Numerical simulating the blood flow model via nonhomogeneous Riemann solver scheme

Abstract

This paper examines a one-dimensional (1D) model that appears in arterial blood flow. The mathematical model for blood flow via arteries is similar to that of unstable incompressible flows in thin-walled collapsible tubes. We present the Riemann invariants of the suggested model, which is one of the fundamental components of this work. For numerical modeling of blood flow model, we present a nonhomogeneous Riemann solver (NHRS) technique. Next, we demonstrate the simulation of how pressure, velocity, and cross section area waveforms propagate through arteries. Specifically, we present numerical test cases with various initial data sets. In addition, we compare the NHRS scheme to the classic Rusanov, Lax–Friedrichs, and Roe schemes. Theoretical models for thin-walled collapsible tubes are applicable to a wide range of physiological events and may be used to build clinical devices for actual biomedical science. The NHRS method’s accuracy and efficiency are demonstrated by the numerical tests.

Keywords

• Blood flow model
• Conservation laws
• Riemann invariants
• NHRS scheme
• Roe scheme