A Roe type energy balanced solver for 1D arterial blood flow and transport

• A novel solver able to handle with blood flow in arteries is presented in this work.
• This solver involves the presence of the source terms and ensures convergence to the exact solution.
• The numerical solver includes transport of chemicals without creating nonphysical oscillations in branching junctions.
• The proposed numerical scheme is compared with models of the systemic arterial tree published in literature.

The approximate solver presented in this work is based on the upwind discretization of the source terms and a genuinely Roe solver for the one-dimensional blood flow equations in arteries. This augmented solver involves the presence of the source terms, ensuring convergence to the exact solution by including an extra wave associated to the change in the material properties and the friction term. The resulting numerical scheme is energy-balanced, that is, ensures equilibrium in rest conditions and is able to ensure numerically a constant level of energy in steady cases with velocity. The resulting numerical solver allows simulating directly mass transport without creating non-physical oscillations. The numerical scheme is assessed using steady and unsteady problems with exact solutions and is compared with models of the systemic arterial tree published in literature.