Cheng-Feng Tai

Multigrid Computations and Conservation Law Treatment of a Sharp Interface Method

ABSTRACT The sharp interface method (SIM) utilizing the Cartesian grid and cut-cell approach can solve fluid flow problems involving multiphase and/or complex geometry with second-order accuracy. Due to the algorithm and data management requirements, the SIM is computationally intensive. In this study, two issues are investigated to help further advance the SIM. First, the conservation-law property at the interface is examined in detail; an artificially assigned interface inside a single-phase, homogeneous fluid domain is devised to examine SIMs performance. Second, an interface-averaging multigrid method, accounting for the presence of irregularly shaped moving boundaries, is developed to speed up the pressure solver. The present work has demonstrated that the SIM satisfies the conservation laws numerically and has identified ways to reduce the computing time.

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.

A Direct Numerical Simulation of the Unsteady Development of a Deformable Rising Bubble in a Quiescent Liquid

An accurate finite-volume based numerical method for the simulation of an isothermal two-phase flow, consisting of a deformable bubble rising in a quiescent, unbounded liquid, is presented. This direct simulation method is built on a sharp interface concept and developed on an Eulerian, Cartesian fixed grid with a cut-cell scheme and marker points to track the moving interface. The unsteady Navier-Stokes equations in both liquid and gas phases are solved separately. The mass continuity and momentum flux conditions are explicitly matched at the true phase boundary to determine the interface shape and movement of the bubble. The highlights of this method are that it utilizes a combined Eulerian-Lagrangian approach, and is capable of treating the interface as a sharp discontinuity. A fixed underlying grid is used to represent the control volume. The interface, however, is denoted by a separate set of marker particles which move along with the interface. A quadratic curve fitting algorithm with marker points is used to yield smooth and accurate information of the interface curvatures. This numerical scheme can handle a wide range of density and viscosity ratios. The bubble is assumed to be spherical and at rest initially, but deforms as it rises through the liquid pool due to buoyancy. Additionally, the flow is assumed to be axisymmetric and incompressible. The bubble deformation and dynamic motion are characterized by the Reynolds number, the Weber number, the density ratio and the viscosity ratio. The effects of these parameters on the translational bubble dynamics and shape are given and the physical mechanisms are explained and discussed. Results for the shape, velocity profile and various forces acting on the bubble are presented here as a function of time until the bubble reaches terminal velocity. The range of Reynolds numbers investigated is 1 < Re < 100 , and that of Weber number is 1 < We < 10 .Copyright