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The goal of this work is to develop a novel splitting approach for thenumerical solution of multiscale problems involving the coupling between Stokesequations and ODE systems, as often encountered in blood flow modelingapplications. The proposed algorithm is based on a semi-discretization in timebased on operator splitting, whose design is guided by the rationale ofensuring that the physical energy balance is maintained at the discrete level.As a result, unconditional stability with respect to the time step choice isensured by the implicit treatment of interface conditions within the Stokessubsteps, whereas the coupling between Stokes and ODE substeps is enforced viaappropriate initial conditions for each substep. Notably, unconditionalstability is attained without the need of subiterating between Stokes and ODEsubsteps. Stability and convergence properties of the proposed algorithm aretested on three specific examples for which analytical solutions are derived.

journal of computational physics

Energy-based operator splitting approach for the time discretization of  coupled systems of partial and ordinary differential equations for fluid  flows: The Stokes case