An Explicit Diffusion Operator for High-Order Entropy-Stable Schemes in an Augmented 1D Blood Flow Model

We propose an entropy-stable numerical scheme for an augmented one-dimensional blood flow model by constructing an explicit diffusion operator independent of the reconstruction method used for the scaled entropy variables. The diffusion term plays an important role in entropy-stable schemes, i.e., schemes satisfying a discrete entropy inequality. In general, the diffusion operator involves a diffusion matrix that depends on the scaled right eigenvectors and on the reconstruction of the scaled variables. We derive a simple, explicit expression for this operator that avoids computing the full set of scaled eigenvectors. The performance of the scheme is assessed through numerical experiments, focusing on Riemann problems, which confirm its ability to capture shock waves accurately and provide numerical evidence of entropy decay for non-smooth solutions.