# On the computation of roll waves

- Volume: 35, Issue: 3, page 463-480
- ISSN: 0764-583X

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topJin, Shi, and Kim, Yong Jung. "On the computation of roll waves." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.3 (2001): 463-480. <http://eudml.org/doc/194058>.

@article{Jin2001,

abstract = {The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation $u_t+uu_x=u,\ u(x,0)=u_0(x),$ which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the numerical solution and yields false roll wave solution at the steady state. In this paper, we first study the analytic behavior of the solution to the above model. We then discuss the numerical difficulty, and introduce a numerical method that predicts precisely the evolution and steady state of its solution. Various numerical experiments are performed to illustrate the numerical difficulty and the effectiveness of the proposed numerical method.},

author = {Jin, Shi, Kim, Yong Jung},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {roll wave; conservation laws with source term; round-off error; shock capturing methods},

language = {eng},

number = {3},

pages = {463-480},

publisher = {EDP-Sciences},

title = {On the computation of roll waves},

url = {http://eudml.org/doc/194058},

volume = {35},

year = {2001},

}

TY - JOUR

AU - Jin, Shi

AU - Kim, Yong Jung

TI - On the computation of roll waves

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 3

SP - 463

EP - 480

AB - The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation $u_t+uu_x=u,\ u(x,0)=u_0(x),$ which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the numerical solution and yields false roll wave solution at the steady state. In this paper, we first study the analytic behavior of the solution to the above model. We then discuss the numerical difficulty, and introduce a numerical method that predicts precisely the evolution and steady state of its solution. Various numerical experiments are performed to illustrate the numerical difficulty and the effectiveness of the proposed numerical method.

LA - eng

KW - roll wave; conservation laws with source term; round-off error; shock capturing methods

UR - http://eudml.org/doc/194058

ER -

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