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**Harvard**

Eskilsson, C. och Engsig-Karup, A. (2014) *On devising Boussinesq-type models with bounded eigenspectra: One horizontal dimension*.

** BibTeX **

@article{

Eskilsson2014,

author={Eskilsson, Claes and Engsig-Karup, A. P.},

title={On devising Boussinesq-type models with bounded eigenspectra: One horizontal dimension},

journal={Journal of Computational Physics},

issn={0021-9991},

volume={271},

pages={261-280},

abstract={The propagation of water waves in the nearshore region can be described by depthintegrated Boussinesq-type equations. The dispersive and nonlinear characteristics of the equations are governed by tuneable parameters. We examine the associated linear eigenproblem both analytically and numerically using a spectral element method of arbitrary spatial order p. It is shown that existing sets of parameters, found by optimising the linear dispersion relation, give rise to unbounded eigenspectra which govern stability. For explicit time-stepping schemes the global CFL time-step restriction typically requires Delta t proportional to p(-2). We derive and present conditions on the parameters under which implicitlyimplicit Boussinesq-type equations will exhibit bounded eigenspectra. Two new bounded versions having comparable nonlinear and dispersive properties as the equations of Nwogu (1993) and Schaffer and Madsen (1995) are introduced. Using spectral element simulations of stream function waves it is illustrated that (i) the bounded equations capture the physics of the wave motion as well as the standard unbounded equations, and (ii) the bounded equations are computationally more efficient when explicit time-stepping schemes are used. Thus the bounded equations were found to lead to more robust and efficient numerical schemes without compromising the accuracy.},

year={2014},

keywords={Nonlinear dispersive water waves, Boussinesq-type equations, Spectral/hp element method; Eigenvalue analysis; Time integration; Implicitly-implicit equations},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 200206

A1 Eskilsson, Claes

A1 Engsig-Karup, A. P.

T1 On devising Boussinesq-type models with bounded eigenspectra: One horizontal dimension

YR 2014

JF Journal of Computational Physics

SN 0021-9991

VO 271

SP 261

OP 280

AB The propagation of water waves in the nearshore region can be described by depthintegrated Boussinesq-type equations. The dispersive and nonlinear characteristics of the equations are governed by tuneable parameters. We examine the associated linear eigenproblem both analytically and numerically using a spectral element method of arbitrary spatial order p. It is shown that existing sets of parameters, found by optimising the linear dispersion relation, give rise to unbounded eigenspectra which govern stability. For explicit time-stepping schemes the global CFL time-step restriction typically requires Delta t proportional to p(-2). We derive and present conditions on the parameters under which implicitlyimplicit Boussinesq-type equations will exhibit bounded eigenspectra. Two new bounded versions having comparable nonlinear and dispersive properties as the equations of Nwogu (1993) and Schaffer and Madsen (1995) are introduced. Using spectral element simulations of stream function waves it is illustrated that (i) the bounded equations capture the physics of the wave motion as well as the standard unbounded equations, and (ii) the bounded equations are computationally more efficient when explicit time-stepping schemes are used. Thus the bounded equations were found to lead to more robust and efficient numerical schemes without compromising the accuracy.

LA eng

DO 10.1016/j.jcp.2013.08.048

LK http://dx.doi.org/10.1016/j.jcp.2013.08.048

OL 30