# On the Computation of Roll Waves

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 35.3 (2010): 463-480. <http://eudml.org/doc/197563>.

@article{Jin2010,

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 ut + uux = u,u(x,0) = u0(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},

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

language = {eng},

month = {3},

number = {3},

pages = {463-480},

publisher = {EDP Sciences},

title = {On the Computation of Roll Waves},

url = {http://eudml.org/doc/197563},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Jin, Shi

AU - Kim, Yong Jung

TI - On the Computation of Roll Waves

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

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 ut + uux = u,u(x,0) = u0(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.; conservation laws with source term; shock capturing methods

UR - http://eudml.org/doc/197563

ER -

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