  In this paper, we propose an arbitrarily high-order accurate fully
well-balanced numerical method for the one-dimensional blood flow model. The
developed method is based on a continuous representation of the solution and a
natural combination of the conservative and primitive formulations of the
studied PDEs. The degrees of freedom are defined as point values at cell
interfaces and moments of the conservative variables inside the cell, drawing
inspiration from the discontinuous Galerkin method. The well-balanced property,
in the sense of an exact preservation of both the zero and non-zero velocity
equilibria, is achieved by a well-balanced approximation of the source term in
the conservative formulation and a well-balanced residual computation in the
primitive formulation. To lowest (3rd) order this method reduces to the method
developed in [Abgrall and Liu, A New Approach for Designing Well-Balanced
Schemes for the Shallow Water Equations: A Combination of Conservative and
Primitive Formulations, arXiv preprint, arXiv:2304.07809]. Several numerical
tests are shown to prove its well-balanced and high-order accuracy properties.
