A fifth-order finite difference well-balanced WENO scheme for a blood flow model in arteries

Document Type : Original Paper

Authors

1 School of Engineering Science, College of Engineering, University of Tehran, Iran

2 Department of Mathematics Education, Farhangian University, Tehran, Iran

Abstract

In this research work, a fifth-order well-balanced weighted essentially non-oscillatory scheme based on finite difference (FDWENO) was presented to solve a blood flow model in arteries. The FDWENO scheme preserves the balanced property for steady-state solutions while achieving fifth-order accuracy in smooth regions. Additionally, it does not exhibit spurious non-oscillatory behavior in discontinuous and shock areas. Several numerical examples were considered to investigate the balanced characteristic, fifth-order accuracy, and prevention of spurious oscillations. The results of these examples demonstrated the effectiveness of the newly developed scheme in this research.

Keywords

Main Subjects

References

[1] Abedian, R. A finite difference Hermite RBF-WENO scheme for hyperbolic conservation laws. Int. J. Numer. Meth. Fluids, 94:583–607, 2022.
[2] Abedian, R., Adibi, H., and Dehghan, M. A high-order symmetrical weighted hybrid ENO-flux limiter scheme for hyperbolic conservation laws. Comput. Phys. Commun., 185:106–127, 2014.
[3] Cavallini, N., Caleffi, V., and Coscia, V. Finite volume and WENO scheme in one-dimensional
vascular system modelling. Comput. Math. Appl., 56:2382–2397, 2008.
[4] Cavallini, N. and Coscia, V. One-dimensional modelling of venous pathologies: Finite volume and WENO schemes. In Advances in Mathematical Fluid Mechanics, Rannacher R, Sequeira A (eds). Springer: Berlin Heidelberg, 2010.
[5] Delestre, O. and Lagrée, P. Y. A well-balanced finite volume scheme for blood flow simulation. Int. J. Numer. Meth. Fluids, 72:177–205, 2013.
[6] Delestre, O., Lucas, C., Ksinant, P. A., Darboux, F., Laguerre, C., Vo, T. N. T., James, F., and Cordier, S. SWASHES: A compilation of shallow water analytic solutions for hydraulic and environmental studies. Int. J. Numer. Meth. Fluids, 72:269–300, 2013.
[7] Gottlieb, S., C.-W.Shu, and Tadmor, E. Strong stability-preserving high-order time discretization
methods. SIAM Rev., 43:89–112, 2001.
[8] Greenberg, J. M. and LeRoux, A. Y. A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal., 33:1–16, 1996.
[9] Jiang, G.-S. and Shu, C.-W. Efficient implementation of weighted ENO schemes. J. Comput. Phys.,126:202–228, 1996.
[10] Jiang, Y., Shu, C.-W., and Zhang, M. P. An alternative formulation of finite difference weighted
ENO schemes with Lax-Wendroff time discretization for conservation laws. SIAM J. Sci. Comput.,
35:A1137–A1160, 2013.
[11] Noelle, S., Xing, Y. L., and Shu, C.-W. High-order well-balanced schemes. In Numerical Methods for Balance Laws (G. Puppo and G. Russo eds). Quaderni di Matematica, 2010.
[12] Peer, A. A. I., Dauhoo, M. Z., Gopaul, A., and Bhuruth, M. A weighted ENO-flux limiter scheme
for hyperbolic conservation laws. Int. J. Comput. Math, 87:3467–3488, 2010.
[13] Ruuth, S. J. and Hundsdorfer, W. High-order linear multistep methods with general monotonicity and boundedness properties. J. Comput. Phys., 209:226–248, 2005.
[14] Xing, Y. L., Shu, C.-W., and Noelle, S. On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations. J. Sci. Comput., 48:339–349, 2011.
[15] Yao, Z., Li, G., and Gao, J. A high order well-balanced finite volume WENO scheme for a blood
flow model in arteries. East Asian J. Applied Math., 7:852–866, 2017.
Journal of Advanced Mathematical Modeling
Volume 13, Issue 3 - Serial Number 31
December 2023
Pages 435-447

Files

History

  • Receive Date: 25 September 2023
  • Revise Date: 29 November 2023
  • Accept Date: 25 December 2023

Share

How to cite

Statistics