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Well‐balanced discontinuous Galerkin method and finite volume WENO scheme based on hydrostatic reconstruction for blood flow model in arteries
Author(s) -
Li Gang,
Delestre Olivier,
Yuan Li
Publication year - 2017
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4463
Subject(s) - finite volume method , hydrostatic equilibrium , discontinuous galerkin method , mathematics , flow (mathematics) , galerkin method , mathematical analysis , steady state (chemistry) , finite element method , geometry , mechanics , physics , quantum mechanics , chemistry , thermodynamics
Summary The blood flow model in arteries admits the steady state solutions, for which the flux gradient is nonzero, and is exactly balanced by the source term. In this paper, by means of hydrostatic reconstruction, we construct a high order discontinuous Galerkin method, which exactly preserves the dead‐man steady state, which is characterized by a discharge equal to zero (analogue to hydrostatic equilibrium). Moreover, the method maintains genuine high order of accuracy. Subsequently, we apply the key idea to finite volume weighted essentially non‐oscillatory schemes and obtain a well‐balanced finite volume weighted essentially non‐oscillatory scheme. Extensive numerical experiments are performed to verify the well‐balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.