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Upwinding of source term at interface for Euler equations with high friction, in "Computers and Mathematics with Applications
, 2006
"... with high friction ..."
Front tracking for scalar balance equations
 J. Hyperbolic Differ. Equ
"... Abstract. We propose and prove convergence of a front tracking method for scalar conservation laws with source term. The method is based on writing the single conservation law as a 2 × 2 quasilinear system without a source term, and employ the solution of the Riemann problem for this system in the f ..."
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Abstract. We propose and prove convergence of a front tracking method for scalar conservation laws with source term. The method is based on writing the single conservation law as a 2 × 2 quasilinear system without a source term, and employ the solution of the Riemann problem for this system in the front tracking procedure. In this way the source term is processed in the Riemann solver, and one avoids using operator splitting. Since we want to treat the resonant regime, classical arguments for bounding the total variation of numerical solutions do not apply here. Instead compactness of a sequence of front tracking solutions is achieved using a variant of the singular mapping technique invented by Temple [69]. The front tracking method has no CFL–condition associated with it, and it does not discriminate between stiff and nonstiff source terms. This makes it an attractive approach for stiff problems, as is demonstrated in numerical examples. In addition, the numerical examples show that the front tracking method is able to preserve steady–state solutions (or achieving them in the long time limit) with good accuracy. 1.
Asymptotic Highorder schemes for integrodifferential problems arising in markets with jumps
, 2006
"... In this paper we deal with the numerical approximation of integrodifferential equations arising in financial applications in which jump processes act as the underlying stochastic processes. Our aim is to find finite differences schemes which are highorder accurate for large time regimes. Therefore ..."
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In this paper we deal with the numerical approximation of integrodifferential equations arising in financial applications in which jump processes act as the underlying stochastic processes. Our aim is to find finite differences schemes which are highorder accurate for large time regimes. Therefore, we study the asymptotic time behavior of such equations and we define as asymptotic highorder schemes those schemes that are consistent with this behavior. Numerical tests are presented to investigate the efficiency and the accuracy of such approximations.
Catastrophic Collapse of Water Supply Reservoirs in Urban Areas
 Journal of Hydraulic Engineering, American Society of Civil Engineers
, 1999
"... 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 damag ..."
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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 disasters have focussed attention on means for assessing public safety and predicting probable damage from the collapse of a dam. Many water authorities are required to assess the risk of failure and develop a flood warning plan for all of their large dams. However, this is not the case for the smaller water supply reservoir which form part of the water reticulation system in many cities. These reservoirs are typically 50 metres in diameter and 10 metres high and contain approximately 20 mega litres of water. They are usually located in elevated positions in residential areas. Due to their proximity to residential areas, water supply r
FLUXGRADIENT AND SOURCE TERM BALANCING FOR CERTAIN HIGH RESOLUTION SHOCKCAPTURING SCHEMES By
, 2006
"... Fluxgradient and source term balancing for certain high resolution shockcapturing schemes ..."
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Fluxgradient and source term balancing for certain high resolution shockcapturing schemes
Numerical Techniques for Conservation Laws with Source Terms, MSc Dissertation
, 1998
"... In this dissertation we will discuss the finite difference method for approximating conservation laws with a source term present which is considered to be a known function of x, t and u. Finite difference schemes for approximating conservation laws without a source term present are discussed and are ..."
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In this dissertation we will discuss the finite difference method for approximating conservation laws with a source term present which is considered to be a known function of x, t and u. Finite difference schemes for approximating conservation laws without a source term present are discussed and are adapted to approximate conservation laws with a source term present. First we consider the source term to be a function of x and t only and then we consider the source term to be a function of u also. Some numerical results of the different approaches are discussed throughout the dissertation and an overall comparison of
ON SOME FAST WELLBALANCED FIRST ORDER SOLVERS FOR NONCONSERVATIVE SYSTEMS
"... Abstract. The goal of this article is to design robust and simple first order explicit solvers for onedimensional nonconservative hyperbolic systems. These solvers are intended to be used as the basis for higher order methods for one or multidimensional problems. The starting point for the developm ..."
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Abstract. The goal of this article is to design robust and simple first order explicit solvers for onedimensional nonconservative hyperbolic systems. These solvers are intended to be used as the basis for higher order methods for one or multidimensional problems. The starting point for the development of these solvers is the general definition of a Roe linearization introduced by Toumi in 1992 based on the use of a family of paths. Using this concept, Roe methods can be extended to nonconservative systems. These methods have good wellbalanced and robustness properties, but they have also some drawbacks: in particular, their implementation requires the explicit knowledge of the eigenstructure of the intermediate matrices. Our goal here is to design numerical methods based on a Roe linearization which overcome this drawback. The idea is to split the Roe matrices into two parts which are used to calculate the contributions at the cells to the right and to the left, respectively. This strategy is used to generate two different oneparameter families of schemes which contain, as particular cases, some generalizations to nonconservative systems of the wellknown LaxFriedrichs, LaxWendroff, FORCE, and GFORCE schemes. Some numerical experiments are presented to compare the behaviors of the schemes introduced here with Roe methods. 1.
Robust and Efficient Solution of the 2D Shallow Water Equation with Domains Containing Dry Beds
, 2000
"... A number of the standard numerical methods used to solve the twodimensional shallow water wave equations are unstable if their domains contain dry beds. We present a robust and stable nite volume method based on an unstructured triangular grid which can deal with dry beds. In particular we pres ..."
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A number of the standard numerical methods used to solve the twodimensional shallow water wave equations are unstable if their domains contain dry beds. We present a robust and stable nite volume method based on an unstructured triangular grid which can deal with dry beds. In particular we present a secondorder explicit method which deal with dry beds in a stable manner. The method uses a simple approximate one dimensional Riemann solver due to Toro which provides the basis for an ecient implementation. 1 Introduction The shallow water equations are used extensively to model the behavior of ows produced by precipitation or as a result of the failure of manmade structures. These problems generally involve sudden releases of water or intense rainfall bursts which produce rapid runo. Both problems are characterized by abrupt changes in water depth and ow rates. In addition, these 1 phenomena also involve water owing over dry terrain, see for example Zoppou and Roberts[18...