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arXiv · 2404.18124

An Arbitrarily High-Order Fully Well-balanced Hybrid Finite Element-Finite Volume Method for a One-dimensional Blood Flow Model

Yongle Liu·Wasilij Barsukow
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Abstract

We propose an arbitrarily high-order accurate, fully well-balanced numerical method for the one-dimensional blood flow model. The developed method employs a continuous solution representation, combining conservative and primitive formulations. Degrees of freedom are point values at cell interfaces and moments of conservative variables within cells. \bla{The well-balanced property -- ensuring exact preservation of zero and non-zero velocity steady-state solutions while accurately capturing small perturbations -- is achieved through two key components. First, in the evolution of the moments, a local reference steady-state solution is obtained and subtracted. Second, the point value update happens in equilibrium variables. Extensive numerical tests are conducted to validate the preservation of various steady-state solutions, robust capturing small perturbations to such solutions, and high-order accuracy for both smooth and discontinuous solutions.

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Yongle Liu, Wasilij Barsukow. 2025-02-05. An Arbitrarily High-Order Fully Well-balanced Hybrid Finite Element-Finite Volume Method for a One-dimensional Blood Flow Model. https://arxiv.org/abs/2404.18124

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