A new finite volume approach for transport models and related applications with balancing source terms

Abreu, Eduardo; Lambert, Wanderson; Pérez, J. M.; Santo, Arthur Espírito

doi:10.1016/j.matcom.2016.12.012

Cited by 25 publications

(46 citation statements)

References 30 publications

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“…We consider a novel Lagrangian-Eulerian formulation that can be viewed as an extension of previous works [2,3,8] for practical construction of numerical solutions for balance law problems, but following innovative recent ideas introduced in [1] to construct weak asymptotic methods for scalar equations and systems of conservation law equations. For simplicity, we consider the particular scalar equation with u = u(x, t)…”

Section: Methodsmentioning

confidence: 99%

“…3 As in [3], the curves σ n j−1/2 (t) are not straight lines in general, but rather solutions of the local nonlinear differential equations [2,4,8]:…”

Section: Methodsmentioning

confidence: 99%

“…The extension of this construction follows naturally from the finite volume formulation of the linear Lagrangian-Eulerian scheme, as in [2,3,8], building block to construct local approximations such as…”

Section: Methodsmentioning

confidence: 99%

“…The Lagrangian-Eulerian approach is a promising tool for numerically solving partial differential equations of several types. Recently, in [2,3,8] such ideas were extended to a wide range of nonlinear purely hyperbolic conservation laws and balance laws scalar and systems. Here, we make use of polynomial reconstruction ideas into the Lagrangian-Eulerian novel approach, but keeping the scheme simple, fast and without any strong restriction over the source term other than integrability on the finite volume.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we make use of polynomial reconstruction ideas into the Lagrangian-Eulerian novel approach, but keeping the scheme simple, fast and without any strong restriction over the source term other than integrability on the finite volume. As in [2,3,8] the hyperbolic part of balance law is written in a space time divergence form so that the inherent conservation properties of the hyperbolic operator are used efficiently to build a numerical method to hyperbolic balance law problems [5]. Such framework presents an interesting property of being rather independent of a particular structure of the source terms.…”

Section: Introductionmentioning

confidence: 99%

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A conservative Lagrangian-Eulerian finite volume approximation method for balance law problems

Abreu¹,

Pérez²,

Santo³

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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We present a simple numerical method based on a Lagrangian-Eulerian framework for approximate solutions of nonlinear balance law problems. This framework has been used for numerically solving partial differential equations of several types, such as hyperbolic conservation laws [3,8], balance laws problems [4]. As in [3,5] the mass conservation takes place in the space-time volume D n j , and this region in the form of [3] is used to define naturally a balance law. This balance law is the central idea to build a efficient numerical method to approximate solution to balance law problems. Verification of the technique is also made by comparison with analytical solutions when they are available.

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Section: Methodsmentioning

confidence: 99%

“…3 As in [3], the curves σ n j−1/2 (t) are not straight lines in general, but rather solutions of the local nonlinear differential equations [2,4,8]:…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations