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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.
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
A ”wellbalanced ” finite volume scheme for blood flow simulation
, 2012
"... We are interested in simulating blood flow in arteries with a one dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the SaintVenant / shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation ..."
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We are interested in simulating blood flow in arteries with a one dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the SaintVenant / shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme which were not previously considered. To emphasize the necessity of this scheme, we present how a too simple numerical scheme may induce spurious flows when the basic static shape of the radius changes. On contrary, the proposed scheme is ”wellbalanced”: it preserves equilibria of Q = 0. Then examples of analytical or linearized solutions with and without viscous damping are presented to validate the calculations. The influence of abrupt change of basic radius is emphasized in the case of an aneurism. Keywords blood flow simulation; wellbalanced scheme; finite volume scheme; hydrostatic reconstruction; man at eternal rest; semianalytical solutions; shallow water 1
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.
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
Signed
, 2004
"... In this dissertation we look at the application of two dimensional conservation laws with source terms to two specific physical examples, the shallow water equations and crowd flow. There are a number of techniques that can be used to numerically approximate such systems. We discuss the Q scheme met ..."
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In this dissertation we look at the application of two dimensional conservation laws with source terms to two specific physical examples, the shallow water equations and crowd flow. There are a number of techniques that can be used to numerically approximate such systems. We discuss the Q scheme method of Bermúdez & Vázquez, focusing on an extension to Roe’s Q scheme. The technique of dimensional splitting is used to decompose the systems into two onedimensional problems that are solved alternately in the x and y directions. For the shallow water equations we examine two different test problems. We begin by considering a nonrotating frame of reference, before extending the equations to include the effects of the Earth’s rotation. The βplane approximation is used to avoid the complications of spherical geometry whilst retaining the leading order effect of the Earth’s curvature. We then move on to develop a two dimensional macroscopic model of crowd flow based on a onedimensional continuum model proposed by Payne and Whitham. The equations are transformed into a system of conservation laws, with source term in the form of a relaxation term. A series of numerical experiments are used to evaluate the accuracy of the model. i Declaration I confirm that this is my own work and the use of all materials from other sources has been properly and fully acknowledged.
arbitrary bed in the presence
"... finitevolume scheme for modeling shallow water flows over an ..."