Keh-Ming Shyue

• Ph. D.
• Professor (Full) at National Taiwan University

The interaction of a solitary wave and a slowly varying mean background or flow for the Serre-Green-Naghdi (SGN) equations is studied using Whitham modulation theory. The exact form of the three SGN-Whitham modulation equations -- two for the mean horizontal velocity and depth decoupled from one for the solitary wave amplitude field -- are obtained...

A complete study of the modulation equations for the Benjamin–Bona–Mahony equation is performed. In particular, the boundary between the hyperbolic and elliptic regions of the modulation equations is found. When the wave amplitude is small, this boundary is approximately defined by , where k is the wave number. This particular value corresponds to...

It is well known that the Benjamin–Bona–Mahony (BBM) equation can be seen as the Euler–Lagrange equation for a Lagrangian expressed in terms of the solution potential. We approximate the Lagrangian by a two-parameter family of Lagrangians depending on three potentials. The corresponding Euler–Lagrange equations can be then written as a hyperbolic s...

We show that the Benjamin–Bona–Mahony (BBM) equation admits stable travelling wave solutions representing a sharp transition from a constant state to a periodic wave train. The constant state is determined by the parameters of the periodic wave train: the wave length, amplitude and phase velocity, and satisfies both the generalized Rankine–Hugoniot...

The Serre–Green–Naghdi (SGN) system is one of the most useful dispersive models for the description of long water waves having good mathematical and physical properties. First, the model is a mathematically justified approximation of the exact water-wave problem. Second, the SGN equations are the Euler–Lagrange equations derived from Hamilton’s pri...

We show that, contrary to popular belief, lower order dispersive regularization of hyperbolic systems does not exclude the development of the localized shock-like transition fronts. To guide the numerical search of such solutions, we generalize Rankine–Hugoniot relations to cover the case of higher order dispersive discontinuities and study their p...

Serre-Green-Naghdi equations (SGN equations) is the most simple dispersive model of long water waves having "good" mathematical and physical properties. First, the model is a mathematically justified approximation of the exact water wave problem. Second, the SGN equations are the Euler-Lagrange equations coming from Hamilton's principle of stationa...

We are interested in multiphase flows involving the liquid and vapor phases of one species and a third inert gaseous phase. We describe these flows by a hyperbolic single-velocity multiphase flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff...

We are interested in three-phase flows involving the liquid and vapor phases of one species and a third inert gaseous phase. We describe these flows by a single-velocity multiphase flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff mechanical...

We are interested in three-phase flows involving the liquid and vapor phases of one species and a third inert gaseous phase. We describe these flows by a single-velocity multiphase flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff mechanic...

We present in this work a new reconstruction scheme, so-called MUSCL-THINC-BVD scheme, to solve the five-equation model for interfacial two phase flows. This scheme employs the traditional shock capturing MUSCL (Monotone Upstream-centered Schemes for Conservation Law) scheme as well as the interface sharpening THINC (Tangent of Hyperbola for INterf...

We present in this work a new reconstruction scheme, so-called MUSCL-THINC-BVD scheme, to solve the five-equation model for interfacial two phase flows. This scheme employs the traditional shock capturing MUSCL (Monotone Upstream-centered Schemes for Conservation Law) scheme as well as the interface sharpening THINC (Tangent of Hyperbola for INterf...

We describe two-phase compressible flows by a hyperbolic six-equation single-velocity two-phase flow model with stiff mechanical relaxation. In particular, we are interested in the simulation of liquid-gas mixtures such as cavitating flows. The model equations are numerically approximated via a fractional step algorithm, which alternates between th...

We describe a novel Eulerian interface-sharpening approach for the efficient numerical resolution of contact discontinuities arising from inviscid compressible flow in more than one space dimension. The algorithm uses the single-phase compressible Euler equations as the model system, and introduces auxiliary differential terms to the model so as to...

We describe a novel interface-sharpening approach for efficient numerical resolution of a compressible homogeneous two-phase flow governed by a quasi-conservative five-equation model of Allaire et al. (2001) [1]. The algorithm uses a semi-discrete wave propagation method to find approximate solution of this model numerically. In the algorithm, in r...

We model liquid–gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry (Saurel et al., 2009) [9]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative...

We describe a simple relaxation scheme for the efficient numerical resolution of compressible two-phase barotropic flow with and without cavitation on moving meshes. The algorithm uses a curvilinear-coordinate formulation of the relaxation model proposed by Saurel et al. (J. Comput. Phys. 228 (2009) 1678–1712) as the basis, and employs a wave-propa...

We describe a simple mapped-grid approach for the efficient numerical simulation of compressible multiphase flow in general multi-dimensional geometries. The algorithm uses a curvilinear coordinate formulation of the equations that is derived for the Euler equations with the stiffened gas equation of state to ensure the correct fluid mixing when ap...

We present a front tracking approach for the numerical simulation of one-dimensional elastic-plastic flow in solids with cavitation. The algorithm uses a simplified model system where the behavior of the materials is modeled by a barotropic equation of state for the hydrostatic pressure, the Hooke's law for the deviatoric stress, and the von Mises...

The objective of this paper is to give a preliminary assessment of several existing approaches (compressible or incompressible, preconditioned or not preconditioned) to the numerical simulation of low Mach compressible two-phase flow problems in more than one space dimension. We consider a broken dam problem of J. C. Martin and W. J. Moyce [An expe...

Computational fluid dynamics uses large scale numerical computation to solve problems of fluid flow. It turns out that the numerical solution for a given flow depends on the coordinates (grid) used to compute the flow. The commonly used Eulerian and Lagrangian coordinate systems both have advantages and drawbacks. In this paper, we first discuss th...

This chapter is concerned with the development of a Cartesian-grid approach for the numerical simulation of general (single or multicomponent) compressible flow problems with complex moving geometries. As a preliminary, in this work, we are interested in a class of moving objects that undergo solely rigid-body motion with the propagation speeds det...

The aim of this paper is to describe a simple Eulerian interface-capturing approach for the efficient numerical resolution of a hybrid barotropic and non-barotropic two-fluid flow problem in more than one space dimension. We use the compressible Euler equations as a model system with the thermodynamic property of each of the barotropic and non-baro...

We present a simple volume-of-fluid approach to interface tracking for inviscid compressible multicomponent flow problems in two space dimensions. The algorithm uses a uniform Cartesian grid with some grid cells subdivided by tracked interfaces, approximately aligned with the material interfaces in the flow field. A standard volume-moving procedure...

Our goal is to present a simple interface-capturing approach for barotropic two-fluid flow problems in more than one space dimension. We use the compressible Euler equations in isentropic form as a model system with the thermodynamic property of each fluid component characterized by the Tait equation of state. The algorithm uses a non-isentropic fo...

We present a fully conservative, high resolution approach to front tracking for nonlinear systems of conservation laws in two space dimensions. An underlying uniform Cartesian grid is used, with some cells cut by the front into two subcells. The front is moved by solving a Riemann problem normal to each segment of the front and using the motion of...

Our goal is to present a simple volume-of-fluid type interface-tracking algorithm to compressible two-phase flow in two space dimensions. The algorithm uses a uniform underlying Cartesian grid with some cells cut by the tracked interfaces into two subcells. A volume-moving procedure that consists of two basic steps: (1) the update of volume fractio...

A simple interface-capturing approach proposed previously by the author for efficient numerical resolution of multicomponent problems with a van der Waals fluid [J. Comput. Phys., 156 (1999), pp. 43–88] is extended to a more general case with real materials characterized by a Mie–Grüneisen equation of state. As before, the flow regime of interests...

We have developed a novel computer code designed to follow the evolution of cosmic-ray modified shocks, including the full momentum dependence of the particles for a realistic diffusion coefficient model. In this form the problem is technically very difficult, because one needs to cover a wide range of diffusive scales, beginning with those slightl...

In previous work by the author, a simple interface-capturing approach has been developed and validated for compressible multicomponent flows with a stiffened gas equation of state in multiple space dimensions. The algorithm uses a mixture type of the model equations written in a quasi-conservative form to ensure a consistent approximation of the en...

We present a simple approach to the computation of a simpliied two-phase ow model involving gases and liquids separated by interfaces in multiple space dimensions. In contrast to the many popular techniques which are mainly concerned with the incompressible ow, we consider a compress-ible version of the model equations without the eeect of surface...

A simple shock-capturing approach to multicomponent flow problems is developed for the compressible Euler equations with a stiffened gas equation of state in multiple space dimensions. The algorithm uses a quasi-conservative formulation of the equations that is derived to ensure the correct fluid mixing when approximating the equations numerically...

We describe a three-dimensional front tracking algorithm, discuss its numerical implementation, and present studies to validate the correctness of this approach. Based on the results of the two-dimensional computations, we expect three-dimensional front tracking to significantly improve computational efficiencies for problems dominated by discontin...

A simple approach to shock tracking is presented in conjunction with conservative high resolution shock-capturing methods in one space dimension. An underlying uniform grid is used with additional grid interfaces introduced at appropriate points for tracked shocks. Conservative high resolution methods based on the large time step wave propagation a...

Thesis (Ph. D.)--University of Washington, 1993. Vita. Includes bibliographical references (leaves [160]-170).

This talk consists of two parts. In the first part, we describe a simple Eulerian interface- capturing approach for the efficient numerical resolution ofa hybrid barotropic and non-barotropic two-fluid flow problem in more than one space dimension. We use the compressible Euler equations as a model system with the thermodynamic property of each of...