A spectral method for the numerical solution of hyperbolic partial differential equations is pres... more A spectral method for the numerical solution of hyperbolic partial differential equations is presented. Any discontinuous solutions which may occur are assumed to be the sum of a step function and a smooth function. A series approximation is then applied to the smooth function in order to eliminate the Gibbs phenomenon. By adding the step function onto the series we
ABSTRACT A two-fluid free surface flow model, that can simulate wave interactions with stationary... more ABSTRACT A two-fluid free surface flow model, that can simulate wave interactions with stationary or moving bodies, has been developed. The incompressible Navier–Stokes (NS) equations are solved using a finite difference solver with an efficient particle level set method to track the interface between water and air. A semi-Lagrangian approach and the fast marching method have been applied to solve the level set equation and, with the aid of the locally deployed particles, to reinitialize the level set function. To represent solid stationary and moving boundaries in the flow field effectively, a partial cell treatment combined with a local relative stationary method has been implemented. A new simple level set boundary condition for both fixed and moving bodies is proposed. The free surface flow model has been validated for a number of 2D and 3D benchmark test cases for applications to complex flow situations involving the violent motions of water, air and their interfaces, as well as their interaction with fixed or moving bodies. Detailed comparisons between the numerical results and available analytical solutions or experimental data show that the model is generic, accurate and holds promise for the numerical simulation of such flow problems.
... and Mathematics, Manchester Metropolitan University, Chester Street, Manchester, M1 5GD, UK E... more ... and Mathematics, Manchester Metropolitan University, Chester Street, Manchester, M1 5GD, UK E-mail: [email protected] ... Hydrodynamics (SPH), a Cartesian Cut Cell method based on an artifi-cial compressibility method with shock capturing for the interface (AMAZON), and ...
The piston-type wave maker is a very popular and important piece of equipment in coastal and ocea... more The piston-type wave maker is a very popular and important piece of equipment in coastal and ocean engineering physical wave model experiments. In this paper we use a numerical model to simulate the ability of the piston-type wave maker to generate a specified wave, which only can be done by theoretical analysis before under ideal conditions. Numerical models are very useful to assist with the design of wave makers, and they are able to simulate the complex status of a wave maker in a flume. Based on solving the Navier-Stokes equations, the numerical model in this paper uses a two-fluid water and air system, in which the interface between the water and air is tracked by a particle level set method and the partial cell technique combined with the local relatively stationary method is used to simulate the motion of the wave maker. Firstly, the power of wave maker from numerical model is compared with the analyzed result under a specified wave condition. Then the avoidance of using abs...
A Cartesian ghost-cell method is developed for solving moving boundary flow problems in this pape... more A Cartesian ghost-cell method is developed for solving moving boundary flow problems in this paper. The flow field is discretized efficiently with a rectangular mesh, in which the solid body is immersed. A small number of ghost mesh cells and their symmetric image cells are distributed in the vicinity of the solid boundary. Then Dirichlet and Neumann boundary conditions are implemented with the aid of ghost and image cells. Chorin's projection method is used for the coupling of the velocity and the pressure. Pointwise Gauss-Seidel iteration is implemented to solve the pressure Poisson equation. To speed up the convergence rate of the corresponding linear system, sub- level coarse meshes embedded with ghost and image cells are introduced and operated in a V-cycle. To validate the proposed method, lid driven cavity and incompressible flows around a fixed cylinder are firstly simulated, and then the basic method is extended to compute incompressible flows around a transversely osci...
On the Validity of the Shallow Water Equations for Violent Wave Overtopping. [ASCE Conference Pro... more On the Validity of the Shallow Water Equations for Violent Wave Overtopping. [ASCE Conference Proceedings 273, 113 (2001)]. Stephen R. Richardson, David M. Ingram, Clive G. Mingham, Derek M. Causon. Abstract. This paper ...
ABSTRACT The piston-type wave maker is a very popular and important piece of equipment in coastal... more ABSTRACT The piston-type wave maker is a very popular and important piece of equipment in coastal and ocean engineering physical wave model experiments. In this paper we use a numerical model to simulate the ability of the piston-type wave maker to generate a specified wave, which only can be done by theoretical analysis before under ideal conditions. Numerical models are very useful to assist with the design of wave makers, and they are able to simulate the complex status of a wave maker in a flume. Based on solving the Navier-Stokes equations, the numerical model in this paper uses a two-fluid water and air system, in which the interface between the water and air is tracked by a particle level set method and the partial cell technique combined with the local relatively stationary method is used to simulate the motion of the wave maker. Firstly, the power of wave maker from numerical model is compared with the analyzed result under a specified wave condition. Then the avoidance of using absorbers in a flume is studied by choosing a suitable position of the wave maker in the flume. This is of practical importance because the use of absorbers is often expensive and the effects are not very well when they are used.
Viscous flow past two circular cylinders in tandem and side-by-side arrangements is investigated ... more Viscous flow past two circular cylinders in tandem and side-by-side arrangements is investigated numerically. The solution to the Navier-Stokes equations is obtained by means of a cell-centred finite volume method (FVM) based on a structured Cartesian grid with collocated variable arrangement. The pressure-velocity coupling is evaluated by using the SIMPLE algorithm. The 2D Cartesian cut cell mesh is generated on the horizontal plane, which is extended vertically to form the 3D grid. The simulations are based on the Reynolds number of 200, and the gap between the two cylinders are 1.5-3D for side-by-side arrangement and 3-4D for tandem. Instantaneous velocity contours of the flow around the cylinders and time histories of force coefficients are presented.
A new boundary condition is developed to enhance numerical stability for moving walls in lattice-... more A new boundary condition is developed to enhance numerical stability for moving walls in lattice-Boltzmann simulations. It includes a population ``adjustment'' procedure at boundaries which allows stable simulations closer to the theoretical limit of tau=0.5. Couette and lid-...
New Trends in Fluid Mechanics Research: Proceedings of the Fifth International Conference on Fluid Mechanics, 2007
ABSTRACT This paper presents a numerical model for simulating wave interaction with porous struct... more ABSTRACT This paper presents a numerical model for simulating wave interaction with porous structures. By using the free surface-capturing approach together with a novel Cartesian cut cell treatment, the Finite Volume Model calculates the two phase flows out side of porous structure based on the Navier-Stokes equations, while the flow in the porous structure is described by Navier-Stokes type model equations. The free surface of water is treated as a contact discontinuity in the density field which is captured automatically as part of the numerical solution by using a time-accurate artificial compressibility method and high resolution Godunov-type scheme. The numerical model is first calibrated by simple test for a steady flow passing through a porous block. Reasonably good agreements with other numerical results are obtained. After that, the numerical model is used to simulate the breaking wave overtopping a caisson breakwater, protected by a layer of armor units. The results show that the porous armor layer is effective in reducing the overtopping rate as well as in protecting the stability of the caisson breakwater.
ABSTRACT This paper focuses on the numerical modelling of wave impact events under air entrapment... more ABSTRACT This paper focuses on the numerical modelling of wave impact events under air entrapment and aeration effects. The underlying flow model treats the dispersed water wave as a compressible mixture of air and water with homogeneous material properties. The corresponding mathematical equations are based on a multiphase flow model which builds on the conservation laws of mass, momentum and energy as well as the gas-phase volume fraction advection equation. A high-order finite volume scheme based on monotone upstream-centred schemes for conservation law reconstruction is used to discretize the integral form of the governing equations. The numerical flux across a mesh cell face is estimated by means of the HLLC approximate Riemann solver. A third-order total variation diminishing Runge–Kutta scheme is adopted to obtain a time-accurate solution. The present model provides an effective way to deal with the compressibility of air and water–air mixtures. Several test cases have been calculated using the present approach, including a gravity-induced liquid piston, free drop of a water column in a closed tank, water–air shock tubes, slamming of a flat plate into still pure and aerated water and a plunging wave impact at a vertical wall. The obtained results agree well with experiments, exact solutions and other numerical computations. This demonstrates the potential of the current method to tackle more general wave–air–structure interaction problems.
Abstract: A generic two-fluid (water/air) numerical model has been developed and applied for the ... more Abstract: A generic two-fluid (water/air) numerical model has been developed and applied for the simulation of the complex fluid flow around a wave driven rotating vane near a shoreline in the context of a novel wave energy device OWSC (Oscillating wave surge ...
ABSTRACT A calculation method is presented for applications to steady supercritical and transcrit... more ABSTRACT A calculation method is presented for applications to steady supercritical and transcritical how in spillway channels. The method solves the two-dimensional nonlinear shallow water equations using a cell-centered finite-volume approach. High spatial resolution of shock waves and other steep flow features is achieved by employing MUSCL reconstruction and an approximate Riemann solver for the flux evaluations at each cell interface. The method can be implemented on boundary-conforming meshes to more accurately map the wide range of geometries that may occur in practice. Six analytical test problems are proposed for the validation of calculation methods applied to steady supercritical flow. These problems are used to validate the proposed flow solver, which is then applied to the case of steady supercritical flow in a curved channel transition, and comparisons are made with published data. Despite limitations in the shallow water model, the results show satisfactory agreement with data for the maximum rise in water level through the standing oblique shock waves.
A spectral method for the numerical solution of hyperbolic partial differential equations is pres... more A spectral method for the numerical solution of hyperbolic partial differential equations is presented. Any discontinuous solutions which may occur are assumed to be the sum of a step function and a smooth function. A series approximation is then applied to the smooth function in order to eliminate the Gibbs phenomenon. By adding the step function onto the series we
ABSTRACT A two-fluid free surface flow model, that can simulate wave interactions with stationary... more ABSTRACT A two-fluid free surface flow model, that can simulate wave interactions with stationary or moving bodies, has been developed. The incompressible Navier–Stokes (NS) equations are solved using a finite difference solver with an efficient particle level set method to track the interface between water and air. A semi-Lagrangian approach and the fast marching method have been applied to solve the level set equation and, with the aid of the locally deployed particles, to reinitialize the level set function. To represent solid stationary and moving boundaries in the flow field effectively, a partial cell treatment combined with a local relative stationary method has been implemented. A new simple level set boundary condition for both fixed and moving bodies is proposed. The free surface flow model has been validated for a number of 2D and 3D benchmark test cases for applications to complex flow situations involving the violent motions of water, air and their interfaces, as well as their interaction with fixed or moving bodies. Detailed comparisons between the numerical results and available analytical solutions or experimental data show that the model is generic, accurate and holds promise for the numerical simulation of such flow problems.
... and Mathematics, Manchester Metropolitan University, Chester Street, Manchester, M1 5GD, UK E... more ... and Mathematics, Manchester Metropolitan University, Chester Street, Manchester, M1 5GD, UK E-mail: [email protected] ... Hydrodynamics (SPH), a Cartesian Cut Cell method based on an artifi-cial compressibility method with shock capturing for the interface (AMAZON), and ...
The piston-type wave maker is a very popular and important piece of equipment in coastal and ocea... more The piston-type wave maker is a very popular and important piece of equipment in coastal and ocean engineering physical wave model experiments. In this paper we use a numerical model to simulate the ability of the piston-type wave maker to generate a specified wave, which only can be done by theoretical analysis before under ideal conditions. Numerical models are very useful to assist with the design of wave makers, and they are able to simulate the complex status of a wave maker in a flume. Based on solving the Navier-Stokes equations, the numerical model in this paper uses a two-fluid water and air system, in which the interface between the water and air is tracked by a particle level set method and the partial cell technique combined with the local relatively stationary method is used to simulate the motion of the wave maker. Firstly, the power of wave maker from numerical model is compared with the analyzed result under a specified wave condition. Then the avoidance of using abs...
A Cartesian ghost-cell method is developed for solving moving boundary flow problems in this pape... more A Cartesian ghost-cell method is developed for solving moving boundary flow problems in this paper. The flow field is discretized efficiently with a rectangular mesh, in which the solid body is immersed. A small number of ghost mesh cells and their symmetric image cells are distributed in the vicinity of the solid boundary. Then Dirichlet and Neumann boundary conditions are implemented with the aid of ghost and image cells. Chorin's projection method is used for the coupling of the velocity and the pressure. Pointwise Gauss-Seidel iteration is implemented to solve the pressure Poisson equation. To speed up the convergence rate of the corresponding linear system, sub- level coarse meshes embedded with ghost and image cells are introduced and operated in a V-cycle. To validate the proposed method, lid driven cavity and incompressible flows around a fixed cylinder are firstly simulated, and then the basic method is extended to compute incompressible flows around a transversely osci...
On the Validity of the Shallow Water Equations for Violent Wave Overtopping. [ASCE Conference Pro... more On the Validity of the Shallow Water Equations for Violent Wave Overtopping. [ASCE Conference Proceedings 273, 113 (2001)]. Stephen R. Richardson, David M. Ingram, Clive G. Mingham, Derek M. Causon. Abstract. This paper ...
ABSTRACT The piston-type wave maker is a very popular and important piece of equipment in coastal... more ABSTRACT The piston-type wave maker is a very popular and important piece of equipment in coastal and ocean engineering physical wave model experiments. In this paper we use a numerical model to simulate the ability of the piston-type wave maker to generate a specified wave, which only can be done by theoretical analysis before under ideal conditions. Numerical models are very useful to assist with the design of wave makers, and they are able to simulate the complex status of a wave maker in a flume. Based on solving the Navier-Stokes equations, the numerical model in this paper uses a two-fluid water and air system, in which the interface between the water and air is tracked by a particle level set method and the partial cell technique combined with the local relatively stationary method is used to simulate the motion of the wave maker. Firstly, the power of wave maker from numerical model is compared with the analyzed result under a specified wave condition. Then the avoidance of using absorbers in a flume is studied by choosing a suitable position of the wave maker in the flume. This is of practical importance because the use of absorbers is often expensive and the effects are not very well when they are used.
Viscous flow past two circular cylinders in tandem and side-by-side arrangements is investigated ... more Viscous flow past two circular cylinders in tandem and side-by-side arrangements is investigated numerically. The solution to the Navier-Stokes equations is obtained by means of a cell-centred finite volume method (FVM) based on a structured Cartesian grid with collocated variable arrangement. The pressure-velocity coupling is evaluated by using the SIMPLE algorithm. The 2D Cartesian cut cell mesh is generated on the horizontal plane, which is extended vertically to form the 3D grid. The simulations are based on the Reynolds number of 200, and the gap between the two cylinders are 1.5-3D for side-by-side arrangement and 3-4D for tandem. Instantaneous velocity contours of the flow around the cylinders and time histories of force coefficients are presented.
A new boundary condition is developed to enhance numerical stability for moving walls in lattice-... more A new boundary condition is developed to enhance numerical stability for moving walls in lattice-Boltzmann simulations. It includes a population ``adjustment'' procedure at boundaries which allows stable simulations closer to the theoretical limit of tau=0.5. Couette and lid-...
New Trends in Fluid Mechanics Research: Proceedings of the Fifth International Conference on Fluid Mechanics, 2007
ABSTRACT This paper presents a numerical model for simulating wave interaction with porous struct... more ABSTRACT This paper presents a numerical model for simulating wave interaction with porous structures. By using the free surface-capturing approach together with a novel Cartesian cut cell treatment, the Finite Volume Model calculates the two phase flows out side of porous structure based on the Navier-Stokes equations, while the flow in the porous structure is described by Navier-Stokes type model equations. The free surface of water is treated as a contact discontinuity in the density field which is captured automatically as part of the numerical solution by using a time-accurate artificial compressibility method and high resolution Godunov-type scheme. The numerical model is first calibrated by simple test for a steady flow passing through a porous block. Reasonably good agreements with other numerical results are obtained. After that, the numerical model is used to simulate the breaking wave overtopping a caisson breakwater, protected by a layer of armor units. The results show that the porous armor layer is effective in reducing the overtopping rate as well as in protecting the stability of the caisson breakwater.
ABSTRACT This paper focuses on the numerical modelling of wave impact events under air entrapment... more ABSTRACT This paper focuses on the numerical modelling of wave impact events under air entrapment and aeration effects. The underlying flow model treats the dispersed water wave as a compressible mixture of air and water with homogeneous material properties. The corresponding mathematical equations are based on a multiphase flow model which builds on the conservation laws of mass, momentum and energy as well as the gas-phase volume fraction advection equation. A high-order finite volume scheme based on monotone upstream-centred schemes for conservation law reconstruction is used to discretize the integral form of the governing equations. The numerical flux across a mesh cell face is estimated by means of the HLLC approximate Riemann solver. A third-order total variation diminishing Runge–Kutta scheme is adopted to obtain a time-accurate solution. The present model provides an effective way to deal with the compressibility of air and water–air mixtures. Several test cases have been calculated using the present approach, including a gravity-induced liquid piston, free drop of a water column in a closed tank, water–air shock tubes, slamming of a flat plate into still pure and aerated water and a plunging wave impact at a vertical wall. The obtained results agree well with experiments, exact solutions and other numerical computations. This demonstrates the potential of the current method to tackle more general wave–air–structure interaction problems.
Abstract: A generic two-fluid (water/air) numerical model has been developed and applied for the ... more Abstract: A generic two-fluid (water/air) numerical model has been developed and applied for the simulation of the complex fluid flow around a wave driven rotating vane near a shoreline in the context of a novel wave energy device OWSC (Oscillating wave surge ...
ABSTRACT A calculation method is presented for applications to steady supercritical and transcrit... more ABSTRACT A calculation method is presented for applications to steady supercritical and transcritical how in spillway channels. The method solves the two-dimensional nonlinear shallow water equations using a cell-centered finite-volume approach. High spatial resolution of shock waves and other steep flow features is achieved by employing MUSCL reconstruction and an approximate Riemann solver for the flux evaluations at each cell interface. The method can be implemented on boundary-conforming meshes to more accurately map the wide range of geometries that may occur in practice. Six analytical test problems are proposed for the validation of calculation methods applied to steady supercritical flow. These problems are used to validate the proposed flow solver, which is then applied to the case of steady supercritical flow in a curved channel transition, and comparisons are made with published data. Despite limitations in the shallow water model, the results show satisfactory agreement with data for the maximum rise in water level through the standing oblique shock waves.
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Papers by C. Mingham