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

Eduardo Abreu, John Pérez, Arthur Santo

Resumo


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 Dn 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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DOI: https://doi.org/10.5540/03.2018.006.01.0296

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