Un schéma TVD-multirésolution pour les équations de Saint-Venant

Louaked, Mohammed; Hanich, L.

doi:10.1016/s0764-4442(00)01715-8

Cited by 5 publications

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“…In effect, the discretizations (2.13) and (2.14) are strictly related, as formally verified by means of standard asymptotic expansions on the numerical functions and simple algebraic calculations with the differences of discrete values (2.1) or (2.12). We also note that many of the second order schemes proposed in the literature do not include the additional term (2.13), but it is probably recovered implicitly in the formulation (see [1], [23] and [28], for instance).…”

Section: First and Second Order Error Estimatesmentioning

confidence: 99%

First and second order error estimates for the Upwind Source at Interface method

Katsaounis

Simeoni

2004

Math. Comp.

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Abstract. The Upwind Source at Interface (U.S.I.) method for hyperbolic conservation laws with source term introduced by Perthame and Simeoni is essentially first order accurate. Under appropriate hypotheses of consistency on the finite volume discretization of the source term, we prove L p -error estimates, 1 ≤ p <+∞, in the case of a uniform spatial mesh, for which an optimal result can be obtained. We thus conclude that the same convergence rates hold as for the corresponding homogeneous problem. To improve the numerical accuracy, we develop two different approaches of dealing with the source term and we discuss the question of deriving second order error estimates. Numerical evidence shows that those techniques produce high resolution schemes compatible with the U.S.I. method.

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Section: First and Second Order Error Estimatesmentioning

confidence: 99%

First and second order error estimates for the Upwind Source at Interface method

Katsaounis

Simeoni

2004

Math. Comp.

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TVD adaptive mesh redistribution scheme for the shallow‐water equations

Louaked

2007

Numerical Methods in Fluids

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SUMMARYThis work presents a high-resolution scheme combined with a moving mesh method for approximating the solution of shallow water system. The main difficulties in deriving stable and convergent numerical approximations can be due to solutions that vanish in nontrivial parts of domain such as dry states in water flows. In these situations, the coupling between characteristic fields gradually increases as water height is stepped down. The basic methodology in our method is to avoid characteristic decompositions in the spatial discretization. Moving dry regions within the computing domain are captured without the appearance of negative values. The high-resolution properties of the scheme as well as its resistance to mesh orientation gives the great potential of the moving mesh methods for reducing computational costs without sacrificing the overall level of accuracy, which is demonstrated in a variety of hydraulic examples.

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