three dimensional volume conserving immersed boundary model for two phase fluid flows abstract we present a volume preserving scheme for two phase immiscible incompressible flows using an immersed boundary method ibm in a three dimensional space the two phase ibm employs a mixture of eulerian and lagrangian variables where the fluid interface is represented by discrete lagrangian markers exerting surface tension forces to the eulerian fluid domain and the markers are advected by the fluid velocity the interactions between the lagrangian markers and the fluid variables are linked by the discretized dirac delta function the present study extends the previous two dimensional research li et al volume preserving immersed boundary methods for two phase fluid flows int j numer meth fluids 69 2012 842 858 to the three dimensional space the key idea of the proposed method is relocating surface points along the normal directions to conserve the total volume we perform a number of numerical experiments to show the efficiency and accuracy of the proposed method

coupling an eulerian fluid calculation to a lagrangian solid calculation with the ghost fluid method we propose a numerical method for modeling multimaterial flows where the domain is decomposed into separate eulerian and lagrangian subdomains that is the equations are written in eulerian form in one subdomain and in lagrangian form in the other subdomain this is of interest for example when considering the effect of underwater explosions on the hull of a ship or the impact of a low speed projectile on a soft explosive target on the one hand high speed fluid flows are traditionally modeled by applying shock capturing schemes to the compressible euler equations to avoid problems associated with tangling of a lagrangian mesh on the other hand solid dynamics calculations are traditionally carried out using lagrangian numerical methods to avoid problems associated with numerical smearing in eulerian calculations we use the ghost fluid method to create accurate discretizations across the eulerian lagrangian interface the numerical method is presented in both one and two spatial dimensions three dimensional extensions to the interface coupling method are straightforward

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

a fast poisson solver for complex geometries robust fast solvers for the poisson equation have generally been limited to regular geometries where direct methods based on fourier analysis or cyclic reduction and multigrid methods can be used while multigrid methods can be applied in irregular domains and to a broader class of partial differential equations they are difficult to implement in a robust fashion since they require an appropriate hierarchy of coarse grids which are not provided in many practical situations in this paper we present a new fast poisson solver based on potential theory rather than on direct discretization of the partial differential equation our method combines fast algorithms for computing volume integrals and evaluating layer potentials on a grid with a fast multipole accelerated integral equation solver the amount of work required is o m log m n where m is the number of interior grid points and n is the number of points on the boundary asymptotically the cost of our method is just twice that of a standard poisson solver on a rectangular domain in which the problem domain can be embedded independent of the complexity of the geometry

modeling a no slip flow boundary with an external force field abstract a novel technique related to peskin s immersed boundary approach is used to introduce solid surfaces into a simulated flow field the navier stokes equations permit the presence of an externally imposed body force that may vary in space and time forces are chosen to lie along a desired surface and to have a magnitude and direction opposing the local flow such that the flow is brought to rest on an element of the surface for unsteady viscous flow the direct calculation of the needed force is facilitated by a feedback scheme in which the velocity is used to iteratively determine the desired value in particular we determine the surface body force from the relation f x 5 t t 0 u x 5 t dt u x 5 t for surface points x 5 velocity u time t and negative constants and examples are presented which include 2d flow around cylinders 3d turbulent channel flow where one boundary is simulated with a force field and turbulent channel flow over a riblet covered surface while the new method may be applied to complex geometries on a non cartesian mesh we have chosen to use a simple cartesian grid all simulations are done with a spectral code in a single computational domain without any mapping of the mesh

the fixed mesh ale approach for the numerical approximation of flows in moving domains in this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization and therefore the formulation to be presented falls within the category of fixed grid methods even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed grid method our approach can be applied together with any technique to impose approximately boundary conditions although we also describe the one we actually favor our main concern is to properly account for the advection of information as the domain boundary evolves to achieve this we use an arbitrary lagrangian eulerian framework the distinctive feature being that at each time step results are projected onto a fixed background mesh that is where the problem is actually solved

a second order accurate symmetric discretization of the poisson equation on irregular domains in this paper we consider the variable coefficient poisson equation with dirichlet boundary conditions on an irregular domain and show that one can obtain second order accuracy with a rather simple discretization moreover since our discretization matrix is symmetric it can be inverted rather quickly as opposed to the more complicated nonsymmetric discretization matrices found in other second order accurate discretizations of this problem multidimensional computational results are presented to demonstrate the second order accuracy of this numerical method in addition we use our approach to formulate a second order accurate symmetric implicit time discretization of the heat equation on irregular domains then we briefly consider stefan problems

large eddy simulation in complex geometric configurations using boundary body forces anumericalmethodispresentedthatallowslargeeddysimulation les ofturbulente owsincomplexgeometric cone gurations with moving boundaries and that retains the advantages of solving the navier stokes equations on e xed orthogonal grids the boundary conditions are applied independently of the grid by assigning body forces over surfaces that need not coincide with coordinate lines the use of orthogonal nondeforming grids simplie es grid generation facilitates theimplementation of high order nondissipativediscretization schemes andminimizes the spatial and temporal variations in e lter width that complicate unstructured deforming grid les dynamic subgrid scaleturbulence models areparticularly appealing in combination with the body forceprocedure because the dynamic model accounts automatically for the presence of solid walls without requiring damping functions the method is validated by simulations of the turbulent e ow in a motored axisymmetric piston cylinder assembly for which detailed experimental measurements are available computed mean and rms velocity proe les show very good agreement with measured ensemble averages thepresent numerical code runs on small personal computerlike workstations for a comparable level of accuracy computational requirements memory and cpu time are at least a factor of 10 lower compared to published simulations for the same cone guration obtained using an unstructured boundary e tted deforming grid approach

a cartesian grid finite volume method for the advection diffusion equation in irregular geometries we present a fully conservative high resolution finite volume algorithm for advection diffusion equations in irregular geometries the algorithm uses a cartesian grid in which some cells are cut by the embedded boundary a novel feature is the use of a capacity function to model the fact that some cells are only partially available to the fluid the advection portion then uses the explicit wave propagation methods implemented in clawpack and is stable for courant numbers up to 1 diffusion is modelled with an implicit finite volume algorithm results are shown for several geometries convergence is verified and the 1 norm order of accuracy is found to between 1 2 and 2 depending on the geometry and peclet number software is available on the web

curvilinear immersed boundary method for simulating fluid structure interaction with complex 3d rigid bodies the sharp interface curvib approach of ge and sotiropoulos l ge f sotiropoulos a numerical method for solving the 3d unsteady incompressible navier stokes equations in curvilinear domains with complex immersed boundaries journal of computational physics 225 2007 1782 1809 is extended to simulate fluid structure interaction fsi problems involving complex 3d rigid bodies undergoing large structural displacements the fsi solver adopts the partitioned fsi solution approach and both loose and strong coupling strategies are implemented the interfaces between immersed bodies and the fluid are discretized with a lagrangian grid and tracked with an explicit front tracking approach an efficient ray tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies numerical experiments are carried out for two fsi problems vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions for both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements the numerical experiments suggest that both the properties of the structure mass geometry and the local flow conditions can play an important role in determining the stability of the fsi algorithm under certain conditions the fsi algorithm is unconditionally unstable even when strong coupling fsi is employed for such cases however combining the strong coupling iteration with under relaxation in conjunction with the aitken s acceleration technique is shown to effectively resolve the stability problems a theoretical analysis is presented to explain the findings of the numerical experiments it is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the fsi algorithm the stabilizing role of under relaxation is also clarified and the upper bound of the under relaxation coefficient required for stability is derived

an immersed boundary method with formal second order accuracy and reduced numerical viscosity a formally second order accurate immersed boundary method is presented and tested in this paper we apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first order method the numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high reynolds number flows with immersed boundaries

an immersed boundary finite volume method for simulations of flow in complex geometries abstract a new immersed boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source sink as well as a momentum forcing the present method is based on a finite volume approach on a staggered mesh together with a fractional step method both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary in the immersed boundary method the choice of an accurate interpolation scheme satisfying the no slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary therefore a stable second order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed three different flow problems decaying vortices and flows over a cylinder and a sphere are simulated using the immersed boundary method proposed in this study and the results agree very well with previous numerical and experimental results verifying the accuracy of the present method

numerical methods based on additive splittings for hyperbolic partial differential equations we derive and analyze several methods for systems of hyperbolic equations with wide ranges of signal speeds these techniques are also useful for problems whose coefficients have large mean values about which they oscillate with small amplitude our methods are based on additive splittings of the operators into components that can be approximated independently on the different time scales some of which are sometimes treated exactly the efficiency of the splitting methods is seen to depend on the error incurred in splitting the exact solution operator this is analyzed and a technique is discussed for reducing this error through a simple change of variables a procedure for generating the appropriate boundary data for the intermediate solutions is also presented

weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes this is the accepted version of the following article codina r and baiges j 2015 weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes int j numer meth engng 104 624 654 doi 10 1002 nme 4815 which has been published in final form at http onlinelibrary wiley com doi 10 1002 nme 4815 abstract

erratum new trace formulae for a quadratic pencil of the schrodinger operator j math phys 51 033506 2010 in this note we correct a mistake made in my paper j math phys 51 033506 2010 using the contour integration method we shall obtain a new regularized trace formula for schrodinger operator with energy dependent potential

a level set based topology optimization method targeting metallic waveguide design problems in this paper we propose a level set based topology optimization method targeting metallic waveguide design problems where the skin effect must be taken into account since the metallic waveguides are generally used in the high frequency range where this effect critically affects performance one of the most reasonable approaches to represent the skin effect is to impose an electric field constraint condition on the surface of the metal to implement this approach we develop a boundary tracking scheme for the arbitrary lagrangian eulerian ale mesh pertaining to the zero iso contour of the level set function that is given in an eulerian mesh and impose dirichlet boundary conditions at the nodes on the zero iso contour in the ale mesh to compute the electric field since the ale mesh accurately tracks the zero iso contour at every optimization iteration the electric field is always appropriately computed during optimization for the sensitivity analysis we compute the nodal coordinate sensitivities in the ale mesh and smooth them by solving a helmholtz type partial differential equation the obtained smoothed sensitivities are used to compute the normal velocity in the level set equation that is solved using the eulerian mesh and the level set function is updated based on the computed normal velocity finally the utility of the proposed method is discussed through several numerical examples copyright 2011 john wiley sons ltd

a non iterative direct forcing immersed boundary method for strongly coupled fluid solid interactions a non iterative direct forcing immersed boundary method is presented for the strongly coupled simulations of fluid solid interactions while it retains many advantages of the immersed boundary framework by yang and stern 2012 30 especially the simplified field extension strategy for moving boundary treatment and the pointwise integration of hydrodynamic force using the momentum forcing term the present approach improves upon the previous method in several aspects including optimized computational cost for a strong coupling scheme reduced algorithm complexity for a straightforward implementation and enhanced numerical stability for low density ratio problems central to these improvements is a simple intermediate step in which the velocity fields around solid bodies are predicted on temporary non inertial reference frames attached to moving solid bodies in a one to one manner this step enables the explicit inverse of the implicit equations for rigid body dynamics thus rendering unnecessary the previous predictor corrector scheme for iteratively adjusting the displacements and velocities of the immersed bodies until reaching a convergence in addition a simple generalized procedure is developed to obtain the interpolation coefficients in a local reconstruction stencil explicitly from the geometric relationship for verification and validation the vortex induced vibration of a circular cylinder and the rotational galloping of a rectangular body are considered first then several particulate flow problems including settling and buoyant particles of low density ratios a settling particle in a small container and the kissing drafting tumbling problem of two settling particles are studied the agreement between the present results and the reference data in the literature is excellent an overall second order accuracy of the algorithm is verified in two systematic grid convergence tests the present idea can be easily applied to similar methods for achieving a strong coupling scheme on top of a weak one with a nominal increase in the computational cost details of the algorithm are provided to facilitate its implementation in other solvers using non boundary conforming grids

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

numerical simulation of a cylinder in uniform flow in this study a virtual boundary technique is applied to the numerical simulation of stationary and moving cylinders in uniform flow this approach readily allows the imposition of a no slip boundary within the flow field by a feedback forcing term added to the momentum equations in the present work this technique is used with a high order finite difference method effectively eliminating spurious oscillations caused by the feedback forcing when used with spectrally discretized flow solvers very good agreement is found between the present calculations and previous computational and experimental results for steady and time dependent flow at low reynolds numbers

high order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources this paper introduces a novel high order interface scheme the matched interface and boundary mib method for solving elliptic equations with discontinuous coefficients and singular sources on cartesian grids by appropriate use of auxiliary line and or fictitious points physical jump conditions are enforced at the interface unlike other existing interface schemes the proposed method disassociates the enforcement of physical jump conditions from the discretization of the differential equation under study to construct higher order interface schemes the proposed mib method bypasses the major challenge of implementing high order jump conditions by repeatedly enforcing the lowest order jump conditions the proposed mib method is of arbitrarily high order in principle in treating straight regular interfaces we construct mib schemes up to 16th order for more general elliptic problems with curved irregular interfaces and boundary up to 6th order mib schemes have been demonstrated by employing the standard high order finite difference schemes to discretize the laplacian the present mib method automatically reduces to the standard central difference scheme when the interface is absent the immersed interface method iim is regenerated for a comparison study of the proposed method the robustness of the mib method is verified against the large magnitude of the jump discontinuity across the interface the nature of high efficiency and low memory requirement of the mib method is extensively validated via solving various elliptic immersed interface problems in two and three dimensions ee dimensions

a non staggered grid fractional step method for time dependent incompressible navier stokes equations in curvilinear coordinates a numerical method for solving three dimensional time dependent incompressible navier stokes equations in curvilinear coordinates is presented the non staggered grid method originally developed by c m rhie and w l chow aiaaj 21 1525 1983 for steady state problems is extended to compute unsteady flows in the computational space the cartesian velocity components and the pressure are defined at the center of a control volume while the volume fluxes are defined at the mid point on their corresponding cell faces the momentum equations are integrated semi implicitly by the approximate factorization technique the intermediate velocities are interpolated onto the faces of the control volume to form the source terms of the pressure poisson equation which is solved iteratively with a multigrid method the compatibility condition of the pressure poisson equation is satisfied in the same manner as in a staggered grid method mass conservation can be satisfied to machine accuracy the pressure boundary condition is derived from the momentum equations solutions of both steady and unsteady problems including the large eddy simulation of a rotating and stratified upwelling flow in an irregular container established the favorable accuracy and efficiency of the present method

a ghost cell immersed boundary method for flow in complex geometry an efficient ghost cell immersed boundary method gcibm for simulating turbulent flows in complex geometries is presented a boundary condition is enforced through a ghost cell method the reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second order accuracy of the base solver both dirichlet and neumann boundary conditions can be treated the current ghost cell treatment is both suitable for staggered and non staggered cartesian grids the accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface numerical results are compared with experimental data and boundary fitted grid results the method is further extended to an existing ocean model mitgcm to simulate geophysical flow over a three dimensional bump the method is easily implemented as evidenced by our use of several existing codes

a cartesian grid projection method for the incompressible euler equations in complex geometries many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow here we present a method for calculating time dependent incompressible inviscid flow which combines a projection method with a cartesian grid approach for representing geometry in this approach the body is represented as an interface embedded in a regular cartesian mesh the advection step is based on a cartesian grid algorithm for compressible flow in which the discretization of the body near the flow uses a volume of fluid representation a redistribution procedure is used to eliminate time step restrictions due to small cells where the boundary intersects the mesh the projection step uses an approximate projection based on a cartesian grid method for potential flow the method incorporates knowledge of the body through volume and area fractions along with certain other integrals over the mixed cells convergence results are given for the projection itself and for the time dependent algorithm in two dimensions the method is also demonstrated on flow past a half cylinder with vortex shedding

an implicit boundary approach for viscous compressible high reynolds flows using a hybrid remeshed particle hydrodynamics method abstract we present an implicit boundary particle method with background mesh adaptation we use a brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high reynolds numbers a penalty term is added to the navier stokes equations to impose the boundary conditions the boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid achieving an implicit approach for flow around complex boundaries geometries simulation the main idea of the brinkman penalisation method is to model the solid obstacle as a porous medium the governing equations for the compressible fluid and penalised navier stokes for the porous medium are solved simultaneously without need for interface conditions the accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel poiseuille flow to more complex problems such as the lid driven cavity with high reynolds numbers the reflection and propagation of a compressible shock wave and finally swirling flow in a model two stroke diesel engine the remeshed particle mesh method coupled with brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions

towards oscillation free implementation of the immersed boundary method with spectral like methods it is known that when the immersed boundary method ibm is implemented within spectral like methods the gibbs oscillation seriously deteriorates the calculation of derivatives near the body surface in this paper a radial basis function rbf based smoothing technique is proposed with the intention of eliminating or efficiently reducing the gibbs oscillation without affecting the flow field outside the body based on this technique a combined ibm spectral scheme is developed to solve the incompressible navier stokes equations numerical simulations of flow through a periodic lattice of cylinders of various cross sections are performed the results demonstrate that the proposed methodology is able to give accurate and nearly oscillation free numerical solutions of incompressible viscous flows

an improved direct forcing immersed boundary method for finite difference applications a modified immersed boundary method is developed using the direct forcing concept an improved bilinear interpolation extrapolation algorithm is implemented for more accurate boundary forcing expressions and easier implementation detailed discussions of the method are presented on the stability velocity interpolation on the immersed boundary direct forcing extrapolation to the grid points resolution of the immersed boundary points and internal treatment the method can achieve second order accurate solutions the method is then applied to a finite difference scheme to compute flow over a stationary cylinder an oscillating cylinder and a stationary sphere the accuracy of the computational results is verified using numerous computational and experimental results in the literature

a cartesian grid method for solving the two dimensional streamfunction vorticity equations in irregular regions we describe a method for solving the two dimensional navier stokes equations in irregular physical domains our method is based on an underlying uniform cartesian grid and second order finite difference finite volume discretizations of the streamfunction vorticity equations geometry representing stationary solid obstacles in the flow domain is embedded in the cartesian grid and special discretizations near the embedded boundary ensure the accuracy of the solution in the cut cells along the embedded boundary we determine a distribution of vorticity sources needed to impose the no slip flow conditions this distribution appears as a right hand side term in the discretized fluid equations and so we can use fast solvers to solve the linear systems that arise to handle the advective terms we use the high resolution algorithms in clawpack we show that our stokes solver is second order accurate for steady state solutions and that our full navier stokes solver is between first and second order accurate and reproduces results from well studied benchmark problems in viscous fluid flow finally we demonstrate the robustness of our code on flow in a complex domain

an efficient immersed boundary treatment for complex moving object an efficient immersed boundary treatment for simulation of flexible moving body immersed in fluid is presented the level set signed distance function is used to indicate body surface a simple mapping strategy is proposed to avoid costly signed distance re initialization computations the strategy is efficient for both rigid and deformable structures and can be extended to 3 d case easily with the use of signed distance function reconstruction of flow variables on a body surface can be easily implemented through linear bilinear or quadratic interpolation in order to suppress the pressure oscillations caused by the role conversion of forcing points and fluid points a modified interpolation scheme is presented by introducing a dynamic weight term to the fluid point together with local grid refinement and using larger time step the pressure oscillations can be effectively diminished by the modified interpolation scheme the proposed method is validated by 2 d numerical simulations on a uniform flow past a fixed cylinder in line and transversely oscillating cylinders a flapping wing a 3 d simulation on a uniform flow past a rectangle plane with an initial attack angle and a moving anguilliform swimmer present numerical results are compared with other cfd solutions as well as experimental results

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

a boundary condition capturing method for poisson s equation on irregular domains interfaces have a variety of boundary conditions or jump conditions that need to be enforced the ghost fluid method gfm was developed to capture the boundary conditions at a contact discontinuity in the inviscid euler equations and has been extended to treat more general discontinuities such as shocks detonations and deflagrations and compressible viscous flows in this paper a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous this new method is robust and easy to implement even in three spatial dimensions furthermore the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient poisson equation in the absence of interfaces allowing for straightforward application of standard black box solvers

a cartesian grid embedded boundary method for the heat equation on irregular domains we present an algorithm for solving the heat equation on irregular time dependent domains it is based on the cartesian grid embedded boundary algorithm of johansen and colella j comput phys 147 2 60 85 for discretizing poisson s equation combined with a second order accurate discretization of the time derivative this leads to a method that is second order accurate in space and time for the case where the boundary is moving we convert the moving boundary problem to a sequence of fixed boundary problems combined with an extrapolation procedure to initialize values that are uncovered as the boundary moves we find that in the moving boundary case the use of crank nicolson time discretization is unstable requiring us to use the l sub 0 stable implicit runge kutta method of twizell gumel and arigu

an immersed boundary method based on discrete stream function formulation for two and three dimensional incompressible flows an immersed boundary method is proposed in the framework of discrete stream function formulation for incompressible flows in order to impose the non slip boundary condition the forcing term is determined implicitly by solving a linear system the number of unknowns of the linear system is the same as that of the lagrangian points representing the body surface thus the extra cost in force calculation is negligible if compared with that in the basic flow solver in order to handle three dimensional flows at moderate reynolds numbers a parallelized flow solver based on the present method is developed using the domain decomposition strategy to verify the accuracy of the immersed boundary method proposed in this work flow problems of different complexity decaying vortices flows over stationary and oscillating cylinders and a stationary sphere and flow over low aspect ratio flat plate are simulated and the results are in good agreement with the experimental or computational data in previously published literatures

generalized inverses and a block rank equation for a square matrix a of index 1 the block rank equationrankabcx rank a is studied geometrical conditions are given to characterize the solution of this equation further all matrices b and c are described for the solution x a where a is the group inverse of a in addition we extend these results to reflexive generalized inverses this contributes to a result recently obtained by wei siam j matrix anal appl 17 1996 744 and it is a generalization of a result by grosz lin alg appl 289 1999 127

an implicit forcing immersed boundary method for simulating viscous flows in irregular domains abstract we present a method for solving the incompressible navier stokes equations in irregular domains these equations are discretized using finite difference method in a uniform cartesian grid stationary rigid boundaries are embedded in the cartesian grid and singular forces are applied at the rigid boundaries to impose the no slip conditions the singular forces are then distributed to the nearby cartesian grid points using the immersed boundary method in the present work the singular forces are computed implicitly by solving a small system of equations at each time step this system of equations is derived from a second order projection method the main advantage of this method is that it imposes the no slip boundary condition exactly and avoids the need for small time step to maintain stability the ability of the method to simulate viscous flows in irregular domains is demonstrated by applying to 2 dimensional flows past a circular cylinder multiple rigid obstacles and 3 dimensional flow past a sphere

parallel computation of unsteady incompressible viscous flows around moving rigid bodies using an immersed object method with overlapping grids a novel immersed object method is developed for simulating two dimensional unsteady incompressible viscous flows around arbitrarily moving rigid bodies it has been implemented in a parallel unstructured finite volume incompressible navier stokes solver based on the artificial compressibility ac approach using a higher order characteristics based upwind scheme and matrix free implicit dual time stepping in the immersed object method an object is immersed in the flow field and it is supposed to contain frozen fluid which moves like a solid body this is realized by introducing source terms in the momentum equations during the ac sub iterations an internal mesh within the object is employed to search and locate all the eulerian nodes within the object in every time step for imposing the source terms unlike many existing methods this method does not require complex searching extrapolation and interpolation to find the intersections of the object boundary with the unstructured background mesh and assign flow condition onto the object boundary if it is necessary to capture the boundary layer accurately then a dense overlapping grid can then be constructed around the object for further refined calculation the immersed object method has been used to simulate steady and unsteady incompressible viscous flows over a stationary circular cylinder rotating square cylinder and moving disk in cavity the results agree well with published numerical solutions and experimental measurements

combined immersed boundary finite difference methods for three dimensional complex flow simulations a second order accurate highly efficient method is developed for simulating unsteady three dimensional incompressible flows in complex geometries this is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid the governing equations therefore can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures two different forcings are tested showing that while the quality of the results is essentially the same in both cases the efficiency of the calculation strongly depends on the particular expression a major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme this ranges from zeroth order for the most commonly used interpolations up to second order for an ad hoc velocity interpolation the present scheme has been used to simulate several flows whose results have been validated by experiments and other results available in the literature finally in the last example we show the flow inside an ic piston cylinder assembly at high reynolds number to our knowledge this is the first example in which the immersed boundary technique is applied to a full three dimensional complex flow with moving boundaries and with a reynolds number high enough to require a subgrid scale turbulence model

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

a representation of curved boundaries for the solution of the navier stokes equations on a staggered three dimensional cartesian grid a method is presented for representing curved boundaries for the solution of the navier stokes equations on a non uniform staggered three dimensional cartesian grid the approach involves truncating the cartesian cells at the boundary surface to create new cells which conform to the shape of the surface we discuss in some detail the problems unique to the development of a cut cell method on a staggered grid methods for calculating the fluxes through the boundary cell faces for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second order accuracy in space in addition a novel cell linking method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell merging approaches techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces the new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at re 40 and is shown to give significant improvement over a staircase boundary formulation finally it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a reynolds number of 800 good agreement is obtained with experimental results for this flow