a domain decomposition method based on weighted interior penalties for advection diffusion reaction problems we propose a domain decomposition method for advection diffusion reaction equations based on nitsche s transmission conditions the advection dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over element boundaries we prove the convergence of the finite element solutions of the discrete problem to the exact solution and propose a parallelizable iterative method the convergence of the resulting domain decomposition method is proved and this result holds true uniformly with respect to the diffusion parameter the numerical scheme that we propose here can thus be applied straightforwardly to diffusion dominated advection dominated and hyperbolic problems some numerical examples are presented in different flow regimes showing the influence of the stabilization parameter on the performance of the iterative method and we compare our method with some other domain decomposition techniques for advection diffusion equations

a nitsche stabilized finite element method for frictional sliding on embedded interfaces part ii intersecting interfaces abstract we extend the weighted nitsche s method proposed in the first part of this study to include multiple intersecting embedded interfaces these intersections arise either inside a computational domain where two internal interfaces intersect or on the boundary of the computational domain where an internal interface intersects with the external boundary we propose a variational treatment of both the interfacial kinematics and the external dirichlet constraints within nitsche s framework we modify the numerical analysis to account for these intersections and provide an explicit expression for the weights and the method parameters that arise in the nitsche variational form in the presence of junctions finally we demonstrate the performance of the method for both perfectly tied interfaces and perfectly plastic sliding interfaces through several benchmark examples

resolution of the 2d navier stokes equations in velocity vorticity form by means of an influence matrix technique abstract an influence matrix technique is proposed to enforce both the continuity equation and the definition of the vorticity in the treatment of the 2d incompressible navier stokes equations it is shown and supported by numerical experiments that at each time step the divergence is actually equal to zero within machine accuracy the same result is obtained for the definition of the vorticity

generalized fictitious methods for fluid structure interactions analysis and simulations we present a new fictitious pressure method for fluid structure interaction fsi problems in incompressible flow by generalizing the fictitious mass and damping methods we published previously in 1 the fictitious pressure method involves modification of the fluid solver whereas the fictitious mass and damping methods modify the structure solver we analyze all fictitious methods for simplified problems and obtain explicit expressions for the optimal reduction factor convergence rate index at the fsi interface 2 this analysis also demonstrates an apparent similarity of fictitious methods to the fsi approach based on robin boundary conditions which have been found to be very effective in fsi problems we implement all methods including the semi implicit robin based coupling method in the context of spectral element discretization which is more sensitive to temporal instabilities than low order methods however the methods we present here are simple and general and hence applicable to fsi based on any other spatial discretization in numerical tests we verify the selection of optimal values for the fictitious parameters for simplified problems and for vortex induced vibrations viv even at zero mass ratio for ever resonance we also develop an empirical a posteriori analysis for complex geometries and apply it to 3d patient specific flexible brain arteries with aneurysms for very large deformations we demonstrate that the fictitious pressure method enhances stability and convergence and is comparable or better in most cases to the robin approach or the other fictitious methods

partitioning strategies for the interaction of a fluid with a poroelastic material based on a nitsche s coupling approach abstract we develop a computational model to study the interaction of a fluid with a poroelastic material the coupling of stokes and biot equations represents a prototype problem for these phenomena which feature multiple facets on one hand it shares common traits with fluid structure interaction on the other hand it resembles the stokes darcy coupling for these reasons the numerical simulation of the stokes biot coupled system is a challenging task the need of large memory storage and the difficulty to characterize appropriate solvers and related preconditioners for the equations at hand are typical shortcomings of classical discretization methods applied to this problem such as the finite element method for spatial discretization and finite differences for time stepping the application of loosely coupled time advancing schemes mitigates these issues because it allows to solve each equation of the system independently with respect to the others at each time step in this work we develop and thoroughly analyze a loosely coupled scheme for stokes biot equations the scheme is based on nitsche s method for enforcing interface conditions once the interface operators corresponding to the interface conditions have been defined time lagging allows us to build up a loosely coupled scheme with good stability properties the stability of the scheme is guaranteed provided that appropriate stabilization operators are introduced into the variational formulation of each subproblem the error of the resulting method is also analyzed showing that splitting the equations pollutes the optimal approximation properties of the underlying discretization schemes in order to restore good approximation properties while maintaining the computational efficiency of the loosely coupled approach we consider the application of the loosely coupled scheme as a preconditioner for the monolithic approach both theoretical insight and numerical results confirm that this is a promising way to develop efficient solvers for the problem at hand

finite element approximation of transmission conditions in fluids and solids introducing boundary subgrid scales terms involving jumps of stresses on boundaries are proposed for the finite element approximation of the stokes problem and the linear elasticity equations these terms are designed to improve the transmission conditions between subdomains at three different levels namely between the element domains between the interfaces in homogeneous domain interaction problems and at the interface between the fluid and the solid in fluid structure interaction problems the benefits in each case are respectively the possibility of using discontinuous pressure interpolations in a stabilized finite element approximation of the stokes problem a stronger enforcement of the stress continuity in homogeneous domain decomposition problems and a considerable improvement of the behavior of iterative schemes to couple the fluid and the solid in fluid structure integration algorithms the motivation to introduce these terms stems from a decomposition of the unknown into a conforming and a non conforming part a hybrid formulation for the latter and a simple approximation for the unknowns involved in the hybrid problem copyright 2011 john wiley sons ltd

accurate navier stokes investigation of transitional and turbulent flows in a circular pipe a new fast accurate and roundoff error robust numerical technique for integrating unsteady incompressible navier stokes equations in cylindrical coordinates is presented the algorithm is based on a special change of dependent variables which avoids the singularity problem and provides high accuracy and computational efficiency accuracy and stability of the method are thoroughly tested for the model problem of transitional and turbulent flows in an infinite circular pipe verification of the algorithm includes two issues first spectral characteristics of the hagen poiseuille flow stability problem are compared with those of the discrete linearized navier stokes operator secondly the results of direct navier stokes simulation of all stages of laminar turbulent transition in a circular pipe at reynolds number of 4000 are presented time evolution of finite amplitude disturbances of laminar flow was calculated until the statistically stationary turbulent flow regime was established in addition to common statistical analysis the possibility of turbulence description by means of velocity fields having certain symmetries is examined thus the algorithm presented seems to be a ready to use robust tool for accurate investigation and further parametric studies of both transition mechanisms and fully developed turbulent flow regimes

convergence analysis of a projection semi implicit coupling scheme for fluid structure interaction problems in this paper we provide a convergence analysis of a projection semi implicit scheme for the simulation of fluid structure systems involving an incompressible viscous fluid the error analysis is performed on a fully discretized linear coupled problem a finite element approximation and a semi implicit time stepping strategy are respectively used for space and time discretization the fluid is described by the stokes equations the structure by the classical linear elastodynamics equations linearized elasticity plate or shell models and all changes of geometry are neglected we derive an error estimate in finite time and we prove that the time discretization error for the coupling scheme is at least sqrt delta t finally some numerical experiments that confirm the theoretical analysis are presented

compatibility conditions for time dependent partial differential equations and the rate of convergence of chebyshev and fourier spectral methods abstract compatibility conditions for partial differential equations pdes are an infinite set of relations between the initial conditions the pde and the boundary conditions which are necessary and sufficient for the solution to be c that is infinitely differentiable everywhere on the computational domain including the boundaries since the performance of chebyshev spectral and spectral element methods is dramatically reduced when the solution is not c one would expect that the compatibility conditions would be a major theme in the spectral literature instead it has been completely ignored therefore we pursue three goals here first we present a proof of the compatibility conditions in a simplified form that does not require functional analysis second we analyze the connection between the compatibility conditions and the rate of convergence of chebyshev methods lastly we describe strategies for slightly adjusting initial conditions so that the compatibility conditions are satisfied

a loosely coupled scheme for the interaction between a fluid elastic structure and poroelastic material abstract we model the interaction between an incompressible viscous fluid thin elastic structure and a poroelastic material the poroelastic material is modeled using the biot s equations of dynamic poroelasticity the fluid elastic structure and the poroelastic material are fully coupled giving rise to a nonlinear moving boundary problem with novel energy estimates we present a modular loosely coupled scheme where the original problem is split into the fluid sub problem elastic structure sub problem and poroelasticity sub problem an energy estimate associated with the stability of the scheme is derived in the case where one of the coupling parameters is equal to zero we present numerical tests where we investigate the effects of the material properties of the poroelastic medium on the fluid flow our findings indicate that the flow patterns highly depend on the storativity of the poroelastic material and cannot be captured by considering fluid structure interaction only

combined interface boundary condition method for fluid rigid body interaction abstract this research is motivated by the recent work which has presented a new loosely coupled partitioned algorithm for fluid structure interaction fsi r jaiman p geubelle e loth x jiao combined interface boundary condition method for unsteady fluid structure interaction comput methods appl mech engrg 200 2011 27 39 the loosely coupled partitioned algorithm is intrinsically exposed to the notorious time lag effect whose remedy promotes the combined interface boundary condition cibc method in this method correction terms for velocity and traction are introduced at two sequential time steps with a coupling parameter that plays an important part in the stability and accuracy of the coupled system the structural traction ratio that appears explicitly in the traction correction is estimated based on the solution of the structural subsystem this handling asks for the structural traction before it is corrected by the cibc method in this paper a new formulation for the cibc method is developed to repair the aforementioned inconvenience after simple manipulation the structural traction ratio is removed in constructing the traction correction therefore the structural traction is no more needed in cibc correction terms meantime the ratio t is employed to tune the interfacial corrections instead of the coupling parameter an arbitrary lagrangian eulerian finite element method is used to analyze fsi the characteristic based split cbs scheme is employed to solve incompressible navier stokes equations while the equation for rigid body dynamics is solved by newmark method a numerical technique called moving submesh approach is performed for the mesh deformation for respecting geometric conservation law a mass source term is implanted into the cbs scheme on the moving mesh several numerical examples are tested to validate the proposed methodology for fluid rigid body interaction the obtained results are in agreement with the existing data and some famous features of flow phenomena have been detected successfully

defect deferred correction method for the two domain convection dominated convection diffusion problem abstract we present a method for solving a fluid fluid interaction problem two convection dominated convection diffusion problems adjoined by an interface which is a simplified version of the atmosphere ocean coupling problem the method resolves some of the issues that can be crucial to the fluid fluid interaction problems it is a partitioned time stepping method yet it is of high order accuracy in both space and time the two step algorithm considered in this report provides second order accuracy it allows for the usage of the legacy codes which is a common requirement when resolving flows in complex geometries yet it can be applied to the problems with very small viscosity diffusion coefficients this is achieved by combining the defect correction technique for increased spatial accuracy and for resolving the issue of high convection to diffusion ratio with the deferred correction in time which allows for the usage of the computationally attractive partitioned scheme yet the time accuracy is increased beyond the usual result of partitioned methods being only first order accurate into the defect deferred correction method ddc the results are readily extendable to the higher order accuracy cases by adding more correction steps both the theoretical results and the numerical tests provided demonstrate that the computed solution is unconditionally stable and the accuracy in both space and time is improved after the correction step

incremental displacement correction schemes for incompressible fluid structure interaction in this paper we introduce a class of incremental displacement correction schemes for the explicit coupling of a thin structure with an incompressible fluid these methods enforce a specific robin neumann explicit treatment of the interface coupling we provide a general stability and convergence analysis that covers both the incremental and the non incremental variants their stability properties are independent of the added mass effect the superior accuracy of the incremental schemes with respect to the original non incremental variant is highlighted by the error estimates and then confirmed in a benchmark by numerical experiments

a strongly conservative finite element method for the coupled stokes biot model abstract in this paper based on interior penalty discontinuous galerkin method and mixed finite element method we consider a strongly conservative discretization for the rearranged stokes biot model theoretical analysis and numerical modeling are carried out from the view of mathematics we firstly present the existence and uniqueness of solution of the numerical scheme then the analysis of stability and priori error estimates are derived from the point of numerical simulation we report the numerical examples under uniform meshes which well validate the analysis of convergence and the strong mass conservation

robust schur stability of control systems with interval plants the main contribution of this paper is a generalization of the box theorem which was originally introduced for the hurwitz case for determining the robust schur stability of linear time invariant discrete time control systems containing an interval plant this generalization provides necessary and sufficient conditions for the stability of a family of closed loop characteristic polynomials z q1 z p1 z qm z pm z where the qis are fixed controller and then pis are interval plant polynomials whose coefficients vary within a prescribed interval this method requires checking a set of prescribed segment polynomials whose number is considerably less than that of the edges required by the edge theorem a summary of the robust schur stability of discrete time interval polynomials is presented

thermal convection in vertical cylinders a method based on potentials of velocity abstract any solenoidal vector field can be written in terms of two scalar fields solving the navier stokes equation for these two so called potentials is a widely used method although difficulties have been reported in using this method to describe non cartesian confined flows in particular cylindrical geometries difficulties arise because the potentials are coupled at the boundaries but also because of possible numerical instabilities associated with the high order of the equations this paper shows how all these difficulties can be circumvented firstly by properly deriving the required boundary conditions but also through an adequate discretization which is the final requirement the use of spectral methods together with a reduction of order for the axisymmetric modes is sufficient for this purpose in this paper as a test a velocity potentials method is used to solve the stability problem for the onset of convection in a fluid confined in a cylindrical container

an unfitted nitsche method for incompressible fluid structure interaction using overlapping meshes we consider the extension of the nitsche method to the case of fluid structure interaction problems on unfitted meshes we give a stability analysis for the space semi discretized problem and show how this estimate may be used to derive optimal error estimates for smooth solutions irrespectively of the mesh interface intersection we also discuss different strategies for the time discretization using either fully implicit or explicit coupling loosely coupled schemes some numerical examples illustrate the theoretical discussion

stabilization of explicit coupling in fluid structure interaction involving fluid incompressibility abstract in this work we propose a stabilized explicit coupling scheme for fluid structure interaction problems involving a viscous incompressible fluid the coupled discrete formulation is based on nitsche s method with a time penalty term giving l 2 control on the fluid pressure variations at the interface for a linear model problem we prove that the scheme is stable in the energy norm irrespectively of the so called added mass effect namely the fluid structure density ratio and the geometry of the domain numerical experiments in the linear and non linear case show that optimal time accuracy can be obtained by performing one defect correction iteration

discontinuous galerkin method for the fully dynamic biot s model abstract in this paper a fully discrete scheme of the fully dynamic biot s model problem is proposed which is constructed by using interior penalty discontinuous galerkin method for the spatial approximation and a tailor difference scheme to approximate the first and second order temporal derivative terms first of all we prove the existence and uniqueness of solutions of proposed fully discrete scheme in proper norms then based on the error equations a priori error estimates shall be derived for both primal variables displacement and pore pressure finally a series of numerical examples are given to examine the convergence results by using the proposed numerical scheme to solve the fully dynamic biot s model problem

a spectral method for the wave equation of divergence free vectors and symmetric tensors inside a sphere the wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence free constraint we describe a numerical method based on the spectral decomposition of vector tensor components onto spherical harmonics that allows for the evolution of only those scalar fields which correspond to the divergence free degrees of freedom of the vector tensor the full vector tensor field is recovered at each time step from these two in the vector case or three symmetric tensor case scalar fields through the solution of a first order system of ordinary differential equations ode for each spherical harmonic the correspondence with the poloidal toroidal decomposition is shown for the vector case numerical tests are presented using an explicit chebyshev tau method for the radial coordinate

fluid structure interaction with large structural displacements the calculation of viscous flows inside deformable structures faces major difficulties when enforcing the kinematic compatibility at the fluid structure interface and updating the geometry of the domain this paper proposes to overcome these problems by considering the fluid and the structure as a unique continuous medium to be studied in a fixed reference configuration the resulting problem is then split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions this approach treats the structure in a fully lagrangian way and uses an associated arbitrary lagrangian eulerian ale formulation for the fluid such a strategy has three advantages which are detailed in the present paper it can be discretised in time by implicit stable energy conserving time integration schemes and solved by simple iterative uncoupled algorithms the fluid and the structural problems can be approximated by independent finite element spaces the most recent geometrically exact nonlinear shell models can be used for the structures the full strategy has been implemented into an industrial cfd code results obtained in the simulation of industrial hydraulic shock absorbers are presented at the end of the paper

a unified stabilized method for stokes and darcy s equations we use the lowest possible approximation order piecewise linear continuous velocities and piecewise constant pressures to compute solutions to stokes equation and darcy s equation applying an edge stabilization term to avoid locking we prove that the formulation satisfies the discrete inf sup condition we prove an optimal a priori error estimate for both problems the formulation is then extended to the coupled case using a nitsche type weak formulation allowing for different meshes in the two subdomains finally we present some numerical examples verifying the theoretical predictions and showing the flexibility of the coupled approach

a partitioned scheme for fluid composite structure interaction problems we present a benchmark problem and a loosely coupled partitioned scheme for fluid structure interaction with composite structures the benchmark problem consists of an incompressible viscous fluid interacting with a structure composed of two layers a thin elastic layer with mass which is in contact with the fluid and modeled by the koiter membrane shell equations and a thick elastic layer with mass modeled by the equations of linear elasticity an efficient modular partitioned operator splitting scheme is proposed to simulate solutions to the coupled nonlinear fsi problem without the need for sub iterations at every time step an energy estimate associated with unconditional stability is derived for the fully nonlinear fsi problem defined on moving domains two instructive numerical benchmark problems are presented to test the performance of numerical fsi schemes involving composite structures it is shown numerically that the proposed scheme is at least first order accurate both in time and space this work reveals a new physical property of fsi problems involving thin interfaces with mass the inertia of the thin fluid structure interface regularizes solutions to the full fsi problem

nitsche s method combined with space time finite elements for ale fluid structure interaction problems we propose a weak method for handling the fluid structure interface in finite element fluid structure interaction based on nitsche s method abh math univ hamburg 36 1971 9 we assume transient incompressible newtonian flow and for the structure undamped linear elasticity for the time discretization we use the time continuous energy conserving galerkin method for the structure and for the fluid we employ the time discontinuous galerkin method this means that the velocity becomes piecewise constant on each timestep for the fluid matching the time derivative of the displacements in the solid which is also piecewise constant over a time step we formulate the method and report some numerical examples using space time oriented elements for the fluid in order to mimic lagrangian or ale type simulations

explicit robin neumann schemes for the coupling of incompressible fluids with thin walled structures abstract we introduce a class of explicit coupling schemes for the numerical solution of fluid structure interaction problems involving a viscous incompressible fluid and a general thin walled structure e g including damping and non linear behavior the fundamental ingredient in these methods is a parameter free explicit robin interface condition for the fluid which enables the fluid solid splitting through appropriate extrapolations of the solid velocity and fluid stress on the interface the resulting solution procedures are genuinely partitioned stability and error estimates are provided for all the variants depending on the extrapolations using energy arguments within a representative linear setting in particular we show that one of them simultaneously yields added mass free unconditional stability and optimal first order time accuracy a comprehensive numerical study involving different examples from the literature supports the theory

a spectral method for polar coordinates a new set of polynomial functions that can be used in spectral expansions of c functions in polar coordinates r is defined by a singular sturm liouville equation with the use of the basis functions the spectral representations remain analytic at the pole despite the coordinate singularity because the pole condition is exactly satisfied at the origin for ag azimuthal modes not just a few of the gravest modes which is the usual case based on recurrence relations fast and stable numerical operators for 1 r r d dr the laplacian and helmholtz operators and their inverses are developed although the spacings in the azimuthal direction of the collocation points near the origin are small i e 1 m2 where m is the number of radial modes the explicit numerical method for euler s equation is not stiff at the origin namely the cfl number is o 1 where the grid size in is defined as m i e the maximum allowable timestep is proportional to 1 m not 1 m2

an efficient spectral projection method for the navier stokes equations in cylindrical geometries an efficient and accurate numerical scheme is presented for the three dimensional navier stokes equations in primitive variables in a cylinder the scheme is based on a spectral galerkin approximation for the space variables and a second order projection scheme for time the new spectral projection scheme is implemented to simulate unsteady incompressible flows in a cylinder

robust schur stability of a polytope of polynomials the main objective of the authors is to provide a necessary and sufficient condition for a polytope of polynomials to have all its zeros inside the unit circle the criterion obtained serves as a discrete time counterpart for results in s bialas 1985 and f fu and b r barmish 1987 for the continuous case also the results are reduced to operations on n 1 n 1 matrices it is concluded that by the edge result of a c bartlett et al 1987 it suffices to check the exposed edges in order to determine whether a polytope of polynomials has all its zeros in a simply connected region d

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

fluid structure interaction in blood flow capturing non zero longitudinal structure displacement we present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid structure interaction fsi in blood flow allowing non zero longitudinal displacement arterial walls are modeled by a linearly viscoelastic cylindrical koiter shell model capturing both radial and longitudinal displacement fluid flow is modeled by the navier stokes equations for an incompressible viscous fluid the two are fully coupled via kinematic and dynamic coupling conditions our numerical scheme is based on a new modified lie operator splitting that decouples the fluid and structure sub problems in a way that leads to a loosely coupled scheme which is unconditionally stable this was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub problems leading to an implicit coupling between the fluid and structure velocities the proposed scheme is a modification of the recently introduced kinematically coupled scheme for which the newly proposed modified lie splitting significantly increases the accuracy the performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme it was shown that the accuracy of our scheme was comparable to that of the monolithic scheme while our scheme retains all the main advantages of partitioned schemes such as modularity simple implementation and low computational costs

a convergence study of a new partitioned fluid structure interaction algorithm based on fictitious mass and damping we develop analyze and validate a new method for simulating fluid structure interactions fsis which is based on fictitious mass and fictitious damping in the structure equation we employ a partitioned method for the fluid and structure motions in conjunction with sub iteration and aitken relaxation in particular the use of such fictitious parameters requires sub iterations in order to reduce the induced error in addition to the local temporal truncation error to this end proper levels of tolerance for terminating the sub iteration procedure have been obtained in order to recover the formal order of temporal accuracy for the coupled fsi problem these fictitious terms have a significant effect leading to better convergence rate and hence substantially smaller number of sub iterations through analysis we identify the proper range of these parameters which we then verify by corresponding numerical tests we implement the method in the context of spectral element discretization which is more sensitive than low order methods to numerical instabilities arising in the explicit fsi coupling however the method we present here is simple and general and hence applicable to fsi based on any other discretization we demonstrate the effectiveness of the method in applications involving 2d vortex induced vibrations viv and in 3d flexible arteries with structural density close to blood density we also present 3d results for a patient specific aneurysmal flow under pulsatile flow conditions examining in particular the sensitivity of the results on different values of the fictitious parameters

a generalization of kharitonov s theorem robust stability of interval plants the robust stability problem is considered for interval plants in the case of single input multioutput or single output multi input systems a necessary and sufficient condition for the robust stabilization of such plants is developed using a generalization of v l kharitonov s theorem 1978 the generalization given provides necessary and sufficient conditions for the stability of a family of polynomials delta s q sub 1 s p sub 1 s q sub m s p sub m s where the q sub i are fixed and the p sub i are interval polynomials the coefficients of which are regarded as a point in parameter space which varies within a prescribed box this generalization called the box theorem reduces the question of the stability of the box in parameter space to the equivalent problem of the stability of a prescribed set of line segments it is shown that for special classes of polynomials q sub i s the set of line segments collapses to a set of points and this version of the box theorem in turn reduces to kharitonov s original theorem

fluid structure partitioned procedures based on robin transmission conditions in this article we design new partitioned procedures for fluid structure interaction problems based on robin type transmission conditions the choice of the coefficient in the robin conditions is justified via simplified models the strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane as in hemodynamics applications we analyze theoretically the new iterative procedures on a model problem which represents a simplified blood vessel system in particular the robin neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures the theoretical results are checked using numerical experimentation

chebyshev 3 d spectral and 2 d pseudospectral solvers for the helmholtz equation two chebyshev solvers are presented for the linear helmholtz equation the first algorithm is a 3 d direct spectral solver based on a diagonalization technique whilst the second performs an iterative pseudospectral 2 d calculation with finite difference preconditioning both techniques handle general nonhomogeneous boundary conditions computing times and accuracies of the two methods are compared

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

divergence free velocity fields in nonperiodic geometries the influence matrix method of enforcing incompressibility in pseudospectral simulations of fluid dynamics as described by kleiser and schumann for channel flow is generalized to other geometries a formalism of projection and matrix operators is introduced in which the influence matrix method is shown to be an application of the classic sherman morrison woodbury formula of numerical linear algebra special attention is paid to the tau correction applications to cartesian geometries illustrate the concepts and highlight the role of symmetry a coded implementation in a cylindrical geometry requiring special treatment of coordinate singularities is used to investigate properties of the influence matrix and to provide estimates of timings

nitsche s method method for mixed dimensional analysis conforming and non conforming continuum beam and continuum plate coupling a nitche s method is presented to couple dierent mechanical models they include coupling of a solid and a beam and of a solid and a plate both conforming and non conforming formulations are presented in a non conforming formulation the structure domain is overlapped by a rened solid model applications can be found in multi dimensional analyses in which parts of a structure are modeled with solid elements and others are modeled using a coarser model with beam and or plate elements discretisations are performed using both standard lagrange elements and high order nurbs non uniform rational bsplines based isogeometric elements we present various examples to demonstrate the performance of the method

poloidal toroidal decomposition in a finite cylinder i influence matrices for the magnetohydrodynamic equations the navier stokes equations and magnetohydrodynamics equations are written in terms of poloidal and toroidal potentials in a finite cylinder this formulation insures that the velocity and magnetic fields are divergence free by construction but leads to systems of partial differential equations of higher order whose boundary conditions are coupled the influence matrix technique is used to transform these systems into decoupled parabolic and elliptic problems the magnetic field in the induction equation is matched to that in an exterior vacuum by means of the dirichlet to neumann mapping thus eliminating the need to discretize the exterior the influence matrix is scaled in order to attain an acceptable condition number

fluid structure algorithms based on steklov poincare operators in this paper we review some classical algorithms for fluid structure interaction problems and we propose an alternative viewpoint mutuated from the domain decomposition theory this approach yields preconditioned richardson iterations on the steklov poincare nonlinear equation at the fluid structure interface

nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a fourier finite element technique and an interior penalty method the maxwell equations in the mhd limit in heterogeneous axisymmetric domains composed of conducting and non conducting regions are solved by using a mixed fourier lagrange finite element technique finite elements are used in the meridian plane and fourier modes are used in the azimuthal direction parallelization is made with respect to the fourier modes continuity conditions across interfaces are enforced using an interior penalty technique the performance of the method is illustrated on kinematic and full dynamo configurations

a decoupling algorithm for fluid structure interaction problems based on optimization abstract simulating fluid structure interactions is challenging due to the tight coupling between the fluid and solid substructures explicit and implicit decoupling methods often either fail or require relaxation when densities of the two materials are close in this paper a fluid structure interaction problem is formulated as a least squares problem where the jump in velocities of the two substructures is minimized by a neumann control enforcing the continuity of stress on the interface a decoupling optimization algorithm is discussed which requires few nonlinear solves at each time step and numerical results are presented

robust parametric classical control design this paper extends well known graphical design tools such as the nyquist plot bode plot and nichols charts to the domain of control systems containing parameter uncertainty we have specifically considered linear interval control systems namely those where the uncertain parameters appear linearly in the characteristic polynomial and vary in intervals because in these cases exact construction of frequency envelopes is possible using these developments we calculate various extremal stability margins for such systems and these are used with standard classical control design techniques to deal with robustness with respect to parametric uncertainty in addition we give an effective technique to iteratively select values of the design parameters within given ranges so that the closed loop system produces improved gain or phase margin

a defect correction method for the incompressible navier stokes equations a defect correction method for the incompressible navier stokes equation with a high reynolds number is considered in the defect step the artificial viscosity parameter s is added to the reynolds number as a stability factor and the residual is taken care of in the correction step h 1 and l 2 error estimations are derived for the one step defect correction method and the results of some numerical experiments are presented these results show that for the driven cavity two defect correction steps antidiffuse the artificial viscosity approximation nearly optimally this combination gives on a very coarse mesh results indistinguishable from a benchmark very fine mesh calculation

nitsche xfem for the coupling of an incompressible fluid with immersed thin walled structures abstract in this paper we introduce a nitsche xfem method for fluid structure interaction problems involving a thin walled elastic structure lagrangian formalism immersed in an incompressible viscous fluid eulerian formalism the fluid domain is discretized with an unstructured mesh not fitted to the solid mid surface mesh weak and strong discontinuities across the interface are allowed for the velocity and pressure respectively the fluid solid coupling is enforced consistently using a variant of nitsche s method with cut elements robustness with respect to arbitrary interface intersections is guaranteed through suitable stabilization several coupling schemes with different degrees of fluid solid time splitting implicit semi implicit and explicit are investigated a series of numerical test in 2d involving static and moving interfaces illustrates the performance of the different methods proposed

a non iterative immersed boundary method for spherical particles of arbitrary density ratio in this paper an immersed boundary method with semi implicit fluidsolid coupling for mobile particles of arbitrary density ratio is developed the new scheme does not require any iterations to balance fluid forces and particle forces at the interface a new formulation of the particle equations of motion is proposed which not only accounts for the particle itself but also for a lagrangian layer surrounding the particle surface furthermore it is shown by analytical considerations that the six equations for the linear and angular velocity of the spherical particle decouple which allows their sequential solution on this basis a new time integration scheme is obtained which is unconditionally stable for all fluidsolid density ratios and enables large time steps with courant numbers around unity the new scheme is extensively validated for various test cases and its convergence is assessed an appealing issue is that compared to existing immersed boundary methods the new scheme only alters coefficients in the particle equations and the order of the steps making it easy to implement in present codes with explicit coupling this substantially extends the field of application of such methods an extremely efficient semi implicit ibm for mobile particles of arbitrary density ratio is developed unconditional stability is achieved without any iterative coupling to balance fluid and particle forces at the interface the new scheme only alters coefficients in the particle equations and the sequence of the operations in each time step extensive validation for various test cases including buoyant particles with zero mass

artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows this note investigates the so called arti cial added mass e ect which is responsible for devastating instabilities within sequentially staggered fluid structure interaction fsi simulations where incompressible fluids are considered a discrete representation of the added mass operatorma is given and instability conditions are evaluated for different temporal discretisation schemes it is proven that for every sequentially staggered scheme and given spatial discretisation of a problem a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable the analysis is quite general and does not depend upon the particular spatial discretisation schemes used however here special attention is put on stabilised finite elements employed on the fluid partition numerical investigations further highlight the results

poloidal toroidal decomposition in a finite cylinder the navier stokes equations in a finite cylinder are written in terms of poloidal and toroidal potentials in order to impose incompressibility regularity of the solutions is ensured in several ways first the potentials are represented using a spectral basis which is analytic at the cylindrical axis second the non physical discontinuous boundary conditions at the cylindrical corners are smoothed using a polynomial approximation to a steep exponential profile third the nonlinear term is evaluated in such a way as to eliminate singularities the resulting pseudo spectral code is tested using exact polynomial solutions and the spectral convergence of the coefficients is demonstrated our solutions are shown to agree with exact polynomial solutions and with previous calculations of axisymmetric vortex breakdown and of onset of non axisymmetric helical spirals parallelization by azimuthal wavenumber is shown to be highly effective

analysis of long time stability and errors of two partitioned methods for uncoupling evolutionary groundwater surface water flows the most effective simulations of the multiphysics coupling of groundwater to surface water must involve employing the best groundwater codes and the best surface water codes partitioned methods which solve the coupled problem by successively solving the subphysics problems have recently been studied for the stokes darcy coupling with convergence established over bounded time intervals with constants growing exponentially in t this report analyzes and tests two such partitioned noniterative domain decomposition methods for the fully evolutionary stokes darcy problem under a modest time step restriction of the form delta t leq c where c c physical parameters we prove unconditional long time over 0 leq t infty stability of both partitioned methods from this we derive an optimal error estimate that is uniform in time over 0 leq t infty

a lagrange multiplier method for a stokes biot fluid poroelastic structure interaction model we study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium the free fluid is governed by the stokes equations while the flow in the poroelastic medium is modeled using the biot poroelasticity system equilibrium and kinematic conditions are imposed on the interface a mixed darcy formulation is employed resulting in continuity of flux condition of essential type a lagrange multiplier method is employed to impose weakly this condition a stability and error analysis is performed for the semi discrete continuous in time and the fully discrete formulations a series of numerical experiments is presented to confirm the theoretical convergence rates and to study the applicability of the method to modeling physical phenomena and the robustness of the model with respect to its parameters

transformations of matrices into banded form abstract a class of full or triangular matrices r is described for which there exist banded matrices b such that the product br is also banded the banded matrices yield recursion relations for solving systems of linear equations examples of such matrices arising from second derivative operators acting on orthogonal function expansions are used to illustrate the main theorem and its application practical considerations in efficient implementation are discussed

some discrete time counterparts to kharitonov s stability criterion for uncertain systems in 1 kharitonov gave an elegant and simple stability criterion for continuous time systems this note reports on similar results for discrete time systems

a projection semi implicit scheme for the coupling of an elastic structure with an incompressible fluid we address the numerical simulation of fluid structure systems involving an incompressible viscous fluid this issue is particularly difficult to face when the fluid added mass acting on the structure is strong as it happens in hemodynamics for example indeed several works have shown that in such situations implicit coupling seems to be necessary in order to avoid numerical instabilities although significant improvements have been achieved during the last years solving implicit coupling often exhibits a prohibitive computational cost in this work we introduce a semi implicit coupling scheme which remains stable for a reasonable range of the discretization parameters the first idea consists in treating implicitly the added mass effect whereas the other contributions geometrical non linearities viscous and convective effects are treated explicitly the second idea relies on the fact that this kind of explicit implicit splitting can be naturally performed using a chorin temam projection scheme in the fluid we prove conditional stability of the scheme for a fully discrete formulation several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches

a partitioned fully explicit lagrangian finite element method for highly nonlinear fluid structure interaction problems summary in this work a fully explicit partitioned method for the simulation of fluid structure interaction fsi problems is presented the fluid domain is modelled with an explicit particle finite element method pfem based on the hypothesis of weak compressibility the lagrangian description of the fluid is particularly effective in the simulation of fsi problems with free surface flows and large structural displacements since the fluid boundaries are automatically defined by the position of the mesh nodes a distinctive feature of the proposed fsi strategy is that the solid domain is modelled using the explicit integration finite element method fem in a off the shelf commercial software abaqus explicit this allows to perform simulations with a complete and advanced description on the structural domain including advanced structural material models and contact the structure to fluid coupling algorithm is based on a technique derived from the domain decomposition methods namely the gravouil and combescure gc algorithm the method allows for arbitrarily large interface displacements using different time incrementation and non conforming meshes in the different domains which is an essential feature for the efficiency of an explicit solver involving different materials the resulting fully explicit and fully lagrangian finite element approach is particularly appealing for the possibility of its efficient application in a large variety of highly nonlinear engineering problems this article is protected by copyright all rights reserved

kinematic splitting algorithm for fluid structure interaction in hemodynamics abstract in this paper we study a kinematic splitting algorithm for fluid structure interaction problems this algorithm belongs to the class of loosely coupled fluid structure interaction schemes we will present stability analysis for a coupled problem of non newtonian shear dependent fluids in moving domains with viscoelastic boundaries fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms for simplicity of presentation the structure is modelled by the generalized string equation but the results presented in the paper may be generalized to more complex structure models the arbitrary lagrangian eulerian approach is used in order to take into account moving computational domain numerical experiments including numerical error analysis and comparison of hemodynamic parameters for newtonian and non newtonian fluids demonstrate reliability of the proposed scheme

projection based reduced order models for a cut finite element method in parametrized domains abstract this work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method such methods and in particular the cutfem method are attractive in the generation of projection based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes the combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems avoiding remeshing as well as the reference domain formulation often used in the reduced order modeling for boundary fitted finite element formulations the resulting novel methodology is presented on linear elliptic and stokes problems together with several test cases to assess its capability the role of a proper extension and transport of embedded solutions to a common background is analyzed in detail

a spectral model for two dimensional incompressible fluid flow in a circular basin in the accompanying paper part i w t m verkley 1997 j comput phys 100 114136 a spectral numerical scheme is developed for two dimensional incompressible fluid flow in a circular basin the model is formulated in terms of basis functions that are products of jacobi polynomials and complex exponentials the jacobi polynomials are used for the radial dependence of the fields and the complex exponentials for the angular dependence the basis functions are orthogonal with respect to the natural inner product for a circular domain the nonlinear advection term is calculated without aliasing using the transform method based on a grid of which the radii are gaussian and the angles are equidistant in the present paper we discuss the performance of the model by showing examples of time integrations the differences between these examples concern the spatial structure of the planetary vorticity plane s plane f plane the temporal and spatial resolution of the model and the form strength and type of the forcing and dissipation

an adaptive fixed mesh ale method for free surface flows in this work we present a fixed mesh ale method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain this mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required some of the main ingredients of the formulation are the use of an arbitrary lagrangian eulerian formulation for computing temporal derivatives the use of stabilization terms for stabilizing convection stabilizing the lack of compatibility between velocity and pressure interpolation spaces and stabilizing the ill conditioning introduced by the cuts on the background finite element mesh and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved the method is tested in several numerical examples the expected convergence rates both in space and time are observed smooth solution fields for both velocity and pressure are obtained as a result of the contribution of the stabilization terms finally a good agreement between the numerical results and the reference experimental data is obtained

generalized robin neumann explicit coupling schemes for incompressible fluid structure interaction stability analysis and numerics we introduce a new class of explicit coupling schemes for the numerical solution of fluid structure interaction problems involving a viscous incompressible fluid and an elastic structure these methods generalize the arguments reported in 13 10 to the case of the coupling with thick walled structures the basic idea lies in the derivation of an intrinsic interface robin consistency at the space semi discrete level using a lumped mass approximation in the structure the fluid solid splitting is then performed through appropriate extrapolations of the solid velocity and stress on the interface based on these methods a new parameter free robin neumann iterative procedure is also proposed for the partitioned solution of implicit coupling a priori energy estimates guaranteeing the added mass free stability of the schemes and the convergence of the iterative procedure are established the accuracy and robustness of the methods are illustrated in several numerical examples

robust pole assignment via reflection coefficients of polynomials a robust version of the output controller design for discrete time systems is introduced instead of a single stable point a stable polytope or simplex is preselected in the closed loop characteristic polynomial coefficients space a constructive procedure for generating stable polytopes is given starting from the unit hypercube of reflection coefficients of monic polynomials this procedure is quite straightforward because for a special family of polynomials the linear cover of so called reflection vectors is stable the roots placement of reflection vectors is studied if a stable target simplex is preselected then the robust output controller design task is solved by quadratic programming approach

an efficient spectral projection method for the navier stokes equations in cylindrical geometries i axisymmetric cases abstract an efficient and accurate numerical scheme is presented for the axisymmetric navier stokes equations in primitive variables in a cylinder the scheme is based on a new spectral galerkin approximation for the space variables and a second order projection scheme for the time variable the new spectral projection scheme is implemented to simulate the unsteady incompressible axisymmetric flow with a singular boundary condition which is approximated to within a desired accuracy by using a smooth boundary condition a sensible comparison is made with a standard second order in time and space finite difference scheme based on a stream function vorticity formulation and with available experimental data the numerical results indicate that both schemes produce very reliable results and that despite the singular boundary condition the spectral projection scheme is still more accurate in terms of a fixed number of unknowns and more efficient in terms of cpu time required for resolving the flow at a fixed reynolds number to within a prescribed accuracy than the finite difference scheme more importantly the spectral projection scheme can be readily extended to three dimensional nonaxisymmetric cases