A numerical method for MHD Stokes model with applications in blood flow

The magnetohydrodynamic (MHD) Stokes equations have several applications in the field of biofluid dynamics. In the present study, we propose the staggered finite volume method (S-FVM) for MHD Stokes equations and establish its equivalence to a nonconforming finite element approximation. We also theoretically establish the convergence of the proposed S-FVM. The error estimation is carried out in an unstructured grid framework which is known for its flexibility and robustness in dealing with complex domains. The apriori estimate shows that the L2{L}_{2}-norm of the error for the pressure and velocity components is of order hh, the spacial grid size. After validating the numerical performance of the scheme against benchmark test cases, we do numerical simulations for the blood flow through an injured arteriole and analyze the influence of the magnetic force on hemodynamics in the arteriole under an injured condition.