Christopher Zoppou

• PhD (Civil Engineering) PhD (Mathematics)
• Australian National University

We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial boundary value problem is well-posed. A finite-volume method is developed based on the summation-by-parts framework...

We present an energy/entropy stable and high order accurate finite difference method for solving the linear/nonlinear shallow water equations (SWE) in vector invariant form using the newly developed dual-pairing (DP) and dispersion-relation preserving (DRP) summation by parts (SBP) finite difference operators. We derive new well-posed boundary cond...

We derive well-posed boundary conditions for the linearized Serre equations in one spatial dimension by using the energy method. An energy stable and conservative discontinuous Galerkin spectral element method with simple upwind numerical fluxes is proposed for solving the initial boundary value problem. We derive discrete energy estimates for the...

A numerical scheme for solving the recently derived generalised Serre-Green–Naghdi equations which produce a family of equations modelling waves in shallow water with varying dispersion relationships, is described. The numerical scheme extends schemes applied to the classical Serre-Green–Naghdi equations written in conservation law form and is the...

We describe a numerical method for solving the Serre equations that can simulate flows over dry bathymetry. The method solves the Serre equations in conservation law form with a finite volume method. A finite element method is used to solve the auxiliary elliptic equation for the depth‐averaged horizontal velocity. The numerical method is validated...

A numerical method for solving the Serre equations that can model flows over dry bathymetry is described. The method solves the Serre equations in conservation law form with a finite volume method. A finite element method is used to solve the auxiliary elliptic equation for the depth-averaged horizontal velocity. The numerical method is validated a...

We use numerical methods to study the behaviour of the Serre equations in the presence of steep gradients because there are no known analytical solutions for these problems. In keeping with the literature we study a class of initial condition problems that are a smooth approximation to the initial conditions of the dam-break problem. This class of...

We use numerical methods to study the behaviour of the Serre equations in the presence of steep gradients because there are no known analytical solutions for these problems. In keeping with the literature we study a class of initial condition problems that are a smooth approximation to the initial conditions of the dam-break problem. This class of...

We demonstrate a numerical approach for solving the one-dimensional non-linear weakly dispersive Serre equations. By introducing a new conserved quantity the Serre equations can be written in conservation law form, where the velocity is recovered from the conserved quantities at each time step by solving an auxiliary elliptic equation. Numerical te...

The nonlinear weakly dispersive Serre equations contain higher-order dispersive terms. This includes a mixed derivative flux term which is difficult to handle numerically. The mix spatial and temporal derivative dispersive term is replaced by a combination of temporal and spatial terms. The Serre equations are re-written so that the system of equat...

The nonlinear and weakly dispersive Serre equations contain higher-order dispersive terms. These include mixed spatial and temporal derivative flux terms which are difficult to handle numerically. These terms can be replaced by an alternative combination of equivalent temporal and spatial terms, so that the Serre equations can be written in conserv...

The nonlinear and weakly dispersive Serre equations contain higher-order dispersive terms. These include mixed spatial and temporal derivative flux terms which are difficult to handle numerically. These terms can be replaced by an alternative combination of equivalent temporal and spatial terms, so that the Serre equations can be written in conserv...

Rapidly-varying free surface flows that arise, for example, from; rapid reservoir releases, dam-breaks, mud slides, tidal bores, storm surges, tsunamis and flows over variable topography, are characterized by abrupt changes in the water surface. These changes produce vertical acceleration of the fluid particles. These vertical accelerations manifes...

The Australian society consists of diverse family forms. The introduction of reforms in the Family Law Act in 1976, making it easier to obtain a divorce has contributed to the increase in diversity in these family forms. Another factor that has contributed to the fluidity in relationships is the increase in economic independence of women[7]. As peo...

The use of Gini coefficient is well established as a measure of income inequality and has been used for this purpose in a variety of fields including health economics, demography and income inequality studies. Using the Beta distribution as a particular functional form of an income distribution, the Gini coefficient is calculated for a variety of i...

This brief report describes a method of defining a return-to-service curve for damaged infrastructure. These curves define the time taken to repair infrastructure and possess a characteristic S-curve shape. The functional form of the return-to-service curve provided only contains a single parameter. It is simple to evaluate, continuous and only req...

A dam break analysis of ring tanks was carried out using an advanced 2-dimensional (pseudo 3D depth-averaged) finite volume numerical modelling algorithm. The objective was to determine the maximum extent of the Failure Impact Zone (where water flow depth exceeded 300 mm) for a range of embankment heights, storage volumes, flood plain bed slopes an...

The permeability of the Earth's crust commonly varies over many orders of magnitude. Flow velocity can range over several orders of magnitude in structures of interest that vary in scale from centimeters to kilometers. To accurately and efficiently model multiphase flow in geologic media, we introduce a fully conservative node-centered finite volum...

The following values have no corresponding Zotero field: ID - 35

The Risk Research Group at Geoscience Australia (GA) in Canberra is a multidisciplinary team engaged in the development of risk models for a range of natural hazards that are applicable to Australian urban areas. The Group includes hazard experts, numerical modellers, engineers, economists, and a specialist researching social vulnerability. The ris...

Abstract The permeability, porosity, and velocity that govern the flow of multi- phase fluids (e.g., water, oil, steam) in the earth’s subsurface can vary over several orders of magnitude. The range over which the flow is observed can vary from the kilometre to centimetre scale due to the hydraulic properties and geometric complexity of geologic st...

Dam-break problems involve the formation of shocks and rarefaction fans. The performance of 20 explicit numerical schemes used to solve the shallow water wave equations for simulating the dam-break problem is examined. Results from these schemes have been compared with analytical solutions to the dam-break problem with finite water depth and dry be...

Dam-break problems involve the formation of shocks and rarefaction fans. The performance of 20 explicit numerical schemes used to solve the shallow water wave equations for simulating the dam-break problem is examined. Results from these schemes have been compared with analytical solutions to the dam-break problem with finite water depth and dry be...

This paper illustrates a simple, accurate and efficient method of estimating the probability offailure of a hydraulic system. The proposed method requires the same information as that of conventional methods. It does not require one to estimate or assume the probability density function of the performance function, describing the behaviour of the h...

In level pool routing, which is the simplest hydrological routing method, the downstream discharge may be expressed explicitly in terms of the inflow and the channel or reservoir characteristics. The level pool routing equation can also be used to estimate the inflow hydrograph given the outflow hydrograph and the water level in the reservoir. Unfo...

This paper describes a major program of research by the Commonwealth Scientific and Industrial Research Organization (CSIRO) into urban water, wastewater and stormwater services. The intent of the program has been to identify opportunities for achieving more sustainable urban water services. The term “sustainable” has been interpreted to mean impro...

This paper reviews models for simulating storm water quantity and quality in an urban environment. This has been achieved by examining a number of storm water models in current use. The important features of twelve models, which represent a wide range of capabilities and spatial and temporal resolution have been described. Specific topics covered a...

INTRODUCTION The study of the catastrophic collapse of a dam is of interest because of the risk to life and property the ensuing flooding may cause. During this century there have been more than 200 failures of dams greater than 15 metres high[1]. They have caused millions of dollars worth of damage and a loss of more than 8,000 lives. These recent...

This paper demonstrates the use of shape-preserving exponential spline interpolation in a characteristic based numerical scheme for the solution of the linear advective-diffusion equation. The results from this scheme are compared with results from a number of numerical schemes in current use using test problems in one and two dimensions. These tes...

It has been known for a number of years that dispersivities increase with the scale of a ground-water dispersion experiment, but little appears to be known about the effect of this scale dependency on solutions of the dispersion equation. Solutions of the dispersion equation with dispersivities that increase directly with the first power of the flo...

A number of efficient and accurate algorithms exist for solving the homogeneous shallow water wave equations. Source terms which account for the influence of bathymetry and frictional forces are generally added to the homogeneous equations. There are a number of schemes which include the source terms in the underlying numerical algorithm, such as t...

Analytical solutions are provided for the two- and three-dimensional advection–diffusion equation with spatially variable velocity and diffusion coefficients. We assume that the velocity component is proportional to the distance and that the diffusion coefficient is proportional to the square of the corresponding velocity component. There is a simp...

In level pool routing, which is the simplest hydrological routing method, the downstream discharge may be expressed explicitly in terms of the inflow and the channel or reservoir characteristics. The level pool routing equation can also be used to estimate the inflow hydrograph given the outflow hydrograph and the water level in the reservoir. Unfo...

A numerical model for the solution of the two-dimensional dam break problem is described. The model which is based on a second-order approximate Riemann solver with a van Leer type limiter is used to solve the shallow water wave equation on a Cartesian grid. The shallow water equations include source terms which account for resistance to the flow a...

. A model based on the finite volume method combined with a first-order approximate Riemann solver is used to solve the two-dimensional shallow water wave equation on an unstructured triangular grid. Verification of the model is achieved by comparing the model results with analytical solutions as well as documented published results with very good...

Ammonia, a common constituent of wastewaters, is toxic to a wide range of aquatic organisms. Fish are the most sensitive species and cold-water, oxygen-sensitive, fish such as trout are the most vulnerable. The US Environmental Protection Agency (USEPA) has developed models of fish-tolerance to ammonia levels. These criteria have been adopted in Au...

The deformation, using linear poroelasticity, of a two-dimensional box of porous material due to fluid flow from a line source is considered as a model of certain filtration processes. Analytical solutions for the steady-state displacement, pressure, and fluid velocity are derived when the side walls of the filter have zero solid stress. A numerica...

. All finite difference equations have an equivalent partial differential equation which is the actual partial differential equation being solved. The equivalent modified partial differential equation will not be identical to the original equation being modelled. It will generally contain additional higher-order spatial terms introduced by the fini...

The flow of fluid from a point source or sink at some arbitrary height in a layer of deformable porous material is considered. This problem is applicable to filtration through beds of sand and flow in soils. The porous material is assumed to be an isotropic, homogeneous, linear elastic solid. The equations governing the behavior of the medium and f...

There is a role for computer models in increasing the understanding of milk extraction from the human teat. A computer model can be used to investigate aspects of extracting milk from the human teat which are not feasible using clinical experiments. In this paper, the behavior of the human teat during an infant suckling and with the use of a breast...

We describe a mathematical model of the flow and deformation in a human teat. Our aim is to compare the theoretical milk yield during infant breast feeding with that obtained through the use of a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk, whereas breast pumps use a cyclic pattern of suctio...

We describe a mathematical model of the flow and deformation in a human teat. Our aim is to compare the theoretical milk yield during infant breast feeding with that obtained through the use of a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk, whereas breast pumps use a cyclic pattern of suctio...

Analytical solutions are provided for the one-dimensional transport of a pollutant in an open channel with steady unpolluted lateral inflow uniformly distributed over its whole length. This practical problem can be described approximately by spatially variable coefficient advection and advection-diffusion equations with the velocity proportional to...

solve the advection-diffusion equation with spatially variable coefficients. The Laplace transform is used to evaluate the temporal derivative in the advection-diffusion equation ana- lytically, thereby eliminating the effects of the time deriva- tive on accuracy and stability. Because the temporal deriv- ative is evaluated using the Laplace transf...

The general public has recently become aware of the problems posed by the indiscriminate discharge of industrial and domestic pollutants in our waterways. This has become particularly acute in aquatic systems adjacent to areas of dense population. The effect of growing public awareness of the abuse of the environment has resulted in legislation to...

A new point estimate method (PEM) suitable for estimating the statistical moments of the response of water resources models is illustrated. The importance of using the correct approach for modeling spatial variability in water resources modeling is also demonstrated using the PEM and the simulation of a backwater profile in an open channel. Random...

A reach of the River Yarra was used to assess the applicability of the diffusion and kinematic wave models which are approximations to the dynamic wave model. Acceptance criteria for these approximate models were established by several researchers for idealized situations and were found deficient for the case study. (A)

Backwater profile computer packages are being widely used in flood studies - in particular for simulating high water levels along river reaches. The equations used in these models can be considered as simplified versions of the complete one-dimensional Saint Venant equations where the known-discharge assumption is used in lieu of the unsteady terms...

This paper examines the quasi-characteristic method for the solution of the Saint Venant equations governing the motion of flows, waves and floods in rivers and channels. The apparently new approach combines the more desirable features of traditional numerical methods, but does riot seem to suffer from their disadvantages. It is explicit, efficient...