Search

Recent interest in unsteady separation and separated flows brings up the need of an accurate and efficient computational scheme for general unsteady three-dimensional boundary-layer flows. Resolution of the singular behavior at separation is a delicate problem. The task is further complicated by the geometrical singularity and the nonstationary stagnation point. The present paper proposes a numerical scheme to sidestep these difficulties. At the first stage of development, the simpler problem of the symmetry-plane solution of the laminar boundary-layer over an impulsively-started prolate spheroid is calculated. Results show that the present Eulerian calculation satisfactorily captures the singular behavior of the boundary layer when separation is approached. Comparison with Xu and Wang’s recent results and those for the two-dimensional elliptic cylinder calculated by the Lagrangian method are also made. Discussions of the results for unsteady separation at zero, small and large incidences are presented.

A treatment of a blade-to-blade flow of nucleating steam in a cascade of supersonic tip section blading by the time-marching method is presented. To reduce the numerical errors associated with the method, an auxilliary mesh is embedded in selected areas of the field thereby increasing the accuracy. The agreement obtained between the solutions and the available experimental results is reasonable.

Subgrid and subcell FDTD (S-FDTD) methods are described. They can be used for the fast and accurate simulation of mask electromagnetic effects in sub-45nm lithography. The accuracies of the S-FDTD methods are verified by comparison with FDTD and with a very accurate pseudospectral reference solution. The S-FDTD methods are an order of magnitude or more faster than FDTD. Furthermore, the S-FDTD methods require much less memory than FDTD for time marching. Hence, much larger mask areas can be simulated with S-FDTD than with FDTD.

Before using a high-accuracy Computational Aeroacoustics (CAA) code, it is desirable to verify that the code is actually solving the governing equations to the design order of accuracy. In this work, the External Verification Analysis (EVA) method is presented, which allows the Verification of unsteady time-accurate CFD or CAA codes without requiring modifications to the source code of the CAA code. Currently, the EVA tool Verifies only the interior equation solver and does not test boundary conditions. The EVA tool can determine the computed order of accuracy of the CAA code in time and space. Verification results are presented for the Air Force Research Laboratory FDL3DI code.

To suppress late-time oscillations in time marching algorithms of solution of time domain electric field integral equation (TD-EFIE), stabilizing techniques are analyzed. Novel backward tilted averaging schemes are proposed. Sometimes better results are got with these schemes than with other schemes. Uncertainties are discussed in application of averaging schemes.

In this paper, we have proposed a time marching intregral equation method which does not have the limitation of the time linearized integral equation method in that the latter method can not satisfactorily simulate the shock-wave motions. Firstly, a model problem—one dimensional initial and boundary value wave problem is treated to clarify the basic idea of the new method. Then the method is implemented for 2-D and 3-D unsteady transonic flow problems. The introduction of the concept of a quasi-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheet condition. The numerical calculations show that the method is reasonable and reliable.

In many realistic unsteady calculations, the computational grid spacing required to resolve the mean flow gradients is much smaller than the grid spacing required to resolve the unsteady propagating waves. Because of this, the high temporal resolution provided by existing explicit optimized time marching schemes used in computational aeroacoustics code can be excessive due to the small time step required for stability in regions of clustered grid. In this work, optimized and high-order A-stable and L-stable implicit time marching schemes were analyzed, implemented into the AFRL high-order Large Eddy Simulation code FDL3DI, and their performance compared to that of the first and second order implicit schemes currently implemented.

The purpose of this paper is to develop a robust and e‐cient high order fully conservative flnite difierence scheme for compressible Navier-Stokes equations. The 5th order WENO scheme is used for the inviscid ∞uxes. A conservative fourth order accuracy flnite central difierencing scheme is developed for the viscous terms. An improved " value of 10 i2 is suggested for the WENO smooth factors calculation, which removes the weight oscillation and signiflcantly improves the convergence rate and level. The wall surface is taken as half-point mesh so that the no slip wall boundary condition can be accurately imposed. A 3th order accurate flnite difierence scheme is given to treat wall boundary condition. The implicit time marching method with unfactored Gauss-Seidel line relaxation is used with the high order scheme to achieve steady state solutions with high convergence rate.

Este artigo apresenta a aplicação de modelo matemático-computacional de simulação e otimização para localização de fugas. O modelo proposto é fundamentado no acoplamento de um simulador hidráulico baseado no Time Marching Approach - TMA com o algoritmo otimizador de Nelder-Mead e foi aplicado em uma rede de distribuição de água da cidade de Jundiaí-SP. Nos testes realizados ficou claro o funcionamento adequado do modelo apresentado, pois a fuga simulada foi localizada, sendo observado, entretanto, a necessidade de um aprimoramento na localização dos pontos de monitoramento durante a execução da simulação. This work presents a computational model as a new tool for leak localization. The considered model was developed through the coupling of hydraulic simulator based in Time Marching Approach - TMA method with the Nelder-Mead optimization algorithm. The model was applied to a real water distribution network, in the city of Jundiaí, Brazil. In the carried through tests it was clearly the adequate functioning of the presented model, therefore the simulated escape was located, being observed, however, the necessity of an improvement in the localization of the monitor points, during the execution of the simulation.

Specific tools devoted to the study of the source mechanisms related to the dynamic of free shear flows are developed. Our analysis methodology is based on a decomposition of the Lighthill source term into ten sub-terms, in which the velocity, vorticity, dilatation and density fields appear explicitly. This decomposition is applied to the source term involved in a 2D spatially evolving mixing-layer, computed by DNS. The compressible Navier-Stokes equations are solved in a computational domain which includes both aerodynamic and acoustic fields. The numerical code is based on sixth-order accurate compact finite difference schemes and a fourth-order Runge-Kutta time marching, while the characteristic analysis is used to specify non-reflecting boundary conditions. Acoustic results show that only five of the ten sub-terms of the decomposition contribute to the sound field.

This paper focuses on the time integration of the nonlinear EOM associated with a very ∞exible aircraft in ∞ight. Various integration methods exist for linear structural dynamics problems. However, a review of the literature indicates little material associated with the integration of nonlinear structural EOM of relatively large order. Moreover, for the problem of simulation of very ∞exible aircraft, a combination of ∞ight dynamics and aeroelastic degrees of freedom must be solved. A modifled flrst and second order Generalizedfi Method along with an implicit sub-iteration scheme were developed. It has shown good agreement with predictor/corrector integration schemes for a reduced set of linear EOM. The method is also seen to be numerically stable when compared to non-dissipative time marching integration schemes and requires less computational time compared to predictor/corrector methods for the full set of nonlinear EOM.

Semi-Lagrangian techniques are proposed for animating water waves in realistic events. The two-dimensional shallow water equations are considered to model the motion of water flow and a second order time marching procedure which combines the characteristic method with a finite differencing discretization is used to integrate the model. Numerical results are carried out on a squared pool without and with obstacles. The obtained results show that our algorithm is robust, stable and highly accurate.

Two different sets of time scales arising in stiff systems of reaction-diffusion PDEs are examined; the first due to the reaction term alone and the second due to the interaction of the reaction and diffusion terms. The fastest time scales of each set are responsible for the development of a low dimensional manifold, the characteristics of which depend on the set of time scales considered. The advantages and disadvantages of employing these two manifolds for the simplification of large and stiff systems of reaction-diffusion PDEs are discussed. It is shown that the two approaches provide a non-stiff simplified system of similar accuracy. The approach based on the reaction time scales allows for a simpler construction of the simplified system, while that based on the reaction/diffusion time scales allows for a simpler time marching scheme.

Validation of CRUNCH CFD ® for problems of relevance to modeling coupled VSTOL-Ship Airwake flow fields is presented. The basic numerical framework consists of an edge based multi-element unstructured Navier-Stokes solver. The governing equations are solved using an upwind biased MUSCL scheme and an implicit scheme is used for time marching. Validation of the spatial and temporal aspects of the numerical framework are presented here, with a special emphasis on bluff body shedding problems as these are of particular relevance to the VSTOL-Ship airwake problem. Results from simulations of several unit problems are presented along with preliminary results from airwake flow field modeling.

Validation of CRUNCH CFD® for problems of relevance to modeling coupled VSTOL-Ship Airwake flow fields is presented. The basic numerical framework consists of an edge based multi-element unstructured Navier-Stokes solver. The governing equations are solved using an upwind biased MUSCL scheme and an implicit scheme is used for time marching. Validation of the spatial and temporal aspects of the numerical framework are presented here, with a special emphasis on bluff body shedding problems as these are of particular relevance to the VSTOL-Ship airwake problem. Results from simulations of several unit problems are presented.Copyright © 2004 by ASME

This paper describes a distributed-memory parallel implementation of a time-domain integral-equation (TDIE) based scheme for analyzing a broad class of EMC/EMI problems. The specific TDIE scheme used is the multilevel plane-wave time-domain (PWTD) accelerated marching-on-in-time (MOT) solver previously used by our group only on serial computing platforms. The proposed parallel MOT-PWTD solver is applied to sample EMC/EMI problems and the efficiency of the algorithm is investigated via speedup analysis.

In this paper we consider the impact of using “time marching” numerical schemes for computing asymptotic solutions of nonlinear differential equations. We show that stable and consistent approximating schemes can produce numerical solutions that do not correspond to the correct asymptotic solutions of the differential equation. In addition, we show that this problem cannot be avoided by placing additional side conditions on the boundary value problem, even if the numerical scheme preserves the side conditions at every step. Examples are given to illustrate the problems that can arise and the implications of using such methods in control design are discussed.

We propose a filtering scheme for stabilizing time-marching solutions of the electric field integral equation. We show, with practical examples, that it is better than other stabilizing schemes. We also show how the stabilized algorithm can be made almost as time-efficient as the original time-marching algorithm.

A 2D fully nonlinear NWT is developed based on the potential theory, mixed Eulerian-Lagrangian (MEL) time marching scheme, and boundary element method (BEM) . Wave profiles and wave kinematics of highly nonlinear waves are calculated using the NWT and the results are compared with linear, Stokes second-order theory and experimental values. It is confirmed that the spatial variation of intermediate-depth waves along the direction of wave propagation is caused by the unintended generation of second-order free waves, which was originally investigated both experimentally and theoretically (3` d order pe turbation theory) by Goda. The various phenomena observed by Goda are clearly reproduced by the present fully nonlinear NWT . It is shown that the wave kinematics above mean water level can be significantly different from the perturbation-based prediction. It is also found that small mean positive or negative flows can be generated below mean water level depending on the water depth and wave condition .

In this chapter, we discuss considerations involved in selecting a time-marching method for a specific application. Examples are given showing how time-marching methods can be compared in a given context. An important concept underlying much of this discussion is stiffness, which is defined in the next section.

Numerical methods for time stepping the Cahn-Hilliard equation are given and discussed. The methods are unconditionally gradient stable, and are uniquely solvable for all time steps. The schemes require the solution of ill-conditioned linear equations, and numerical methods to accurately solve these equations are also discussed.

A better understanding of the flow inside the multi-stage turbomachines will be very useful to both the designer and operator. The numerical calculation for single blade row has been well established with the time marching computation of the Navier-Stokes equations. But there will exist much more difficulties for the multi-blade rows due to the rotor-stator interaction. The major problems are related to the unsteady flow which will inevitably exist in the blade passages due to the different rotating speed and possible the different in blade number. A method is presented for simulating various turbine blade rows in single-stage environment. A solver has been developed for studying the complex flow analysis of ‘proposed high pressure turbine’ (HPT) using quasi-3-D Reynolds-averaged Navier-Stokes (Q3D RNS) equations. The code achieves good quality solutions quickly even with relatively coarse mesh sizes. The work is first validated both with UTRC's and Zeschky and Gallus' subsonic turbine test cases covering inlet boundary conditions and Reynolds-averaged values. A H-type grid is adopted as it is easy to generate and can readily extend to 3D application. When rows are closely spaced, there can be a strong interaction which will impact the aerodynamic, thermal and structural performance of the blade.

An efficient multigrid driven scheme, originally developed for the solution of Reynolds Averaged Navier-Stokes equations is modified and tested for large eddy simulation. The formulation is initially based on a Smagorinsky model, but it is general enough to allow for more advanced SGS models. The fully implicit time marching method is implemented on parallel computers using message-passing. This study concentrates on two aspects: Verification and validation against results of Direct Numerical Simulation and evaluation of efficiency of our approach. This is a first step towards performing large eddy simulations at high Reynolds number and on realistic geometry.