Computational Fluid Dynamics: Contents

The term transcritical flow denotes the existence of both subcritical and supercritical flow regimes in an open-channel system. It is similar to transonic flow in gas dynamics. Transcritical flow is encountered in many engineering problems of practical interest; irrigation networks, for example, often involve transcritical flow caused by the dynamic operation of hydraulic structures. This paper presents a two-step, predictor-corrector, implicit numerical scheme for simulating transcritical flows of practical interest. The proposed scheme is second-order accurate in time and space and requires inversion of only bidiagonal matrices. It is, therefore, computationally efficient and can readily accommodate hydraulic structures. To suppress spurious oscillations near regions of steep gradients and facilitate the resolution of hydraulic jumps, nonlinear (adaptive) second-difference artificial dissipation terms are added explicitly. The scheme is validated by calculating a series of applications of practical interest. The computed solutions are compared with previously published results and exact solutions where available. It is shown that the proposed scheme is robust and accurate, has reasonable shock-capturing capabilities, and can easily simulate hydraulic structures.

Numerical Simulation of Transcritical Flow in Open Channels

The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations is examined for initial boundary-value problems of the hyperbolic type. For the numerical experiments the one-dimensional inviscid gasdynamic equations in conservation law form are selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit vs implicit boundary schemes, and unconditionally stable schemes. HEN finite-difference schemes are used to solve initial boundary-value problems for the equations of fluid dynamics, it is well known that most methods require more boundary conditions than those required by the governing partial differential equations. These additional boundary conditions for the finite-difference equations are often called "numerical boundary conditions." The numerical boundary conditions cannot be imposed arbitrarily but are determined, in general, using interior information, for example, by extrapolation or uncentered approximations. In this paper, any numerical procedure used to provide a numerical boundary condition will be called a "boundary scheme/' Whatever schemes are used for the numerical boundary conditions, it is a common practice to assume that the boundary scheme has a local effect and will not affect the solution globally. During the early 1970s, Kreiss,1'2 Osher,3 Gustafsson et al.,4 Varah,5 and Gustafsson6 published a series of papers establishing methods for checking the stability and accuracy of difference approximations with boundary schemes included. Since then, further progress has been made in the theory of linear difference approximations for initial boundary-value problems of the hyperbolic and parabolic type.7'12 Because improper treatment of the boundary conditions can lead to instability and inaccuracy, even though we start with a stable interior scheme (i.e., scheme for the interior points), it is appropriate to adopt an approach that includes the stability and accuracy of the combined interior and boundary schemes. Surveys of recent developments and extensive bibliographies are included in papers by Coughran13 and Yee.14 The purpose of this paper is to examine the applicability to practical calculations (for nonlinear gasdynamic problems) of recent theoretical stability analyses of implicit difference approximations for initial boundary-value problems of the hyperbolic type. As numerical computations have progressed, the use of the conservative form of the gasdynamic equations has gained popularity. For physical reasons it is sometimes desirable to specify boundary conditions in the nonconservative variables and to compute with conservative variables in the interior. We will consider the additional complications introduced by this procedure.

Boundary Approximations for Implicit Schemes for One-Dimensional Inviscid Equations of Gasdynamics

Nonoscillatory solution of the steady-state inviscid Burgers' equation by mathematical programming

In this article, the authors introduce a Grid-based virtual reactor, a High Level Architecture (HLA)- supported problem-solving environment that allows for detailed numerical study of industrial thin-film production in plasma-enhanced chemical vapor deposition (PECVD) reactors. They briefly describe the physics and chemistry underpinning the deposition process, the numerical approach to simulate these processes on advanced computer architectures, and the associated software environment supporting computational experiments. The authors built an efficient problem-solving environment for scientists studying PECVD processes and end users working in the chemical industry and validated the resulting virtual reactor against real experiments.

/pdf/grid-based-simulation-of-industrial-thin-film-production-2dc40oimly.pdf

Grid-Based Simulation of Industrial Thin-Film Production

A class of implicit bidiagonal schemes is developed for the conservative Euler equations. The schemes are based on a predictor-corrector approach for the characteristic variables, adapted according to the sign of the characteristic speeds of information. They are second-order accurate in space and time and have intrinsic dissipative properties. A new fully implicit boundary treatment is developed for this class of schemes, allowing high CFL numbers in all regions of the flow domain. Results are presented for the quasi-one-dimensional flow in a nozzle. N recent years, substantial progress has been made in the development of numerical methods for solving conservative systems of hyperbolic equations such as the Euler equations describing inviscid fluid flow.M One of the main achievements has been the development of implicit methods based on tridiagonal solution procedures.2 The use of explicit-impl icit artificial viscosity5 and of implicit boundary conditions6'7 has made these algorithms very robust and efficient. Recently, an implicit method based on a bidiagonal solution technique has been introduced by MacCormack.1 The first part of this paper is concerned with further developments related to the bidiagonal solution technique. A general class of second-order accurate bidiagonal schemes is proposed, containing a class of implicit schemes and one of semiexplicit schemes. It is shown that these schemes are in- trinsically dissipative so that no artificial viscosity is necessary for linear stability. The second part of the paper introduces an implicit boundary treatment for these bidiagonal schemes that preserves the stability properties of the interior scheme. In- deed, while a number of successful boundary procedures have been proposed for explicit and tridiagonal implicit schemes, this stability remained an unsolved problem in earlier ap- plications of bidiagonal techniques.8'9 Numerical experiments for the Euler flow in a nozzle confirm the unconditional linear stability, allowing the use of very high CFL numbers.

A class of bidiagonal schemes for solving the Euler equations

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A class of bidiagonal schemes for solving the Euler equations