accurate computation of surface stresses and forces with immersed boundary methods many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body these surface stresses may contain spurious oscillations that make them ill suited for representing the physical surface stresses on the body moreover these inaccurate stresses often lead to unphysical oscillations in the history of integrated surface forces such as the coefficient of lift while the errors in the surface stresses and forces do not necessarily affect the convergence of the velocity field it is desirable especially in fluid structure interaction problems to obtain smooth and convergent stress distributions on the surface to this end we show that the equation for the surface stresses is an integral equation of the first kind whose ill posedness is the source of spurious oscillations in the stresses we also demonstrate that for sufficiently smooth delta functions the oscillations may be filtered out to obtain physically accurate surface stresses the filtering is applied as a post processing procedure so that the convergence of the velocity field is unaffected we demonstrate the efficacy of the method by computing stresses and forces that converge to the physical stresses and forces for several test problems

an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

numerical simulation of dilute particle laden flows by wavelet bem fem abstract a wavelet transform based bem and fem numerical scheme was used to simulate laminar viscous flow the velocity vorticity formulation of the navier stokes equations was used the flow simulation algorithm was coupled with a lagrangian particle tracking scheme for dilute suspensions of massless particles and particles without inertia the proposed numerical approach was used to simulate flow and particle paths for two test cases flow over a backward facing step and flow past a circular cylinder we present methods of calculating the pressure and stream function field at the end of each time step the pressure field was used to calculate drag and lift coefficients which enable qualitative comparison of our results with the benchmark the stream function enabled the comparison of streamlines and massless particle paths in steady state low reynolds number value flow fields and thus provided an estimate on the accuracy of the particle tracking algorithm unsteady higher reynolds number value flows were investigated in terms of particle distributions in vortex streets in the wake of the cylinder and behind the step sedimentation of particles without inertia was studied in the flow field behind a backward facing step at reynolds number value 5000

upwind differencing scheme for the time accurate incompressible navier stokes equations the two dimensional incompressible navier stokes equations are solved in a time accurate manner using the method of pseudocompres sibility using this method subiterations in pseudotime are required to satisfy the continuity equation at each time step an upwind differencing scheme based on flux difference splitting is used to compute the convective terms the upwind differencing is biased based on the sign of the local eigenvalue of the jacobian matrix of the convective fluxes both third order and fifth order differencing schemes are used on the convective fluxes throughout the grid s interior the equations are solved using an implicit line relaxation scheme this solution scheme is stable and is capable of running at large time steps in pseudo time leading to fast convergence for each physical time step a variety of computed results are presented to validate the present scheme results for the flow over an oscillating plate are compared with the exact analytic solution and good agreement is seen excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure flow solutions over a circular cylinder with vortex shedding are also presented finally the flow past an airfoil at 90 angle of attack is computed

simulation of incompressible viscous flows past a circular cylinder by hybrid fd scheme and meshless least square based finite difference method in this paper we describe an efficient method for simulating the two dimensional steady and unsteady incompressible flows the method is a hybrid approach which combines the conventional finite difference fd scheme and the meshfree least square based finite difference mlsfd method in this method the mlsfd method is adopted to deal with the complex geometry for its truly mesh free property and it is responsible for the spatial discretization in the region around the complex geometry which represents the stationary solid obstacle correspondingly conventional fd scheme is applied in the rest of the flow domain to take advantage of its high computational efficiency numerical simulation is carried out for the steady flow with reynolds numbers of 10 20 and 40 and unsteady flow with reynolds numbers of 100 and 200 the obtained numerical results agree very well with computational and experimental data available in the literature compared with the fully mlsfd method this new approach greatly improves the computational efficiency 2003 elsevier b v all rights reserved

a stabilised immersed boundary method on hierarchical b spline grids for fluid rigid body interaction with solid solid contact abstract an accurate efficient and robust numerical scheme is presented for the simulation of the interaction between flexibly supported rigid bodies and incompressible fluid flow with topology changes and solid solid contact the solution of the incompressible navier stokes equations is approximated by employing a stabilised formulation on cartesian grids discretised with hierarchical b splines the solid is modelled as a rigid body and represented by linear segments along its boundary kinematic conditions along the fluid rigid body interface are enforced weakly using nitsche s method while ghost penalty operators are employed to avoid excessive ill conditioning of the system matrix arising from small cut cells a staggered scheme is used for resolving the coupled fluid rigid body interaction the contact between moving or moving and fixed solid bodies is modelled with lagrange multipliers the excellent performance and wide range of applicability of the proposed scheme are demonstrated in a number of benchmark tests as well as industrially relevant model problems the examples cover the galloping phenomena particulate flow hydraulic check valves and a model turbine

a dffd simulation method combined with the spectral element method for solid fluid interaction problems a 2d simulation method for a rigid body moving in an incompressible viscous fluid is proposed it combines one of the immersed boundary methods the dffd direct forcing fictitious domain method with the spectral element method the former is employed for efficiently capturing the two way fsi fluid structure interaction and the geometric flexibility of the latter is utilized for any possibly co existing stationary and complicated solid or flow boundary a pseudo body force is imposed within the solid domain to enforce the rigid body motion and a lagrangian mesh composed of triangular elements is employed for tracing the rigid body in particular a so called sub cell scheme is proposed to smooth the discontinuity at the fluid solid interface and to execute integrations involving eulerian variables over the moving solid domain the accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literatures the direct forcing fictitious domain method and the spectral element method are combined direct interpolation of eulerian variables onto lagrangian mesh is not necessary non fluctuating pressure fields are obtained with a smoothed pseudo body force the proposed method possesses a spectral accuracy both small and large solid to fluid density ratios are applicable

fast multigrid method for solving incompressible hydrodynamic problems with free surfaces we develop of a finite volume multigrid euler scheme for solving three dimensional fully nonlinear ship wave problems the flowfield and the a priori unknown free surface location are calculated by coupling the free surface kinematic and dynamic equations with the equations of motion for the bulk flow the evolution of the free surface boundary condition is linked to the evolution of the bulk flow via a novel iteration strategy that allows temporary leakage through the surface before the solution is converged the method of artificial compressibility is used to enforce the incompressibility constraint for the bulk flow a multigrid algorithm is used to accelerate convergence to a steady state

a high order characteristics upwind fv method for incompressible flow and heat transfer simulation on unstructured grids abstract this paper presents a new unstructured grid upwind finite volume algorithm for accurate numerical simulation of incompressible flows and convection heat transfer on unstructured grids it is an upwind method at both the differential equation level and discretized equation level based on the method of characteristics this is made possible with the introduction of chorin s j comput phys 2 1967 12 26 artificial compressibility formulation to the incompressible flow equations flow variables are calculated along characteristics and their initial values are interpolated based on the signs of the corresponding characteristic speed in addition an upwind biased interpolation method of third order accuracy is used for interpolating flow variables on unstructured grids with these inherent upwinding techniques for evaluating convection fluxes at control volume surfaces no artificial viscosity is required and the method is accurate and less sensitive to the grid orientation thus suitable for unstructured grid application the use of the finite volume method combined with unstructured grids makes the scheme very flexible in dealing with very complex boundary geometries while remaining to be fully conservative at the cell as well as global level the discretized equations are solved by an explicit multistage runge kutta time stepping scheme which is found to be efficient in terms of cpu and memory overheads a computer code has been developed which uses the numerical methods presented and a highly efficient edge based data structure for flux calculation and data storage a number of well documented test cases including 2d laminar flow in a channel with a backward facing step forced and natural convection flows have been calculated in order to validate the code and evaluate the performance of the numerical algorithm good agreement between the computed and measured results have been obtained for all the cases to demonstrate the accuracy of the third order scheme flow in another channel with a backward facing step studied by gartling int j numer meth fluids 1990 11 is simulated with both the third order and first order schemes it is shown that the third order scheme can produce a velocity profile across the channel that has perfect agreement with that of gartling local citation whilst the first order scheme cannot even predict the separation near the upper wall the proposed numerical methods are also used to calculate 3d incompressible inviscid flows and results show that the method is accurate and robust for general 3d simulation the 3d navier stokes code is later used to study a lid driven cavity flow at a reynolds number of 400 the unstructured grid used has 97 336 nodes and 455 625 tetrahedral elements with strong grid clustering near the walls the convergence rate is found to be satisfactory which shows that the method is also robust for 3d navier stokes simulation the results obtained agree well with those reported by jiang et al comput meth appl mech eng 114 109 1994 results obtained using the second order central scheme with artificial viscosity are also presented for comparison it is observed that the third order characteristics scheme is more accurate than the latter thus confirming its third order accuracy

a smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations the effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods the problem with this representation is that the volume force exhibits non physical oscillations in moving boundary simulations a smoothing technique for discrete delta functions has been developed in this paper to suppress the non physical oscillations in the volume forces we have found that the non physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions it has been shown that the smoothed discrete delta functions constructed in this paper have one order higher derivative than the regular ones moreover not only the smoothed discrete delta functions satisfy the first two discrete moment conditions but also their derivatives satisfy one order higher moment condition than the regular ones the smoothed discrete delta functions are tested by three test cases a one dimensional heat equation with a moving singular force a two dimensional flow past an oscillating cylinder and the vortex induced vibration of a cylinder the numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations

a cartesian grid method for modeling multiple moving objects in 2d incompressible viscous flow we present an efficient method for solving 2d incompressible viscous flows around multiple moving objects our method employs an underlying regular cartesian grid to solve the system using a streamfunction vorticity formulation and with discontinuities representing the embedded objects the no penentration condition for the moving geometry is satisfied by superposing a homogenous solution to the poisson s equation for the streamfunction the no slip condition is satisfied by generating vorticity on the surfaces of the objects both the initial poisson solution and the evaluation of the homogenous solution require embedding irregular discontinuities in a fast poisson solver computation time is dictated by the time required to do a fast poisson solution plus solve an integral form of laplace s equation there is no significant increase in computational cost if the geometry of the embedded objects is variable and moving relative to the underlying grid we test the method against the canonical example of flow past a cylinder and obtained new results on the flow and forces of two cylinders moving relative to each other

a cartesian based embedded geometry technique with adaptive high order finite differences for compressible flow around complex geometries an immersed boundary methodology to solve the compressible navier stokes equations around complex geometries in cartesian fluid dynamics solvers is described the objective of the new approach is to enable smooth reconstruction of pressure and viscous stresses around the embedded objects without spurious numerical artifacts a standard level set represents the boundary of the object and defines a fictitious domain into which the flow fields are smoothly extended boundary conditions on the surface are enforced by an approach inspired by analytic continuation each fluid field is extended independently constrained only by the boundary condition associated with that field unlike most existing methods no jump conditions or explicit derivation of them from the boundary conditions are required in this approach numerical stiffness that arises when the fluid solid interface is close to grid points of the mesh is addressed by preconditioning in addition the embedded geometry technique is coupled with a stable high order adaptive discretization that is enabled around the object boundary to enhance resolution the stencils used to transition the order of accuracy of the discretization are derived using the summation by parts technique that ensures stability applications to shock reflections shock ramp interactions and supersonic and low mach number flows over two and three dimensional geometries are presented

a differentially interpolated direct forcing immersed boundary method for predicting incompressible navier stokes equations in time varying complex geometries a dispersion relation preserving dual compact scheme developed in cartesian grids is applied together with the immersed boundary method to solve the flow equations in irregular and time varying domains the artificial momentum forcing term applied at certain points in cells containing fluid and solid allows an imposition of velocity condition to account for the motion of solid body we develop in this study a differential based interpolation scheme which can be easily extended to three dimensional simulation the results simulated from the proposed immersed boundary method agree well with other numerical and experimental results for the chosen benchmark problems the accuracy and fidelity of the ib flow solver developed to predict flows with irregular boundaries are therefore demonstrated

solution of eigenvalue problems for non classically damped systems with multiple frequencies abstract an efficient solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of non classically damped structural systems with multiple eigenvalues the proposed method is obtained by applying the modified newton raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem through matrix augmentation of the quadratic eigenvalue problem in the iteration methods such as the inverse iteration method and the subspace iteration method singularity may occur during the factorizing process when the shift value is close to an eigenvalue of the system however even though the shift value is an eigenvalue of the system the proposed method provides non singularity and that is analytically proved since the modified newton raphson technique is adapted to the proposed method initial values are needed because the lanczos method effectively produces better initial values than other methods the results of the lanczos method are taken as the initial values of the proposed method two numerical examples are presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well known subspace iteration method and the lanczos method

eigenvalue counting methods for non proportionally damped systems abstract this paper presents numerical methods of counting the number of eigenvalues for non proportionally damped system in some interested regions on the complex plane most of the eigenvalue analysis methods for proportionally damped systems use the well known sturm sequence property to check the missed eigenvalues when only a set of the lowest modes is used however in the case of the non proportionally damped systems such as the soil structure interaction system the structural control system and composite structures no counterpart of the sturm sequence property for undamped systems has been established yet in this study a numerical method based on argument principle is explained with emphasis on the discretization of the contour and a new method based on gleyse s theorem is proposed to verify the applicability of the methods two numerical examples are considered

staggered upwind method for solving navier stokes and k omega turbulence model equations a staggered finite volume upwind algorithm for solving the compressible navier stokes equations and the k w turbulence model equations has been developed for computing cascade flows roe s upwind scheme is used to discretize the convective terms of the navier stokes equations and a third order upwind scheme is used for the convective terms of the k equations all of the diffusion terms are discretized with the central difference method by the use of a combination of cell centered and cell vertex schemes the method maintains a small stencil for all of the diffusion terms and makes the navier stokes equations and k equations strongly coupled the algorithm was first tested for a flat plate flow the results compare well with empirical correlations further investigations are conducted on a supersonic wedge cascade flow and a low pressure turbine cascade flow at design and off design conditions the calculation results demonstrate the ability of the algorithm on shock capturing and separation prediction

implementation of a high order compact finite difference lattice boltzmann method in generalized curvilinear coordinates abstract in this work the implementation of a high order compact finite difference lattice boltzmann method cfdlbm is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non uniform grids the incompressible form of the discrete boltzmann equation with the bhatnagar gross krook bgk approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates herein the spatial derivatives in the resulting lattice boltzmann lb equation in the computational plane are discretized by using the fourth order compact finite difference scheme and the temporal term is discretized with the fourth order runge kutta scheme to provide an accurate and efficient incompressible flow solver a high order spectral type low pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions flow non linearities and grid non uniformity all boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates the accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems a sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are unsteady couette flow and steady flow in a 2 d cavity with non uniform grid and steady and unsteady flows over a circular cylinder and the naca0012 hydrofoil at different flow conditions results obtained for the above test cases are in good agreement with the existing numerical and experimental results the study shows the present solution methodology based on the implementation of the high order compact finite difference lattice boltzmann method cfdlbm in the generalized curvilinear coordinates is robust efficient and accurate for solving steady and unsteady incompressible flows over practical geometries

on eigenproblem solution of damped vibrations associated with gyroscopic moments a new efficient approach is presented for solving the quadratic eigenvalue problem of weakly nonproportionally damped vibration systems in the analysis of these systems gyroscopic moments and external damping are both considered traditional restriction of symmetry of inertia damping and stiffness matrices is slightly relaxed a second order perturbation theory is developed such that the perturbed solution is based on the eigensolution of an unperturbed subproblem this subproblem considers the unperturbed system in two different forms i a conservative gyroscopic part of an original problem or ii a nonconservative gyroscopic part of an original problem that is proportionally damped to cope with asymmetry of the system matrices a duncan s like state formulation is used to bring these matrices into a suitable form for perturbations two numerical examples are introduced for explaining the detailed implementation of the presented approach additionally a practical problem of rotor supported by two tilting pad bearings is investigated the eigensolutions obtained by the current approach match to a great extent other solutions obtained by time consuming exact methods the investigation procedure given here gives a framework to handle vibration problems of weakly nonproportional damping and or weakly asymmetric inertia damping and stiffness matrices

an immersed interface method for viscous incompressible flows involving rigid and flexible boundaries we present an immersed interface method for the incompressible navier stokes equations capable of handling both rigid and flexible boundaries the immersed boundaries are represented by a number of lagrangian control points in order to ensure that the no slip condition on the rigid boundary is satisfied singular forces are applied on the fluid the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity and are interpolated using cubic splines the strength of the singular forces at the rigid boundary is determined by solving a small system of equations at each timestep for flexible boundaries the forces that the boundary exerts on the fluid are computed from the constitutive relation of the flexible boundary and are applied to the fluid through the jump conditions the position of the flexible boundary is updated implicitly using a quasi newton method bfgs within each timestep the navier stokes equations are discretized on a staggered cartesian grid by a second order accurate projection method for pressure and velocity and the overall scheme is second order accurate

the shifted boundary method for embedded domain computations part ii linear advection diffusion and incompressible navier stokes equations abstract we propose a new embedded finite element method for the linear advection diffusion equation and the laminar and turbulent incompressible navier stokes equations the proposed method belongs to the class of surrogate approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary accordingly boundary conditions enforced weakly are appropriately modified to preserve optimal error convergence rates we include the full analysis of stability and convergence of the method in the linear advection diffusion equation and a battery of tests for the case of laminar and turbulent incompressible navier stokes equations we also discuss the conservation properties of the proposed method in all cases

boundary data immersion method for cartesian grid simulations of fluid body interaction problems a new robust and accurate cartesian grid treatment for the immersion of solid bodies within a fluid with general boundary conditions is described the new approach the boundary data immersion method bdim is derived based on a general integration kernel formulation which allows the field equations of each domain and the interfacial conditions to be combined analytically the resulting governing equation for the complete domain preserves the behavior of the original system in an efficient cartesian grid method including stable and accurate pressure values on the solid boundary the kernel formulation allows a detailed analysis of the method and it is demonstrated that bdim is consistent obtains second order convergence relative to the kernel width and is robust with respect to the grid and boundary alignment formulation for no slip and free slip boundary conditions are derived and numerical results are obtained for the flow past a cylinder and the impact of blunt bodies through a free surface the bdim predictions are compared to analytic experimental and previous numerical results confirming the properties efficiency and efficacy of this new boundary treatment for cartesian grid methods

a fictitious domain distributed lagrange multiplier based fluid structure interaction scheme with hierarchical b spline grids abstract we present a numerical scheme for fluid structure interaction based on hierarchical b spline grids and fictitious domain distributed lagrange multipliers the incompressible navier stokes equations are solved over a cartesian grid discretised with b splines the fluid grid near the immersed solids is refined locally using hierarchical b splines the immersed solid is modelled as geometrically exact beam discretised with standard linear lagrange shape functions the kinematic constraint at the fluid solid interface is enforced with distributed lagrange multipliers the unconditionally stable and second order accurate generalised method is used for integration in time for both the fluid and solid domains a fully implicit and fully coupled solution scheme is developed by using the newton raphson method to solve the non linear system of equations obtained with galerkin weak formulation first the spatial and temporal convergence of the proposed scheme is assessed by studying steady and unsteady flow past a fixed cylinder then the scheme is applied to several benchmark problems to demonstrate the efficiency and robustness of the proposed scheme the results obtained with the present scheme are compared with the reference values

central moment lattice boltzmann schemes with fixed and moving immersed boundaries lattice boltzmann lb schemes based on the relaxation of central moments have recently proved valuable in simulating flows with an improved stability with respect to the original single relaxation time bgk formulation while preserving the accuracy of the latter this has been assessed mainly for flows in simple geometries e g in periodic domains or with fixed rigid straight boundaries in the present study the properties of central moment lb schemes have been investigated against flow configurations involving arbitrarily shaped possibly moving boundaries within the framework of the so called immersed boundary ib method namely the presence of boundaries is accounted by an external force acting on the fluid that is encompassed in the central moment lb algorithm accuracy and stability issues are examined in comparison with existing results from the literature and lb simulations based on the original bgk scheme our results show that central moment lb schemes accompanied by the ib method provide an efficient tool for fluid structure interaction simulations

a direct forcing fictitious domain method for particulate flows a direct forcing fictitious domain df fd method for the simulation of particulate flows is reported the new method is a non lagrange multiplier version of our previous dlm fd code and is obtained by employing a discrete d function in the form of bi tri function to transfer explicitly quantities between the eulerian and lagrangian nodes as in the immersed boundary method due to the use of the collocation point approach for the rigidity constraint and the integration over the particle domain the lagrangian nodes are retracted a little from the particle boundary our method in case of a prescribed velocity on the boundary is verified via the comparison to the benchmark results on the flow over a fixed cylinder in a wide channel and to our spectral element results for a channel with the width of four cylinder diameters we then verify our new method for the case of the particulate flows through various typical flow situations including the sedimentation of a circular particle in a vertical channel the sedimentation of a sphere in a vertical pipe the inertial migration of a sphere in a circular poiseuille flow the behavior of a neutrally buoyant sphere in couette flow and the rotation of a prolate spheroid in couette flow the accuracy and robustness of the new method are fully demonstrated in particular for the case of relatively low reynolds numbers and the neutrally buoyant case

preconditioned multigrid methods for unsteady incompressible flows a highly efficient numerical approach based on multigrid and preconditioning methods is developed for modeling 3d steady and time dependent incompressible flows thek turbulence model is used to estimate the effects of turbulence the model equations are solved together with the n s equations in a strongly coupled way and acceleration techniques like the multigrid method are also used for the turbulence model equations for unsteady problems a dual time stepping procedure is adopted to satisfy the divergence free constraint and to obtain a time accurate solution to improve the performance of this approach for small physical time steps a modification to residual smoothing parameters is proposed the numerical algorithm and the turbulence model are validated first by calculating unsteady inviscid flow around an oscillating cylinder unsteady laminar flow past a circular cylinder and steady high reynolds number turbulent flow over a 6 1 prolate spheroid then the three dimensional time dependent turbulent flow over a spheroid when it is undergoing a pitch up maneuver is calculated and compared with experimental data

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

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

efficient and non reflecting far field boundary conditions for incompressible flow calculations abstract traditionally the artificial compressibility ac method of chorin is used for simulation of low speed and incompressible flows in this method the difficulty of continuity and momentum equations decoupling is removed by adding an artificial time derivative of pressure to the continuity equation for the first time a fully two dimensional upwind scheme was presented for ac equations by using characteristic structure of equations by the authors in this paper a new remote boundary calculation method is presented by using the idea of characteristics for these equations instead of simple boundary conditions which usually are employed for incompressible flows the flow quantities at the far field boundaries are evaluated by compatibility relations of characteristic equations this is implemented by assuming a row of ghost cells outside of the far field boundary and using the flux calculation method based on characteristics similar to the inside of computational domain the idea in conjunction with multidimensional characteristic based scheme was tested for incompressible flow around circular cylinder in comparison with conventional far field boundary condition and showed good improvements in the terms of accuracy and convergence speed

staggered finite volume scheme for solving cascade flow with a k omega turbulence model a k turbulence model by wilcox is applied to cascade flow calculations a staggered finite volume scheme is proposed to solve the compressible reynolds averaged navier stokes equations and the k equations are solved on staggered control volumes with k and defined at the cell vertices of the original grid by use of this combination of the cell centered and cell vertex schemes the method maintains a small stencil for all diffusion terms and closely couples the navier stokes and k equations

proteus a coupled iterative force correction immersed boundary multi domain cascaded lattice boltzmann solver abstract most realistic fluid flow problems are characterized by high reynolds numbers and complex boundaries over the last ten years immersed boundary methods that are able to cope with realistic geometries have been applied to lattice boltzmann lb methods these methods however have normally been applied to low reynolds number problems here we present a novel coupling between an iterative force correction immersed boundary zhang et al 2016 and a multi domain cascaded lb method the iterative force correction immersed boundary method has been selected due to the improved accuracy of the computation while the cascaded lb formulation is used due to its superior stability at high reynolds numbers the coupling is shown to improve both the stability and numerical accuracy of the solution the resulting solver has been applied to viscous flow up to a reynolds number of 100000 passed a naca 0012 airfoil at a 10 degree angle of attack good agreement with results obtained using a body fitted navier stokes solver has been obtained the formulation provides a straight forward and efficient method for modeling realistic geometries and could easily be extended to problems with moving boundaries

very high order compact finite difference schemes on non uniform grids for incompressible navier stokes equations this article presents a family of very high order non uniform grid compact finite difference schemes with spatial orders of accuracy ranging from 4th to 20th for the incompressible navier stokes equations the high order compact schemes on non uniform grids developed in shukla and zhong r k shukla x zhong derivation of high order compact finite difference schemes for non uniform grid using polynomial interpolation j comput phys 204 2005 404 for linear model equations are extended to the full navier stokes equations in the vorticity and streamfunction formulation two methods for the solution of helmholtz and poisson equations using high order compact schemes on non uniform grids are developed the schemes are constructed so that they maintain a high order of accuracy not only in the interior but also at the boundary second order semi implicit temporal discretization is achieved through an implicit backward differentiation scheme for the linear viscous terms and an explicit adam bashforth scheme for the non linear convective terms the boundary values of vorticity are determined using an influence matrix technique the resulting discretized system with boundary closures of the same high order as the interior is shown to be stable when applied to the two dimensional incompressible navier stokes equations provided enough grid points are clustered at the boundary the resolution characteristics of the high order compact finite difference schemes are illustrated through their application to the one dimensional linear wave equation and the two dimensional driven cavity flow comparisons with the benchmark solutions for the two dimensional driven cavity flow thermal convection in a square box and flow past an impulsively started cylinder show that the high order compact schemes are stable and produce extremely accurate results on a stretched grid with more points clustered at the boundary

an immersed boundary method for fluid flexible structure interaction an immersed boundary method for simulation of fluid flexible structure interaction has been proposed in the method an efficient navier stokes solver adopting the fractional step method and a staggered cartesian grid system is used to solve the incompressible fluid motion in an eulerian domain on the other hand a moving lagrangian grid is used to discretize the structure domain and the equation of structure motion is derived by the energy method and is solved by an iterative method the fluid structure interaction is formulated by an additional momentum forcing which is obtained on the lagrangian grid using the structure motion equation and is spread to the nearby eulerian girds by applying a smoothed approximation of the dirac delta function in this way the massive boundary is handled easily without any special treatment while for the neutrally buoyant case our formulation becomes equivalent with previous ones in the simulations we mainly use small additional boundary mass toward biofluid applications three numerical examples are simulated a lid driven cavity with a deformable volume at the bottom a swimming jellyfish and a deformable circular ring moving through a channel with contraction the results are compared with those of previous studies and the theoretical solutions the temporal and spatial convergence rates of the present method are specified the tendency of the numerical solution as the additional boundary mass approaches zero is investigated

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

incompressible moving boundary flows with the finite volume particle method abstract mesh free methods offer the potential for greatly simplified modeling of flow with moving walls and phase interfaces the finite volume particle method fvpm is a mesh free technique based on interparticle fluxes which are exactly analogous to intercell fluxes in the mesh based finite volume method consequently the method inherits many of the desirable properties of the classical finite volume method including implicit conservation and a natural introduction of boundary conditions via appropriate flux terms in this paper we describe the extension of fvpm to incompressible viscous flow with moving boundaries an arbitrary lagrangian eulerian approach is used in conjunction with the mesh free discretisation to facilitate a straightforward treatment of moving bodies non uniform particle distribution is used to concentrate computational effort in regions of high gradients the underlying method for viscous incompressible flow is validated for a lid driven cavity problem at reynolds numbers of 100 and 1000 to validate the simulation of moving boundaries flow around a translating cylinder at reynolds numbers of 20 40 and 100 is modeled results for pressure distribution surface forces and vortex shedding frequency are in good agreement with reference data from the literature and with fvpm results for an equivalent flow around a stationary cylinder these results establish the capability of fvpm to simulate large wall motions accurately in an entirely mesh free framework

an improved subspace iteration method with shift for structures with multiple natural frequencies an efficient and numerically stable eigensolution method for structures with multiple natural frequencies is presented the proposed method is developed by improving the well known subspace iteration method with shift a major difficulty of the subspace iteration method with shift is that because of singularity problem a shift close to an eigenvalue cannot be used resulting in slower convergence in this paper the above singularity problem has been solved by introducing side conditions without sacrifice of convergence the proposed method is always non singular even if a shift is on a distinct eigenvalue or multiple ones this is one of the significant characteristics of the proposed method the non singularity is proved analytically the convergence of the proposed method is at least equal to that of the subspace iteration method with shift and the operation counts of the above two methods are almost the same when a large number of eigenpairs are required to show the effectiveness of the proposed method two numerical examples are considered

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

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

diffuse interface modeling of three phase contact line dynamics on curved boundaries we introduce a simple and efficient lattice boltzmann method for immiscible multiphase flows capable of handling large density and viscosity contrasts the model is based on a diffuse interface phase field approach within this context we propose a new algorithm for specifying the three phase contact angle on curved boundaries within the framework of structured cartesian grids the proposed method has superior computational accuracy compared with the common approach of approximating curved boundaries with stair cases we test the model by applying it to four benchmark problems i wetting and dewetting of a droplet on a flat surface and ii on a cylindrical surface iii multiphase flow past a circular cylinder at an intermediate reynolds number and iv a droplet falling on hydrophilic and superhydrophobic circular cylinders under differing conditions where available our results show good agreement with analytical solutions and or existing experimental data highlighting strengths of this new approach

parallel multigrid computation of unsteady incompressible viscous flows using a matrix free implicit method and high resolution characteristics based scheme abstract a three dimensional parallel unstructured non nested multigrid solver for solutions of unsteady incompressible viscous flow is developed and validated the finite volume navier stokes solver is based on the artificial compressibility approach with a high resolution method of characteristics based scheme for handling convection terms the unsteady flow is calculated with a matrix free implicit dual time stepping scheme the parallelization of the multigrid solver is achieved by multigrid domain decomposition approach mg dd using single program multiple data spmd and multiple instruction multiple data mimd programming paradigm there are two parallelization strategies proposed in this work first strategy is a one level parallelization strategy using geometric domain decomposition technique alone second strategy is a two level parallelization strategy that consists of a hybrid of both geometric domain decomposition and data decomposition techniques message passing interface mpi and openmp standard are used to communicate data between processors and decompose loop iterations arrays respectively the parallel multigrid code is used to simulate both steady and unsteady incompressible viscous flows over a circular cylinder and a lid driven cavity flow a maximum speedup of 22 5 could be achieved on 32 processors for instance the lid driven cavity flow of re 1000 the results obtained agree well with numerical solutions obtained by other researchers as well as experimental measurements a detailed study of the time step size and number of pseudo sub iterations per time step required for simulating unsteady flow are presented in this paper

an efficient fluid solid coupling algorithm for single phase flows we present a simple and efficient fluid solid coupling method in two and three spatial dimensions in particular we consider the numerical approximation of the navier stokes equations on irregular domains and propose a novel approach for solving the hodge projection step on arbitrary shaped domains this method is straightforward to implement and leads to a symmetric positive definite linear system for both the projection step and for the implicit treatment of the viscosity we demonstrate the accuracy of our method in the l 1 and l norms and present its removing the errors associated with the conventional rasterization type discretizations we apply this method to the simulation of a flow past a cylinder in two spatial dimensions and show that our method can reproduce the known stable and unstable regimes as well as correct lift and drag forces we also apply this method to the simulation of a flow past a sphere in three spatial dimensions at low and moderate reynolds number to reproduce the known steady axisymmetric and non axisymmetric flow regimes we further apply this algorithm to the coupling of flows with moving rigid bodies

the gauss map of a genus three theta divisor a smooth complex curve is determined by the gauss map of the theta divisor of the jacobian variety of the curve the gauss map is invariant with respect to the 1 map of the jacobian we show that for a generic genus three curve the gauss map is locally z 2 stable one method of proof is to analyze the first order z 2 deformations of the gauss map of a hyperelliptic theta divisor