on the continuity of mean total normal stress in geometrical multiscale cardiovascular problems in this work an iterative strategy to implicitly couple dimensionally heterogeneous blood flow models accounting for the continuity of mean total normal stress at interface boundaries is developed conservation of mean total normal stress in the coupling of heterogeneous models is mandatory to satisfy energetic consistency between them nevertheless existing methodologies are based on modifications of the navier stokes variational formulation which are undesired when dealing with fluid structure interaction or black box codes the proposed methodology makes possible to couple one dimensional and three dimensional fluid structure interaction models enforcing the continuity of mean total normal stress while just imposing flow rate data or even the classical neumann boundary data to the models this is accomplished by modifying an existing iterative algorithm which is also able to account for the continuity of the vessel area when required comparisons are performed to assess differences in the convergence properties of the algorithms when considering the continuity of mean normal stress and the continuity of mean total normal stress for a wide range of flow regimes finally examples in the physiological regime are shown to evaluate the importance or not of considering the continuity of mean total normal stress in hemodynamics simulations

uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries abstract we present a stochastic finite volume ader sfv ader methodology for uncertainty quantification uq in the general framework of systems of hyperbolic balance laws with uncertainty in parameters the resulting method is weakly intrusive meaning that deterministic solvers need minor modifications to include random contributions and has no theoretical accuracy barrier an illustration of the second order version for the viscous burgers equation with uncertain viscosity coefficient is first given in detail under different deterministic initial conditions the attainment of the theoretically expected convergence rate is demonstrated empirically results and features of our scheme are discussed we then extend the sfv ader method to a non linear hyperbolic system with source terms that models one dimensional blood flow in arteries assuming uncertainties in a set of parameters of the problem results are then compared with measurements in a well defined 1 1 experimental replica of the network of largest arteries in the human systemic circulation for a 99 confidence level severe influence of parameter fluctuations is seen in pressure profiles while secondary effects on flow rate profiles become visible particularly in terminal branches results suggest that the proposed methodology could successfully be applied to other physical problems involving hyperbolic balance laws

black box decomposition approach for computational hemodynamics one dimensional models abstract increasing efforts exist in integrating different levels of detail in models of the cardiovascular system for instance one dimensional representations are employed to model the systemic circulation in this context effective and black box type decomposition strategies for one dimensional networks are needed so as to i employ domain decomposition strategies for large systemic models 1d 1d coupling and ii provide the conceptual basis for dimensionally heterogeneous representations 1d 3d coupling among various possibilities the strategy proposed in this article works for both of these two scenarios though the several applications shown to illustrate its performance focus on the 1d 1d coupling case a one dimensional network is decomposed in such a way that each coupling point connects two and not more of the sub networks at each of the m connection points two unknowns are defined the flow rate and pressure these 2 m unknowns are determined by 2 m equations since each sub network provides one non linear equation per coupling point it is shown how to build the 2 m 2 m non linear system with arbitrary and independent choice of boundary conditions for each of the sub networks the idea is then to solve this non linear system until convergence which guarantees strong coupling of the complete network in other words if the non linear solver converges at each time step the solution coincides with what would be obtained by monolithically modeling the whole network the decomposition thus imposes no stability restriction on the choice of the time step size effective iterative strategies for the non linear system that preserve the black box character of the decomposition are then explored several variants of matrix free broyden s and newton gmres algorithms are assessed as numerical solvers by comparing their performance on sub critical wave propagation problems which range from academic test cases to realistic cardiovascular applications a specific variant of broyden s algorithm is identified and recommended on the basis of its computer cost and reliability

new low roundoff noise realizations of second order digital filter sections new structures for second order filter sections are proposed that yield lower output roundoff noise than many well known structures and are free of zero input limit cycle oscillations these new low roundoff structures are based on these suggested by bomar 1989 and are obtained by putting the constraint that some of the state space coefficients be sum of two power of two terms numerical results are included to illustrate the performance of the proposed structures for narrow band filters and to compare them with other structures

iterative strong coupling of dimensionally heterogeneous models in this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone the novel methodology takes full advantage of the small number of interface unknowns in this kind of problems existing algorithms can be viewed as variants of the natural staggered algorithm in which each domain transfers function values to the other and receives fluxes or forces and vice versa this natural algorithm is known as dirichlet to neumann in the domain decomposition literature essentially we propose a framework in which this algorithm is equivalent to applying gauss seidel iterations to a suitably defined linear or nonlinear system of equations it is then immediate to switch to other iterative solvers such as gmres or other krylov based method which we assess through numerical experiments showing the significant gain that can be achieved indeed the benefit is that an extremely flexible automatic coupling strategy can be developed which in addition leads to iterative procedures that are parameter free and rapidly converging further in linear problems they have the finite termination property copyright 2009 john wiley sons ltd

low roundoff noise and normal realizations of fixed point iir digital filters explicit design and performance equations are given in terms of the parameters of the desired transfer function h z for two classes of realizations these realizations offer the digital circuit designer an alternative to the usual designs based on direct forms in addition to low roundoff noise these new realizations offer other desirable properties such as low coefficient sensitivities and freedom from overflow oscillations numerical results are presented which detail the design process and verify the theory

dtn based mixed dimensional coupling using a boundary stress recovery technique abstract a new computational approach for the mixed dimensional modeling of time harmonic waves in elastic structures is proposed a two dimensional 2d structure is considered which includes a part that is assumed to behave in a one dimensional 1d way the 2d and 1d structural regions are discretized by using 2d and 1d finite element fe formulations the hybrid model if designed properly is much more efficient than the standard 2d model taken for the entire problem one important issue related to such hybrid 2d 1d models is the way the 2d 1d coupling is done and the coupling error generated here three closely related coupling methods are considered they are all based on the dirichlet to neumann dtn map associated with the 1d problem on the interface the first coupling method is the dtn method in its usual form where the dtn map is calculated numerically and where the 1d and 2d problems are solved separately the second coupling method is the one devised by carka mear and landis cml which is equivalent to the former one but in which the 2d and 1d interface solutions are solved for simultaneously in the third coupling method the dtn map is enforced on the interface iteratively direct application of these three methods results in low accuracy as a recent study shows therefore these methods are used here in conjunction with a boundary stress recovery bsr technique originally proposed by hughes which provides the same order of accuracy for the stress as for the primary variable the performance of the three methods is demonstrated and they are compared via numerical examples conclusions are drawn on their relative merit

on the accuracy of the rotation form in simulations of the navier stokes equations the rotation form of the navier stokes equations nonlinearity is commonly used in high reynolds number flow simulations it was pointed out by a few authors and not widely known apparently that it can also lead to a less accurate approximate solution than the usual email protected u form we give a different explanation of this effect related to i resolution of the bernoulli pressure and ii the scaling of the coupling between velocity and pressure error with respect to the reynolds number we show analytically that i the difference between the two nonlinearities is governed by the difference in the resolution of the bernoulli and kinematic pressures and ii a simple linear grad div stabilization ameliorates much of the bad scaling of the velocity error with respect to re the rotation form does have superior conservation properties to the alternatives and it appears to be amenable to more efficient preconditioners thus the rotational form with grad div stabilization is a promising method we also give experiments that show bad velocity approximation is tied to poor pressure resolution in either form

sensitivity analysis in kinematically incompatible models abstract a natural question that arises when working with the so called kinematically incompatible models is about the positioning of the internal artificial boundary that splits the domain of analysis into the sub domains for which the different incompatible models are established although the experience in modeling might provide an ad hoc solution to such matter it may also draw misleading conclusions here the sensitivity analysis furnishes a systematic and reliable framework to study the impact of the positioning of the artificial boundary over the solution of the problem in this sense the present work is concerned with the sensitivity analysis of the variational formulation corresponding to the kinematically incompatible models when the boundary over which the incompatibility between the models takes place is changed assuming the presence of a discontinuity in the fields over a given interface between two incompatible models this analysis allows to measure the sensitivity of a given cost functional when the location of such interface is changed the application for which this analysis is envisaged is to assess the correctness or incorrectness in the definition of the positioning of such coupling interface between dimensionally heterogeneous domains also some numerical results are provided to give numerical evidence of the usefulness of the present tool

on the potentialities of 3d 1d coupled models in hemodynamics simulations this work comprises a step towards the quantitative and qualitative analysis of coupled local and global hemodynamics phenomena in the arterial system the aim of this work is to present some numerical examples to put in evidence the importance of the use of 3d 1d coupled models in hemodynamics problems when carrying out simulations of rather complex situations accordingly some cases for which classical modeling cannot be applied are identified and solved the results obtained here allow us to assess some interrelations between local pointwise quantities defined at the level of the 3d model and global mean quantities defined at the level of the 1d model

outflow boundary conditions for three dimensional finite element modeling of blood flow and pressure in arteries flow and pressure waves emanate from the heart and travel through the major arteries where they are damped dispersed and reflected due to changes in vessel caliber tissue properties and branch points as a consequence solutions to the governing equations of blood flow in the large arteries are highly dependent on the outflow boundary conditions imposed to represent the vascular bed downstream of the modeled domain the most common outflow boundary conditions for three dimensional simulations of blood flow are prescribed constant pressure or traction and prescribed velocity profiles however in many simulations the flow distribution and pressure field in the modeled domain are unknown and cannot be prescribed at the outflow boundaries an alternative approach is to couple the solution at the outflow boundaries of the modeled domain with lumped parameter or one dimensional models of the downstream domain we previously described a new approach to prescribe outflow boundary conditions for simulations of blood flow based on the dirichlet to neumann and variational multiscale methods this approach termed the coupled multidomain method was successfully applied to solve the non linear one dimensional equations of blood flow with a variety of models of the downstream domain this paper describes the extension of this method to three dimensional finite element modeling of blood flow and pressure in the major arteries outflow boundary conditions are derived for any downstream domain where an explicit relationship of pressure as a function of flow rate or velocities can be obtained at the coupling interface we developed this method in the context of a stabilized semi discrete finite element method flow rate and pressure distributions are shown for different boundary conditions to illustrate the dramatic influence of alternative boundary conditions on these quantities

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

explicit strategies for incompressible fluid structure interaction problems nitsche type mortaring versus robin robin coupling we discuss explicit coupling schemes for fluid structure interaction problems where the added mass effect is important in this paper we show the close relation between coupling schemes using nitsche s method and a robin robin type coupling in the latter case the method may be implemented either using boundary integrals of the stresses or the more conventional discrete lifting operators recalling the explicit method proposed in comput methods appl mech engrg 198 5 8 766 784 2009 we make the observation that this scheme is stable under a hyperbolic type cfl condition but that optimal accuracy imposes a parabolic type cfl conditions due to the splitting error two strategies to enhance the accuracy of the coupling scheme under the hyperbolic cfl condition are suggested one using extrapolation and defect correction and one using a penalty free non symmetric nitsche method finally we illustrate the performance of the proposed schemes on some numerical examples in two and three space dimensions

numerical method of characteristics for one dimensional blood flow mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one dimensional nonlinear hyperbolic system describing flow in a single vessel this model is often simulated by computationally intensive methods like finite elements and discontinuous galerkin while some recent applications require more efficient approaches e g for real time clinical decision support phenomena occurring over multiple cardiac cycles iterative solutions to optimization inverse problems and uncertainty quantification further the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes we address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous galerkin implementation lastly we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant

a finite element solver and energy stable coupling for 3d and 1d fluid models the paper develops a solver based on conforming finite element method fem for a 3d 1d coupled incompressible flow problem new coupling conditions are introduced to ensure a suitable bound for the cumulative energy of the model we study the stability and the accuracy of the discretization method and the performance of some state of the art linear algebraic solvers for such flow configurations motivated by the simulation of the flow over inferior vena cava ivc filter we consider the coupling of a 1d fluid model and a 3d fluid model posed in a domain with anisotropic inclusions the relevance of our approach to realistic cardiovascular simulations is demonstrated by computing blood flows over a model ivc filter

new second order state space structures for realizing low roundoff noise digital filters several new second order state space digital filter structures are introduced each of the new structures requires one or two less multiplies than the minimum noise structure while achieving a round off noise performance which is nearly as good thus they provide an excellent means of realizing second order subfilters when such subfilters are used to construct nth order filters the reduction in multiplies as compared to using minimum noise subfilters is from about 4n to about 3n an approach to developing simple algebraic real arithmetic design equations for l 2 norm scaled second order structures is presented and then applied to obtaining design equations for the new structures and for the minimum noise structure

a discontinuous galerkin method with nonoverlapping domain decomposition for the stokes and navier stokes problems a family of discontinuous galerkin finite element methods is formulated and analyzed for stokes and navier stokes problems an inf sup condition is established as well as optimal energy estimates for the velocity and l 2 estimates for the pressure in addition it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces

mixed stabilized finite element method for the stationary stokes dual permeability fluid flow model abstract this article proposes a stabilized mixed finite element method to investigate the stationary stokes dual permeability fluid flow model which couples the free flow region modeled by the stokes equations and dual porous medium modeled by the dual permeability equations the robust mixed finite element method developed here does not require any lagrange multiplier but a mesh dependent stabilization term with a relaxation parameter is introduced essentially to ensure the numerical stability of the algorithm the well posedness and the optimal error estimate of the finite element scheme are derived furthermore an iterative scheme is developed based on the traditional coupled algorithm we prove that the iterative scheme converges to the coupled scheme and the rate of convergence is estimated the feature of the model is illustrated by considering five numerical examples which reveal the applicability of the fluid flow model as well as the accuracy of the numerical method

modeling dimensionally heterogeneous problems analysis approximation and applications in the present work a general theoretical framework for coupled dimensionally heterogeneous partial differential equations is developed this is done by recasting the variational formulation in terms of coupling interface variables in such a general setting we analyze existence and uniqueness of solutions for both the continuous problem and its finite dimensional approximation this approach also allows the development of different iterative substructuring solution methodologies involving dimensionally homogeneous subproblems numerical experiments are carried out to test our theoretical results

computer modeling of cardiovascular fluid structure interactions with the deforming spatial domain stabilized space time formulation hemodynamic factors such as the wall shear stress are believed to affect a number of cardiovascular diseases including atherosclerosis and aneurysm since resolving phenomena in a living human body is currently beyond the capabilities of in vivo measurement techniques computer modeling is expected to play an important role in gaining a better understanding of the relationship between the cardiovascular diseases and the hemodynamic factors we have developed a computer modeling technique for cardiovascular hemodynamic simulations with this modeling technique patient specific 3d geometry of an artery can be analyzed we take into account some of the important factors in human body for the purpose of demonstrating in vivo situations in a virtual world the interaction between the blood flow and the deformation of the arterial walls is a factor that we are specifically focusing on for such fluid structure interactions we have developed a computer modeling tool based on the deforming spatial domain stabilized space time dsd sst formulation this simulation tool is applied to a patient specific model under pulsatile blood flow conditions the simulations show that the flow behavior with compliant arterial walls is different from what we see with rigid arterial walls consequently the distribution of the wall shear stress on the compliant arterial walls is significantly different from that on the rigid arterial walls we deduce that the compliance of the arterial walls needs to be taken into account in cardiovascular hemodynamic simulations and the computer modeling tool we have developed can be effective in investigation of cardiovascular diseases

a stabilized nitsche overlapping mesh method for the stokes problem we develop a nitsche based formulation for a general class of stabilized finite element methods for the stokes problem posed on a pair of overlapping non matching meshes by extending the least squares stabilization to the overlap region we prove that the method is stable consistent and optimally convergent to avoid an ill conditioned linear algebra system the scheme is augmented by a least squares term measuring the discontinuity of the solution in the overlap region of the two meshes as a consequence we may prove an estimate for the condition number of the resulting stiffness matrix that is independent of the location of the interface finally we present numerical examples in three spatial dimensions illustrating and confirming the theoretical results

a unified variational approach for coupling 3d 1d models and its blood flow applications in this work we propose an extended variational formulation in order to handle the problem of the flow of an incompressible fluid in compliant vessels with discontinuous fields this approach makes possible to tackle in a consistent variational manner problems like the coupling between models of different dimensionality the main ideas of the work are presented for a simple heat transfer problem and then are used in the context of modelling blood flow in large vessels a computational implementation of the proposed formulation is also shown and discussed by presenting examples of practical applications

fractional step schemes for the coupling of distributed and lumped models in hemodynamics in three dimensional 3d blood flow simulations lumped parameter models 0d are often used to model the neglected parts of the downstream circulatory system we analyze two 3d 0d coupling approaches in which a fractional step projection scheme is used in the fluid our analysis shows that explicit approaches might yield numerical instabilities particularly in the case of realistic geometries with multiple outlets we introduce and analyze an implicitly 3d 0d coupled formulation with enhanced stability properties and which requires a negligible additional computational cost furthermore we also address the extension of these methods to fluid structure interaction problems the theoretical stability results are confirmed by meaningful numerical experiments in patient specific geometries coming from medical imaging

a partitioned fluid structure algorithm for elastic thin valves with contact we present a numerical method to simulate the movements of a thin valve immersed in an incompressible viscous fluid the fluid and structure meshes are not matching the kinematic continuity is imposed using lagrange multipliers the method therefore belongs to the fictitious domain fd family this approach allows very large displacements we propose a partitioned fluid structure algorithm which keeps the fluid and structure solvers independent and which is able to manage contact without assuming that the structure solvers include contact capabilities various numerical tests are proposed in particular when the displacement is moderate we show that the results are in good agreement with arbitrary lagrangian eulerian ale simulations we then present results with contact on a rigid wall finally we show that the proposed approach can be mixed with ale when the wall is elastic

analytic continuation of the doubly periodic barnes zeta function the aim of this work is to study the analytic continuation of the doubly periodic barnes zeta function by using a suitable complex integral representation as a starting point we find the meromorphic extension of the doubly periodic barnes zeta function to the entire complex plane in terms of a real integral containing the hurwitz zeta function and the first jacobi theta function these allow us to explicitly give expressions for the derivative at all non positive integer points

numerical treatment of defective boundary conditions for the navier stokes equations we present a formulation for accommodating defective boundary conditions for the incompressible navier stokes equations where only averaged values are prescribed on measurable portions of the boundary in particular we consider the case where the flow rate is imposed on several domain sections this methodology has an interesting application in the numerical simulation of flow in blood vessels when only a reduced set of boundary data are generally available for the upstream and downstream sections

multidimensional modelling for the carotid artery blood flow abstract in this work a multidimensional 3d 1d fem model of the whole arterial tree is implemented it comprises a 3d compliant model of the carotid bifurcation coupled with a 1d model for the remaining part of the arterial tree with this approach difficulties arising from the treatment of boundary conditions for the 3d model are naturally handled the navier stokes equations are used as the governing equations for the blood flow while an elastic compliant model is implemented for the arterial wall also the a l e formulation is considered within the 3d blood regions taking into account the domain deformations produced by the moving artery wall this 3d model is complemented with a 1d model of the entire arterial tree in order to appropriately set inflow and outflow boundary conditions for the former the reduced 1d model solves the momentum and continuity equations in compliant tubes so as to reproduce the propagation of the pressure pulse in the arterial network also a volumetric flow rate is imposed at the inlet to model the systolic work of the heart the peripheral arteriole beds are simulated with the well known lumped windkessel model a standard geometry of the carotid bifurcation is discretized with p1 bubble p1 tetrahedral elements the obtained results properly reproduce the general flow patterns reported in the literature very good agreement between the outcomes of a pure 1d model and those of the combined multidimensional model was obtained it is worth noting that this kind of model may provide useful information to gain understanding in the genesis and development of arterial diseases

augmented lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three dimensional finite element simulations of blood flow in three dimensional blood flow simulations of the cardiovascular system velocity and pressure fields in the computational domain are highly affected by outlet boundary conditions this fact has motivated the development of novel methods to couple three dimensional computational domains with one dimensional numerical models or alternatively with zero dimensional or one dimensional analytic models in all such methods described to date whether they are explicit or implicit the relationship between flow and pressure at the outlet boundary is enforced weakly this coupling does not include any constraints on the shape of the velocity profiles nor on the distribution of pressure at the interface as a result there remain some classes of problems that are at best difficult to solve and at worst intractable with current numerical methods for simulating blood flow these include problems with significant flow reversal during part of the cardiac cycle or geometric complexity in the proximity of the outlet of the computational domain we have implemented a novel method to resolve these challenging problems whereby an augmented lagrangian method is used to enforce constraints on the shape of the velocity profile at the interface between the upstream computational domain and the downstream analytic domain these constraints on the shape of the velocity profile are added to the coupled multidomain method in order to implicitly couple the computational domain with downstream analytic models in this study an axisymmetric profile is imposed after ensuring that each constrained outlet boundary is circular we demonstrate herein that including constraints on the shape of the velocity profile does not affect velocity and pressure fields except in the immediate vicinity of the constrained outlet boundaries furthermore this new method enables the solution of problems which diverged with an unconstrained method

finite element simulation of blood flow in the cerebral artery abstract the purpose of the paper is to develop a numerical simulation system for the clinical study of a cerebral aneurysm this paper presents the system which consists of three processes pre processing numerical simulation and post processing in the pre processing process the three dimensional solid model was constructed from the computed tomography ct angiography raw data the finite element method fem is used in order to simulate flow in a complicated geometry the simulation is conducted to investigate hemodynamics of blood flow in the carotid siphon under real flow conditions measured by doppler ultrasound velocimetry technique the results are visualized for a better understanding of the flow characteristics such as distributions of the flow pattern and the wall shear stress in the carotid siphon

a three term theta function identity and its applications in this paper we establish a three term theta function identity using the complex variable theory of elliptic functions this simple identity in form turns out to be quite useful and it is a common origin of many important theta function identities from which the quintuple product identity and one general theta function identity related to the modular equations of the fifth order and many other interesting theta function identities are derived we also give a new proof of the addition theorem for the weierstrass elliptic function an identity involving the products of four theta functions is given and from which one theta function identity by mccullough and shen is derived the quintuple product identity is used to derive some eisenstein series identities found in ramanujan s lost notebook and our approach is different from that of berndt and yee the proofs are self contained and elementary

brain venous haemodynamics neurological diseases and mathematical modelling a review behind medicine m is physiology p behind physiology is physics p and behind physics is always mathematics m for which i expect that the symmetry of the quadruplet mppm will be compatible with the characteristic bias of hyperbolic partial differential equations a theme of this paper i start with a description of several idiopathic brain pathologies that appear to have a strong vascular dimension of which the most prominent example considered here is multiple sclerosis the most common neurodegenerative disabling disease in young adults other pathologies surveyed here include retinal abnormalities transient global amnesia transient monocular blindness meniere s disease and idiopathic parkinson s disease it is the hypothesised vascular aspect of these conditions that links medicine to mathematics through fluid mechanics in very complex networks of moving boundary blood vessels the second part of this paper is about mathematical modelling of the human cardiovascular system with particular reference to the venous system and the brain a review of a recently proposed multi scale mathematical model then follows consisting of a one dimensional hyperbolic description of blood flow in major arteries and veins coupled to a lumped parameter description of the remaining main components of the human circulation derivation and analysis of the hyperbolic equations is carried out for blood vessels admitting variable material properties and with emphasis on the venous system a much neglected aspect of cardiovascular mathematics veins unlike their arterial counterparts are highly deformable even collapsible under mild physiological conditions we address mathematical and numerical challenges regarding the numerical analysis of the hyperbolic pdes we deploy a modern non linear finite volume method of arbitrarily high order of accuracy in both space and time the ader methodology in vivo validation examples and brain haemodynamics computations are shown we also point out two preliminary but important new findings through the use of mathematical models namely that extracranial venous strictures produce chronic intracranial venous hypertension and that augmented pressure increases the blood vessel wall permeability

explicit coupling schemes for a fluid fluid interaction problem arising in hemodynamics in this work we propose a new approach to the loosely coupled time marching of fluid fluid interaction problems involving the incompressible navier stokes equations the methods combine a specific explicit robin robin treatment of the interface coupling with a weakly consistent interface pressure stabilization in time a priori energy estimates guaranteeing stability of the splitting are obtained for a total pressure formulation of the coupled problem the performance of the proposed schemes is illustrated on several numerical experiments related to simulation of aortic blood flow