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On some spurious modes issues in shallow water models using a linear algebra approach
Le Roux, D.Y.; Sène, A.; Rostand, V.; Hanert, E. (2005). On some spurious modes issues in shallow water models using a linear algebra approach. Ocean Modelling 10(1-2): 83-94. dx.doi.org/10.1016/j.ocemod.2004.07.008
In: Ocean Modelling. Elsevier: Oxford. ISSN 1463-5003, more
Peer reviewed article  

Available in  Authors 
    VLIZ: Open Repository 235827 [ OMA ]

Keyword
    Marine
Author keywords
    ocean modelling; shallow-water equations; spurious computational modes; finite-difference method; finite-element method

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  • Second-generation Louvain-la-Neuve Ice-ocean Model, more

Authors  Top 
  • Le Roux, D.Y.
  • Sène, A.
  • Rostand, V.
  • Hanert, E., more

Abstract
    Numerical methods that are usually employed in ocean modelling are typically finite-difference, finite and spectral-element techniques. For most of these methods the coupling between the momentum and continuity equations is a delicate problem and it usually leads to spurious solutions in the representation of inertia-gravity waves. The spurious modes have a wide range of characteristics and may take the form of pressure (surface-elevation), velocity and/or Coriolis modes. The modes usually cause aliasing and an accumulation of energy in the smallest-resolvable scale, leading to noisy solutions. The Fourier analysis has proven practical and beneficial to describe the spurious solutions of several classical schemes. However it is restricted to uniform meshes on which the variables are regularly distributed. In this paper, a linear algebra approach is proposed to study the existence and the behaviour of stationary spurious modes associated with zero frequency, for some popular finite-difference and finite-element grids. The present approach is performed on uniform meshes but it applies equally well to regular as well as unstructured meshes with irregular geometry for the finite-element schemes.

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