Author

# Philip La-Fan Liu

Bio: Philip La-Fan Liu is an academic researcher from Cornell University. The author has contributed to research in topics: Breaking wave & Darcy's law. The author has an hindex of 4, co-authored 5 publications receiving 84 citations.

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TL;DR: Several types of singularities which threaten the integrity of numerical solutions occur in potential flow problems as mentioned in this paper, such as the singularity at the tip of a cutoff wall, which cannot be mistreated without unsatisfactory results.

Abstract: Several types of singularities which threaten the integrity of numerical solutions occur in potential flow problems The singularity at the tip of a cutoff wall is strong and cannot be mistreated without unsatisfactory results Special elements can be used to represent the analytical behavior of the potential and its derivatives For the flow around a corner of less severity than the sheet pile the use of special elements becomes less important The intersection between zones of an inhomogeneous aquifer represents a singularity which is similar to the cutoff wall The interzonal singularity is weak for nonextreme differences in permeabilities and in such a case it can be ignored without a significant effect on the total solution if the numerical discretization is sufficiently fine The presence of wells in a potential flow field produces a logarithmic singularity which can be modeled by using superposition of the analytic solution for a source in the neighborhood of the well

39 citations

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TL;DR: In this article, the Boundary Integral Equation Method (BIEM) is applied to transient water wave problems and the stability limits and frequency distortion of the numerical method are examined and given.

Abstract: The Boundary Integral Equation Method (BIEM) is applied to transient water wave problems. Only two-dimensional linearized waves are considered. As is general practice, free-surface boundary conditions are applied at the equilibrium surface rather than the actual free surface; thus the problems become fixed-boundary problems rather the free-surface problems. For the cases in which fluid domain is unbounded in the horizontal direction, a radition condition is formulated such that waves pass through the computational boundaries without reflection. The stability limits and frequency distortion of the numerical method are examined and given. Numerical results are compared with analytical solutions or experimental data in three examples. Excellent agreement is observed.

22 citations

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TL;DR: The boundary integral equation method (BIEM) was used to solve free surface ground-water problems as mentioned in this paper, and two methods were presented which treated infinite domains efficiently using the BIEM, illustrated by a two-dimensional recharge problem and by the flow through a dike on a pervious foundation.

Abstract: The boundary integral equation method (BIEM) is used to solve free surface ground-water problems. The formulation includes those problems in which the domain of the solution is infinite. Two methods are presented which treat infinite domains efficiently using the BIEM. These methods are illustrated by a two-dimensional recharge problem and by the flow through a dike on a pervious foundation. The BIEM solutions are compared to experimental data. Excellent agreement is observed.

18 citations

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TL;DR: In this paper, a finite element model is developed to compute the nearshore currents induced by breaking waves in the surf zone, and the normal incident wave system is employed so as to study the effects of beach topography on the current circulation patterns.

Abstract: A finite element model is developed to compute the nearshore currents induced by breaking waves in the surf zone. The normal incident wave system is employed so as to study the effects of beach topography on the current circulation patterns. The beach topography considered here is of linear plane beach shape with minor undulations in the longshore direction. Ignoring the lateral turbulent diffusion, the finite element representation of the governing equations of mean currents is obtained by the method of weighted residuals. It is shown that, due to the flexible grid discretization, this model can be used to study problems containing more complex beach topography within a large area of interest. Two types of alongshore beach undulations are investigated: rhythmic topography and localized irregular topography. The locations of rip currents depend on the surf zone width and the on-offshore variation of beach profile.

7 citations

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TL;DR: Several types of singularities which threaten the integrity of numerical solutions occur in potential flow problems, e.g., the singularity at the tip of a cutoff wall is strong and cannot be mistreated without unsatisfactory results.

Abstract: Several types of singularities which threaten the integrity of numerical solutions occur in potential flow problems. The singularity at the tip of a cutoff wall is strong and cannot be mistreated without unsatisfactory results. Special elements can be used to represent the analytical behavior of the potential and its derivatives. For the flow around a corner of less severity than the sheet pile the use of special elements becomes less important. The intersection between zones of an inhomogeneous aquifer represents a singularity which is similar to the cutoff wall. The interzonal singularity is weak for nonextreme differences in permeabilities and in such a case it can be ignored without a significant effect on the total solution if the numerical discretization is sufficiently fine. The presence of wells in a potential flow field produces a logarithmic singularity which can be modeled by using superposition of the analytic solution for a source in the neighborhood of the well.

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TL;DR: An overview of the rip current kinematics based on these observations and the scientific advances obtained from these efforts are synthesized in this article, where rip current flows are partitioned into mean, infragravity, very low frequency (vorticity), and tidal contributions, and it is found that each contributes significantly to the total.

Abstract: Rip currents are shore-normal, narrow, seaward-flowing currents that originate within surf zone, extend seaward of the breaking region (rip head), and can obtain relatively high velocities. Within the last decade, there have been a significant number of laboratory and field observations within rip current systems. An overview of rip current kinematics based on these observations and the scientific advances obtained from these efforts are synthesized. Rip current flows are partitioned into mean, infragravity, very low frequency (vorticity), and tidal contributions, and it is found that each contributes significantly to the total. Data from the laboratory and the field suggest that the rip current strength increases with increasing wave energy and decreasing water depths. The maximum mean current occurs inside the surf zone, where the maximum forcing is present owing to the dissipation of waves.

292 citations

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TL;DR: The mild-slope equation is a vertically integrated refraction-diffraction equation, used to predict wave propagation in a region with uneven bottom slopes as mentioned in this paper, which is based on the assumption of a mild bottom slope.

Abstract: The mild-slope equation is a vertically integrated refraction-diffraction equation, used to predict wave propagation in a region with uneven bottom. As its name indicates, it is based on the assumption of a mild bottom slope. The purpose of this paper is to examine the accuracy of this equation as a function of the bottom slope. To this end a number of numerical experiments is carried out comparing solutions of the three-dimensional wave equation with solutions of the mild-slope equation. For waves propagating parallel to the depth contours it turns out that the mild-slope equation produces accurate results even if the bottom slope is of order 1. For waves propagating normal to the depth contours the mild-slope equation is less accurate. The equation can be used for a bottom inclination up to 1:3.

198 citations

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TL;DR: In this article, the source of nonlinear gravity waves in a boundary integral method is reported, and it is demonstrated that virtually any type of two-dimensional wave field can be generated.

Abstract: The source generation of nonlinear gravity waves in a boundary integral method is reported. Through a number of computational results it is demonstrated that virtually any type of two-dimensional wave field can be generated. It is furthermore shown that scattered waves can pass through the line of generation without significant reflection and that the process of generation is not affected by the scattered waves.

137 citations

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TL;DR: In this article, boundary integral equation (BIEM) was applied to the tilting of a vertical interface in a Hele-Shaw cell, where nonlinear effects were demonstrated during the initial stage of the interfacial movement.

Abstract: The boundary integral equation method is formulated for and applied to problems concerning a moving interface between two fluids in porous media. The mixing between two fluids is assumed to be insignificant; a sharp interface exists between them. Numerical and experimental results are presented for the tilting of a vertical interface in a Hele-Shaw cell. During the initial stage of the interfacial movement, nonlinear effects are clearly demonstrated. The BIEM results are also compared to experimental results for a transient salt water intrusion problem.

75 citations

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TL;DR: The boundary integral equation method (BIEM) is used for the solution of unsteady flow in confined aquifers as mentioned in this paper, where flows are described by a diffusion equation.

Abstract: The boundary integral equation method )BIEM( is used for the solution of unsteady flow in confined aquifers Such flows are described by a diffusion equation Two approaches are presented The first method removes the time derivatives with a Laplace transform first and solves an associated equation with the BIEM for several values of the transform parameter A numerical transform inversion is then used to express the results in physical terms The second method solves the differential equation directly with the BIEM Both of these techniques are compared to the exact solutions of two simple problems The Laplace transform method is found to be superior for general use, although the direct method is simpler and requires less judgment on the part of the analyst

74 citations