability.     

Recent Developments in the Pure Streamfunction Formulation of the Navier-Stokes System

In this paper we review fourth-order approximations of the biharmonic operator in one, two and three dimensions. In addition, we describe recent developments on second and fourth order finite difference approximations of the two dimensional Navier-Stokes equations. The schemes are compact both for the biharmonic and the Laplacian operators. For the convective term the fourth order scheme invokes also a sixth order Pade approximation for the first order derivatives, using an approximation suggested by Carpenter-Gottlieb-Abarbanel (J. Comput. Phys. 108:272–295, 1993). We also introduce the derivation of a pure streamfunction formulation for the Navier-Stokes equations in three dimensions.     

High-resolution finite difference schemes using curvilinear coordinate grids for DNS of compressible turbulent flow over wavy walls

Direct numerical simulations of compressible turbulent flow over wavy wall geometries have been carried out by solving N–S equations on general curvilinear coordinates. A 6th order WENO scheme with minimized dispersion and controllable dissipation is employed to compute the inviscid fluxes, a 4th order central difference scheme is applied to compute the viscous fluxes, and a 6th order conservative compact scheme is used for computing the geometrical metrics. An implicit LU-SGS method is used for time integration to improve computational efficiency over the explicit schemes such as the Runge–Kutta approach. The validity and applicability of the present algorithm is confirmed by comparing our results with laboratory experimental measurements and DNS results in the literature.     

A fourth-order accurate compact scheme for the solution of steady Navier-Stokes equations on non-uniform grids

This paper deals with the formulation of a higher-order compact (HOC) scheme on non-uniform grids in complex geometries to simulate two-dimensional (2D) steady incompressible viscous flows governed by the Navier-Stokes (N-S) equations. The proposed scheme which is spatially fourth-order accurate is then tested on three nonlinear problems, namely (i) a problem governed by N-S equations with a constructed analytical solution, (ii) lid-driven cavity flow problem, and (iii) constricted channel flow problem. In the process, we have also expanded the scope of fourth-order 9-point compact schemes to geometries beyond rectangular. It is seen to efficiently capture steady-state solutions of the N-S equations with Dirichlet as well as Neumann boundary conditions. In addition to this, it captures viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variations. Our results are in excellent agreement with analytical and numerical results whenever available and they clearly demonstrate the superior scale resolution of the proposed scheme.