A two-layer finite volume model for flows through channels with irregular geometry: Computation of maximal exchange solutions

Castro, Manuel J.; Macı́as, Jorge; Parés, Carlos; Garcia-Rodriguez, Jose; Vázquez-Cendón, Elena

doi:10.1016/s1007-5704(03)00115-1

Cited by 14 publications

(16 citation statements)

References 12 publications

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“…The obtained results, shown in Figure 2.6 (right), are very similar to the ones obtained in [6]. We note that no interface instabilities have been observed in this example, even though initially h 1 = 0 for x > 0 and h 2 = 0 for x < 0 and at small times, either h 1 or h 2 is (almost) zero in a significant part of the computational domain.…”

Section: Lock Exchange Problemsupporting

confidence: 85%

“…In this example, taken from [6], the two layers are initially separated-the lighter water is on the left while the heavier one is on the right:…”

Section: Lock Exchange Problemmentioning

confidence: 99%

“…Computing their solutions is a challenging problem due to several reasons: they contain nonconservative product terms, they are only conditionally hyperbolic, and their eigenstructure cannot be obtained in explicit form. Even though these factors make it quite difficult to design upwind methods for the two-layer shallow water equations, several upwind-based schemes, including the finite-volume [5,6,12] and finite-element [28] ones, were developed during the past decade. An interesting approach to overcome the above difficulties has been recently proposed in [1], where two artificial equations have been added to the system (1.1) so that the extended system becomes hyperbolic and thus could be solved by a second-order Roe-type scheme in a rather straightforward manner.…”

Section: Introductionmentioning

confidence: 99%

“…Some of the above methods, [1,4,5,6,12], are well-balanced in the sense that they exactly preserve stationary steady-state solutions given by tationally friendly form and describe the central-upwind scheme for the modified system. The description includes a special discretization of the bottom topography function B ( §2.1), the nonconservative products ( §2.4), and a well-balanced discretization of the geometric source term ( §2.5).…”

Section: Introductionmentioning

confidence: 99%

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Central-Upwind Schemes for Two-Layer Shallow Water Equations

Kurganov¹,

Petrova²

2009

SIAM J. Sci. Comput.

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We derive a second-order semi-discrete central-upwind scheme for one-and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is wellbalanced in the sense that stationary steady-state solutions are exactly preserved by the scheme, and positivity preserving, that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new technique for the treatment of the nonconservative products describing the momentum exchange between the layers.The performance of the proposed method is illustrated on a number of numerical examples, in which we successfully capture (quasi) steady-state solutions and propagating interfaces.

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Section: Lock Exchange Problemsupporting

confidence: 85%

“…In this example, taken from [6], the two layers are initially separated-the lighter water is on the left while the heavier one is on the right:…”

Section: Lock Exchange Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Central-Upwind Schemes for Two-Layer Shallow Water Equations

Kurganov¹,

Petrova²

2009

SIAM J. Sci. Comput.

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“…This model is formally derived in [1] in the two dimensional case. Such a model appears naturally in geophysical flows, see for example [2,3]. Let us give a non-exhaustive list of the results on the existence of solutions to equations describing the motion of fluid substances.…”

Section: Introductionmentioning

confidence: 99%

Strong solutions for a 1D viscous bilayer shallow water model

Zabsonré

Lucas

Ouédraogo

2013

Nonlinear Analysis: Real World Applications

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In this paper, we consider a viscous bilayer shallow water model in one space dimension that represents two superposed immiscible fluids. For this model, we prove the existence of strong solutions in a periodic domain. The initial heights are required to be bounded above and below away from zero and we get the same bounds for every time. Our analysis is based on the construction of approximate systems which satisfy the BD entropy and on the method developed by A. Mellet and A. Vasseur to obtain the existence of global strong solutions for the one dimensional Navier-Stokes equations.

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An efficient splitting technique for two-layer shallow-water model

Berthon

Foucher

Morales

2014

Numer. Methods Partial Differential Eq.

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We consider the numerical approximation of the weak solutions of the two-layer shallow-water equations. The model under consideration is made of two usual one-layer shallow-water model coupled by nonconservative products. Because of the nonconservative products of the system, which couple both one-layer shallow-water subsystems, the usual numerical methods have to consider the full model. Of course, uncoupled numerical techniques, just involving finite volume schemes for the basic shallow-water equations, are very attractive since they are very easy to implement and they are costless. Recently, a stable layer splitting technique was introduced [Bouchut and Morales de Luna, M2AN Math Model Numer Anal 42 (2008), 683-698]. In the same spirit, we exhibit new splitting technique, which is proved to be well balanced and non-negative preserving. The main benefit issuing from the here derived uncoupled method is the ability to correctly approximate the solution of very severe benchmarks.

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A two-layer finite volume model for flows through channels with irregular geometry: Computation of maximal exchange solutions

Cited by 14 publications

References 12 publications

Central-Upwind Schemes for Two-Layer Shallow Water Equations

Central-Upwind Schemes for Two-Layer Shallow Water Equations

Strong solutions for a 1D viscous bilayer shallow water model

An efficient splitting technique for two-layer shallow-water model

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