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

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

a simple and efficient direct forcing immersed boundary framework for fluid structure interactions a direct forcing immersed boundary framework is presented for the simple and efficient simulation of strongly coupled fluid structure interactions the immersed boundary method developed by yang and balaras j yang e balaras an embedded boundary formulation for large eddy simulation of turbulent flows interacting with moving boundaries j comput phys 215 1 2006 12 40 is greatly simplified by eliminating several complicated geometric procedures without sacrificing the overall accuracy the fluid structure coupling scheme of yang et al j yang s preidikman e balaras a strongly coupled embedded boundary method for fluid structure interactions of elastically mounted rigid bodies j fluids struct 24 2008 167 182 is also significantly expedited by moving the fluid solver out of the predictor corrector iterative loop without altering the strong coupling property central to these improvements are the reformulation of the field extension strategy and the evaluation of fluid force and moment exerted on the immersed bodies by taking advantage of the direct forcing idea in a fractional step method several cases with prescribed motions are examined first to validate the simplified field extension approach then a variety of strongly coupled fluid structure interaction problems including vortex induced vibrations of a circular cylinder transverse and rotational galloping of rectangular bodies and fluttering and tumbling of rectangular plates are computed the excellent agreement between the present results and the reference data from experiments and other simulations demonstrates the accuracy simplicity and efficiency of the new method and its applicability in a wide range of complicated fluid structure interaction problems

nonlocal filtration equations with rough kernels abstract we study the nonlinear and nonlocal cauchy problem t u l u 0 in r n r u 0 u 0 where l is a levy type nonlocal operator with a kernel having a singularity at the origin as that of the fractional laplacian the nonlinearity is nondecreasing and continuous and the initial datum u 0 is assumed to be in l 1 r n we prove existence and uniqueness of weak solutions for a wide class of nonlinearities including the porous media case u u m 1 u m 1 these solutions turn out to be bounded and holder continuous for t 0 we also describe the large time behaviour when the nonlinearity resembles a power for u 0 and the kernel associated to l is close at infinity to that of the fractional laplacian

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 boundary condition capturing immersed interface method for 3d rigid objects in a flow to simulate the flow around an object we can replace the object with the fluid enclosed by a singular force we can then simulate the flow on a fixed domain with a fluid fluid interface supporting the singular force in this paper we present a boundary condition capturing approach to determine the singular force for a 3d rigid object we apply a discontinuous body force to enforce the rigid motion of the fluid replacing the object and compute the singular force based on the kinematics of the object due to the singular force and the body force the flow is not smooth across the interface we solve the flow using the immersed interface method our boundary condition capturing immersed interface method is very efficient and stable and its accuracy based on the infinity norm is near second order for the velocity and above first order for the pressure

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

on the accuracy of direct forcing immersed boundary methods with projection methods direct forcing methods are a class of methods for solving the navier stokes equations on nonrectangular domains the physical domain is embedded into a larger rectangular domain and the equations of motion are solved on this extended domain the boundary conditions are enforced by applying forces near the embedded boundaries this raises the question of how the flow outside the physical domain influences the flow inside the physical domain this question is particularly relevant when using a projection method for incompressible flow in this paper analysis and computational tests are presented that explore the performance of projection methods when used with direct forcing methods sufficient conditions for the success of projection methods on extended domains are derived and it is shown how forcing methods meet these conditions bounds on the error due to projecting on the extended domain are derived and it is shown that direct forcing methods are in general first order accurate in the max norm numerical tests of the projection alone confirm the analysis and show that this error is concentrated near the embedded boundaries leading to higher order accuracy in integral norms generically forcing methods generate a solution that is not smooth across the embedded boundaries and it is this lack of smoothness which limits the accuracy of the methods additional computational tests of the navier stokes equations involving a direct forcing method and a projection method are presented and the results are compared with the predictions of the analysis these results confirm that the lack of smoothness in the solution produces a lower order error the rate of convergence attained in practice depends on the type of forcing method used

a novel iterative direct forcing immersed boundary method and its finite volume applications we present a novel iterative immersed boundary ib method in which the body force updating is incorporated into the pressure iterations because the body force and pressure are solved simultaneously the boundary condition on the immersed boundary can be fully verified the computational costs of this iterative ib method is comparable to those of conventional ib methods we also introduce an improved body force distribution function which transfers the body force in the discrete volume of ib points to surrounding cartesian grids totally to alleviate the demanding computational requirements of a full resolved direct numerical simulation a wall layer model is presented the accuracy and capability of the present method is verified by a variety of two and three dimensional numerical simulations ranging from laminar flow past a cylinder and a sphere to turbulent flow around a cylinder the improvement of the iterative ib method is fully demonstrated and the influences of different body force distribution strategies is discussed

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

implicit heat flux correction based immersed boundary finite volume method for thermal flows with neumann boundary conditions abstract in the frameworks of immersed boundary method ibm and finite volume method fvm an implicit heat flux correction based ib fvm is proposed for thermal flows with neumann boundary conditions with the use of a fractional step technique the preconditioned navier stokes n s equations are solved by the fvm to obtain the intermediate solution in the prediction step and the heat flux is corrected by enforcing the neumann condition in the correction step different from existing ibms the cell face centers are defined as the eulerian points due to the heat flux computation at each face in the fvm the neumann condition is implemented in such a way that the interpolated temperature gradient is equal to the specified boundary value at the same point when the corrected gradient field is interpolated from the face centers to the lagrangian points to achieve an implicit algorithm the temperature derivative corrections at the lagrangian points are set as unknowns and a system of algebraic equations is established by constructing hybrid thin plate splines tps interpolation delta function distribution in the derivative interpolation process the much more accurate tps is introduced because the use of cosine delta function yields a less accurate solution after the distribution process the heat flux correction of a fluid cell is evaluated by using the solved temperature derivative corrections at the face centers but that of a solid cell is calculated by using their additive inverses to supplement the same amount of heat flux into the solid domain as that flowing into the fluid domain across the boundary finally the heat flux of a cell is corrected by adding the correction to the intermediate value and the corrected heat flux is utilized to solve the n s equations in the prediction step as compared with the available implicit ibms for neumann conditions the present method avoids the introduction of auxiliary layers of lagrangian points as well as the approximate conversion from the neumann to dirichlet condition and thus is suitable for an arbitrary geometry the proposed method is verified by simulating several benchmark thermal flows with neumann conditions the natural convection in an annulus and the steady or unsteady forced convection over a stationary or oscillating cylinder all the computed results agree well with the literature data

boundary condition enforced immersed boundary lattice boltzmann flux solver for thermal flows with neumann boundary conditions a boundary condition enforced immersed boundary lattice boltzmann flux solver is proposed in this work for effective simulation of thermal flows with neumann boundary conditions in this method two auxiliary layers of lagrangian points are introduced and respectively placed inside and outside of the solid body on which the temperature corrections related to the heat source are set as unknowns to effectively consider the fluid boundary interaction these unknowns are expressed as algebraic summations of the temperature correction on eulerian points which are in turn obtained from biased distributions of unknown temperature corrections on the immersed boundary by enforcing the temperature gradient at the solid boundary being equal to that approximated by the corrected temperature field a set of algebraic equations are formed and solved to obtain all the unknowns simultaneously they are then distributed biasedly to the inner region of the auxiliary layer so that the diffusion from the smooth delta function can be reduced substantially in addition the solutions of the flow and temperature fields are obtained by the thermal lattice boltzmann flux solver with the second order of accuracy the proposed method is well validated through its applications to simulate several benchmarks of natural forced and mixed convection problems it has been demonstrated that the present solver has about 1 724 order of accuracy and the error between the present result and theoretical value for the temperature gradient on the solid surface is in the order of 10 13 which indicates that the proposed method is able to satisfy the neumann boundary condition accurately

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

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

numerical simulation of two dimensional flows over a circular cylinder using the immersed boundary method in this work a virtual boundary method is applied to the numerical simulation of a uniform flow over a cylinder the force source term added to the two dimensional navier stokes equations guarantees the imposition of the no slip boundary condition over the body fluid interface these equations are discretized using the finite differences method the immersed boundary is represented with a finite number of lagrangian points distributed over the solid fluid interface a cartesian grid is used to solve the fluid flow equations the key idea is to propose a method to calculate the interfacial force without ad hoc constants that should usually be adjusted for the type of flow and the type of the numerical method when this kind of model is used in the present work this force is calculated using the navier stokes equations applied to the lagrangian points and then distributed over the eulerian grid the main advantage of this approach is that it enables calculation of this force field even if the interface is moving or deforming it is unnecessary to locate the eulerian grid points near this immersed boundary the lift and drag coefficients and the strouhal number calculated for an immersed cylinder are compared with previous experimental and numerical results for different reynolds numbers

immersed boundary methods for general finite difference and finite volume navier stokes solvers we present an immersed boundary algorithm for incompressible flows with complex boundaries suitable for cartesian or curvilinear grid system the key stages of any immersed boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary a line in 2d a surface in 3d and the spreading of a force field from the immersed boundary to the neighboring mesh points to enforce the desired boundary conditions on the immersed boundary points we propose a technique that uses the reproducing kernel particle method w k liu s jun y f zhang reproducing kernel particle methods int j numer methods fluids 20 8 1995 1081 1106 for the interpolation and spreading unlike other methods presented in the literature the one proposed here has the property that the integrals of the force field and of its moment on the grid are conserved independent of the grid topology uniform or non uniform cartesian or curvilinear the technique is easy to implement and is able to maintain the order of the original underlying spatial discretization applications to two and three dimensional flows in cartesian and non cartesian grid system with uniform and non uniform meshes are presented

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

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

optimal decay for a porous elasticity system with memory abstract in this paper we consider a one dimensional linear porous system with finite memory effective on the equilibrated stress vector by assuming minimal conditions on the relaxation function we establish an optimal explicit and energy decay rate for which exponential and polynomial rates are special cases this result is new and substantially improves earlier results in the literature

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