Mikael A. Langthjem¹, Masami Nakano²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 227-241, 2013, DOI:10.3970/cmes.2013.096.227

Abstract This paper is concerned with a mathematical model of a simple axisymmetric silencer-like model, consisting of a hole-tone feedback system equipped with a tailpipe. The unstable shear layer is modeled via a discrete vortex method, based on axisymmetric vortex rings. The aeroacoustic model is based on the Powell- Howe theory of vortex sound. Boundary integrals are discretized via the boundary element method; but the tailpipe is represented by the exact (one-dimensional) solution. It is demonstrated though numerical examples that this numerical model can display lock-in of the self-sustained flow oscillations to the resonant acoustic oscillations. More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 157-176, 2006, DOI:10.3970/cmes.2006.016.157

Abstract To characterize largely deformed spin-free reference configuration of materials, we have to construct an orthogonal transformation tensor Q relative to the fixed frame, such that the tensorial equation Q^˙ = WQ holds for a given spin history W. This paper addresses some interesting issues about this equation. The Euler's angles representation, and the (modified) Rodrigues parameters representation of the rotation group SO(3) unavoidably suffer certain singularity, and at the same time the governing equations are nonlinear three-dimensional ODEs. A decomposition Q = FQ₁ is first derived here, which is amenable to a simpler treatment of Q₁ than Q, and… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 157-176, 2007, DOI:10.3970/cmes.2007.020.157

Abstract In many engineering applications the Lie group calculation is very important. With this in mind, the subject of this paper is for an in-depth investigation of time-varying linear systems, and its accompanied Lie group calculations. In terms of system matrix A in Eq. (11) and a one-order lower fundamental solution matrix associated with the sub-state matrix function A_s^s, we propose two methods to nilpotentlize the time-varying linear systems. As a consequence, we obtain two different calculations of the general linear group. Then, the nilpotent systems are further transformed to a unique new system Ż(t) = B(t)Z(t), which having a… More >