Mihaela Popescu

ASSESSMENT OF DISPERSION-RELATION-PRESERVING AND SPACE-TIME CE/SE SCHEMES FOR WAVE EQUATIONS

Two interesting numerical methods for treating convective transport are investigated: the dispersion-relation-preservation (DRP) scheme, proposed by Tam and Webb, and the unified space-time a- k method, developed by Chang. The space-time a- k method directly controls the level of dispersion and dissipation via a free parameter, k , while the DRP scheme minimizes the error by matching the characteristics of the wave. Insight into the dispersive and dissipative aspects in each scheme is gained from analyzing the truncation error. Even though both methods are explicit in time, the appropriate ranges of the CFL number, w , are different between them. For the DRP scheme, it is preferable if w is close to 0.2 for short waves, and close to 0.1 for intermediate and long waves. With w less than but close to 1, matching between w and k can substantially affect the accuracy of the space-time method. For both methods, different performance characteristics are observed between long and short waves. It seems that for long waves, errors grow more slowly with the space-time a- k scheme, while for short waves, errors accumulate more slowly with the DRP scheme.

Modelling of aero-acoustic wave propagation in low Mach number corrugated pipe flow

This paper sets out to investigate parameters that determine flow-induced vibrations in flexible, corrugated pipes. A central element in this paper is a mathematical model that describes the phenomenon. The presented model is designed to capture the aero-acoustic wave behaviour of gas that flows in a corrugated pipe, exploring the feedback analysis. This model involves the coupling between the large-scale acoustic behaviour in a pipe and a line of self-excited oscillators representing vortex excitation caused by flow over corrugations.

A finite volume-based high order Cartesian cut-cell method for computational aeroacoustics

A finite volume-based high-order scheme with optimized dispersion and dissipation characteristics in cooperation with the Cartesian cut-cell technique is presented for aero- acoustics computations involving geometric complexities and nonlinearities. The field equation is solved based on an optimized prefactored compact finite volume (OPC-fv) scheme. The cut-cell approach handles the boundary shape by sub-dividing the computational cells in accordance with the local geometric characteristics and facilitates the use of numerical procedures with a desirable level of accuracy. The resulting technique is assessed by several test problems that demonstrate satisfactory performance.

Cartesian Cut-Cell Method with Local Grid Refinement for Wave Computations

Sound generation from a vibrating circular piston is a classical acoustic problem. The goal of this paper is to simulate numerically the sound radiation produced by oscillating baffled pistons, using both linear and nonlinear model, and to consider the interplay between wave propagation and geometric complexities. The linear solution, based on the linear Euler equations, will be compared to the Rayleigh integral approximation. The nonlinear solution, based on the Navier-Stokes equations, will be compared against linear model for low speed (less than 0.01 of sound speed). A main practical interest in this problem is to capture the behavior of the waves resulting from the source pistons with other solid objects or waves. The waves properties in terms of frequency, amplitude and wavenumber are influenced by the initial frequencies and coordinates of the pistons, and the geometry. The wave equations in Cartesian coordinate with cut-cell and local grid refinement technique are employed along with the Optimized Prefactored Compact finite volume (OPC-fv) scheme for spatial discretization, the Low-Dispersion Low-Dissipation Runge-Kutta (LDDRK) scheme for time discretization. Problems for the waves around different geometries, and with varied frequencies and amplitudes are considered and presented.

The significance of lift forces in intensely stirred bubble plumes

A preceding study concluded that the lift force in dense bubble plumes in mixing vessels had no influence on the flow. Since the lift force is generally assumed to be of importance, a new study has been conducted in order to shed more light on the issue. It is found that the lift force seems to be insignificant, but there is some uncertainty in the conclusion.

Modelling of Fluid Dynamics Interacting With Ductile Fraction Propagation in High Pressure Pipeline

This paper presents a computational model for describing the behavior of the fluid dynamics in a fractured ductile pipe under high pressure. The pressure profile in front of the crack tip, which is the main source of the crack driving source, is computed by using nonlinear wave equation. The solution is coupled with one dimensional gas flow analysis behind the crack, choked flow. The simulation utilizes a high order optimized prefactored compact–finite volume method for space discretization, and low dispersion and dissipation Runge-Kutta for time discretization. As the pipe fractures the rapid depressurization take place inside the pipe and the propagation of the crack induce waves which strongly influence the nature of the outflow dynamics. Consistent with the experimental observation, the model predicts the expansion wave inside the pipe, and the reflection and outflow of the wave. The model also helps characterize the propagation of the crack dynamics and fluid flows around the tip of the crack.© 2008 ASME

A study of dispersion-relation-preserving and optimized prefactored compact schemes for wave equations

In the present study, the Dispersion-RelationPreserving (DRP) scheme by Tam and coworkers, and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang, are assessed. The original schemes are developed in the finite difference framework; in the present effort, their corresponding finite volume versions are developed. Both DRP and OPC schemes, based on either finite difference or finite volume approach, attempt to optimize the coefficients for high resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. Highlighting the principal characteristics of the schemes and utilizing simple linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes again perform comparably, and offer substantially better solutions in regions of high gradient or discontinuity.