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Numerical Simulation of Free Surface by an Area-Preserving Level Set Method

Communications in Computational Physics 2012年第4期11卷 1347-1371页

作者： tony w.h.sheu C.h.Yu Department of Engineering Science and Ocean Engineering National Taiwan UniversityNo.1Sec.4Roosevelt RoadTaipeiTaiwan Taida Institute of Mathematical Sciences(TIMS) National Taiwan University Center for Quantum Science and Engineering(CQSE) National Taiwan University

we apply in this study an area preserving level set method to simulate gas/water interface *** the sake of accuracy,the spatial derivative terms in the equations of motion for an incompressible fluid flow are approximated by the fifthorder accurate upwinding combined compact difference(UCCD)*** scheme development employs two coupled equations to calculate the first-and second-order derivative terms in the momentum *** accurately predicting the level set value,the interface tracking scheme is also developed to minimize phase error of the first-order derivative term shown in the pure advection *** the purpose of retaining the long-term accurate hamiltonian in the advection equation for the level set function,the time derivative term is discretized by the sixth-order accurate symplectic Runge-Kutta ***,to keep as a distance function for ensuring the front having a finite thickness for all time,the re-initialization equation is *** the verification of the optimized UCCD scheme for the pure advection equation,two benchmark problems have been chosen to investigate in this *** level set method with excellent area conservation property proposed for capturing the interface in incompressible fluid flows is also verified by solving the dam-break,Rayleigh-Taylor instability,two-bubble rising in water,and droplet falling problems.

关键词： Level set method phase error upwinding combined compact scheme hamiltonian symplectic Runge-Kutta area conservation property

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Development of an Explicit Symplectic Scheme that Optimizes the Dispersion-Relation Equation of the Maxwell’s Equations

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Communications in Computational Physics 2013年第4期13卷 1107-1133页

作者： tony w.h.sheu L.Y.Liang J.h.Li Department of Engineering Science and Ocean Engineering National TaiwanUniversityNo.1Sec.4Roosevelt RoadTaipeiTaiwan Taida Institute of Mathematical Science(TIMS) National Taiwan UniversityTaiwan Center for Quantum Science and Engineering(CQSE) National Taiwan UniversityTaiwan

In this paper an explicit finite-difference time-domain scheme for solving the Maxwell’s equations in non-staggered grids is *** proposed scheme for solving the Faraday’s and Amp`ere’s equations in a theoretical manner is aimed to preserve discrete zero-divergence for the electric and magnetic *** inherent local conservation laws in Maxwell’s equations are also preserved discretely all the time using the explicit second-order accurate symplectic partitioned Runge-Kutta *** remaining spatial derivative terms in the semi-discretized Faraday’s and Amp`ere’s equations are then discretized to provide an accurate mathematical dispersion relation equation that governs the numerical angular frequency and the wavenumbers in two space *** achieve the goal of getting the best dispersive characteristics,we propose a fourth-order accurate space centered scheme which minimizes the difference between the exact and numerical dispersion relation *** the computational exercises,the proposed dual-preserving solver is computationally demonstrated to be efficient for use to predict the long-term accurate Maxwell’s solutions.

关键词： Maxwell’s equations non-staggered grids zero-divergence fourth-order dualpreserving solver dispersion relation equations

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Positivity-preserving finite element solutions for turbulent quantities k and ε

Positivity-preserving finite element solutions for turbulent...

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第四届海峡两岸计算流体力学学术研讨会

作者： tony w. h. sheu and S. K. wANG Department of Engineering Science and Ocean Engineering, National Taiwan University. 73 Chou-Shan Road, Taipei, Taiwan

＜正＞ In this paper, we apply a monotone convection-diffusion-reaction finite element model to simulate multi-dimensional constitutive equations for k （turbulent kinetic energy） and e （turbulent dissipation rate）. To obtain physically correct positive values of these turbulent field variables, working equations for k and e are solved in their logarithmic forms. The paper presents a rigorous validation of the proposed upwind finite element model by solving scalar problems which are amenable to analytic solutions. The model is then applied to simulate turbulent flows in a driven cavity and in a backward-facing step channel.

关键词： Generalized characteristic coordinate system Riemann problem Expansion fan.

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