Numerical approximation of living-man steady state solutions for blood flow in arteries using a well-balanced discontinuous Galerkin scheme

Abstract

This study developed a well-balanced discontinuous Galerkin method for the one-dimensional blood flow model capable of preserving zero and non-zero velocity steady state solutions. The strategy used was to incorporate the source term into the flux function to rewrite the law of balance in a conservative form, in terms of global equilibrium variables that remained constant in space and time under steady states. Subsequently, the conservative variables were recalculated using the equilibrium variables. Recently, this concept was applied to shallow water and the Euler equations of gas dynamics. Numerical tests verified the well-balanced property of the designed scheme and its ability to capture small steady-state perturbations on relatively coarse meshes accurately.

Keywords

• Well-balanced methods
• Blood flow models
• Non-trivial steady solutions