inverse shape and surface heat transfer coefficient identification in this paper an inverse geometric problem for the modified helmholtz equation arising in heat conduction in a fin is considered this problem which consists of determining an unknown inner boundary of an annular domain and possibly its surface heat transfer coefficient from one or two pairs of boundary cauchy data boundary temperature and heat flux is solved numerically using the meshless method of fundamental solutions mfs a nonlinear unconstrained minimisation of the objective function is regularised when noise is added to the input boundary data the stability of the numerical results is investigated for several test examples with respect to noise in the input data and various values of the regularisation parameters

a cartesian grid embedded boundary method for hyperbolic conservation laws we present a second order godunov algorithm to solve time dependent hyperbolic systems of conservation laws on irregular domains our approach is based on a formally consistent discretization of the conservation laws on a finite volume grid obtained from intersecting the domain with a cartesian grid we address the small cell stability problem associated with such methods by hybridizing our conservative discretization with a stable nonconservative discretization at irregular control volumes and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation the resulting method is second order accurate in l 1 for smooth problems and is robust in the presence of large amplitude discontinuities intersecting the irregular boundary

a sharp interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations a method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp interface immersed boundary methods ibms is proposed by first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary we adopt a cut cell based approach to strictly enforce geometric conservation in order to limit the complexity associated with the cut cell method the cut cell based discretization is limited only to the pressure poisson and velocity correction equations in the fractional step method and the small cell problem tackled by introducing a virtual cell merging technique the method is shown to retain all the desirable properties of the original finite difference based ibm while at the same time reducing pressure oscillations for moving boundaries by roughly an order of magnitude

exact static solutions of a generalized discrete φ 4 model including short periodic solutions we carry out a comprehensive analysis of a generalized discrete 4 model of which virtually all 4 models discussed in the literature are particular cases for this model we construct the exact solutions in the form of the basic jacobi elliptic hyperbolic and sine functions and also give a list of short periodic and even aperiodic solutions some of those solutions coincide with the known ones others generalize the existing solutions and the rest of them are new we then discuss the relation between the models supporting exact static solutions and the two point maps in particular we show that some of the short periodic and sine solutions can be found from factorized difference equations and even from a set of two difference equations one of the first and another of the second order particular attention is paid to the discussion of the exceptional discrete ed models defined as models supporting the translationally invariant ti static solutions that can be placed arbitrarily with respect to the lattice we show that some of the derived short periodic solutions are ti ones while the others are not for the ti static solutions we demonstrate the existence of the translational goldstone mode for any location of the solution with respect to the lattice we then analyze numerically the stability and other properties of the ti kink solutions in conclusion we divide the ed models into two classes the ed i models support a two parameter set of ti static solutions while the ed ii models support only a one parameter set of such solutions

a conservative immersed interface method for large eddy simulation of incompressible flows we propose a conservative second order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered cartesian grid the method is based on a finite volume discretization of the incompressible navier stokes equations which is modified locally in cells that are cut by the interface in such a way that accuracy and conservativity are maintained a level set technique is used for description and tracking of the interface geometry so that an extension of the method to moving boundaries and flexible walls is straightforward numerical stability is ensured for small cells by a conservative mixing procedure discrete conservation and sharp representation of the fluid solid interface render the method particularly suitable for large eddy simulations of high reynolds number flows accuracy second order grid convergence and robustness of the method is demonstrated for several test cases inclined channel flow at re 20 flow over a square cylinder at re 100 flow over a circular cylinder at re 40 re 100 and re 3900 as well as turbulent channel flow with periodic constrictions at re 10 595

a new barrier to the existence of moving kinks in frenkel kontorova lattices an explanation is offered for an observed lower bound on the wave speed of travelling kinks in frenkel kontorova lattices kinks exist at discrete wavespeeds within a parameter regime where there is a resonance with linear waves phonons however they fail to exist even in this codimension one sense whenever there is more than one phonon branch in the dispersion relation inside such bands only quasi kinks with nondecaying oscillatory tails are possible the results are presented for a discrete sine gordon lattice with an onsite potential that has a tunable amount of anharmonicity novel numerical methods are used to trace kinks with topological charge q 1 and 2 in three parameters representing the propagation speed lattice discreteness and anharmonicity although none of the analysis is presented as rigorous mathematics numerical results suggest that the bound on allowable wavespeeds is sharp the results also explain why the vanishing at discrete values of anharmonicity of the peierls nabarro barrier between stationary kinks as discovered by savin et al does not lead to bifurcation of kinks with small wave speed 2003 elsevier b v all rights reserved

regularized method of fundamental solutions for boundary identification in two dimensional isotropic linear elasticity we investigate the stable numerical reconstruction of an unknown portion of the boundary of a two dimensional domain occupied by an isotropic linear elastic material from a prescribed boundary condition on this part of the boundary and additional displacement and traction measurements i e cauchy data on the remaining known portion of the boundary this inverse geometric problem is approached by combining the method of fundamental solutions mfs and the tikhonov regularization method whilst the optimal value of the regularization parameter is chosen according to the discrepancy principle various geometries are considered i e convex and non convex domains with a smooth or piecewise smooth boundary in order to show the numerical stability convergence consistency and computational efficiency of the proposed method

exact static solutions for discrete ϕ 4 models free of the peierls nabarro barrier discretized first integral approach we propose a generalization of the discrete klein gordon models free of the peierls nabarro barrier derived in spreight nonlinearity 12 1373 1999 and barashenkov et al phys rev e 72 035602 r 2005 such that they support not only kinks but a one parameter set of exact static solutions these solutions can be obtained iteratively from a two point nonlinear map whose role is played by the discretized first integral of the static klein gordon field as suggested by dmitriev et al j phys a 38 7617 2005 we then discuss some discrete ensuremath phi 4 models free of the peierls nabarro barrier and identify for them the full space of available static solutions including those derived recently by cooper et al phys rev e 72 036605 2005 but not limited to them these findings are also relevant to standing wave solutions of discrete nonlinear schr odinger models we also study stability of the obtained solutions as an interesting aside we derive the list of solutions to the continuum ensuremath phi 4 equation that fill the entire two dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models

an efficient conservative cut cell method for rigid bodies interacting with viscous compressible flows a cartesian cut cell method for viscous flows interacting with freely moving boundaries is presented the method enables a sharp resolution of the embedded boundaries and strictly conserves mass momentum and energy a new explicit runge kutta scheme pc rk is introduced by which the overall computational time is reduced by a factor of up to 2 5 the new scheme is a predictor corrector type reformulation of a popular class of runge kutta methods which substantially reduces the computational effort for tracking the moving boundaries and subsequently reinitializing the solver impairing neither stability nor accuracy the structural motion is computed by an implicit scheme with good stability properties due to a strong coupling strategy and the conservative discretization of the flow solver at the material interfaces a new formulation for the treatment of small cut cells is proposed with high accuracy and robustness for arbitrary geometries based on a weighted taylor series approach solved via singular value decomposition the efficiency and the accuracy of the new method are demonstrated for several three dimensional cases of laminar and turbulent particulate flow it is shown that the new method remains fully conservative even for large displacements of the boundaries leading to a fast convergence of the fluid solid coupling while spurious force oscillations inherent to this class of methods are effectively suppressed the results substantiate the good stability and accuracy properties of the scheme even on relatively coarse meshes an efficient cartesian cut cell method for freely moving solid boundaries is presented the new predictor corrector runge kutta scheme pc rk enables simulation speedups of up to 2 5 mass momentum and energy are strictly conserved at the sharply resolved solid fluid interfaces the method exhibits very good stability and accuracy properties even for large displacements of the boundaries spurious force oscillations inherent to this class of methods are suppressed

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

cut element based immersed boundary method for moving geometries in compressible liquid flows with cavitation the conservative immersed interface method for representing complex immersed solid boundaries or phase interfaces on cartesian grids is improved and extended to allow for the simulation of weakly compressible fluid flows through moving geometries we demonstrate that an approximation of moving interfaces by a level set field results in unphysical oscillations in the vicinity of sharp corners when dealing with weakly compressible fluids such as water by introducing an exact reconstruction of the cut cell properties directly based on a surface triangulation of the immersed boundary we are able to recover the correct flow evolution free of numerical artifacts the new method is based on cut elements it provides sub cell resolution of the geometry and handles flows through narrow closing or opening gaps in a straightforward manner we validate our method with canonical flows around oscillating cylinders we demonstrate that the method allows for an accurate prediction of flows around moving obstacles in weakly compressible liquid flows with cavitation effects in particular we show that the cavitating flow through a closing fuel injector control valve which is an example for a complex application with interaction of stationary and moving parts can be predicted by the method

exact static solutions to a translationally invariant discrete phi4 model for a discrete translationally invariant 4 model introduced by barashenkov et al 2005 phys rev e 72 35602r we provide the momentum conservation law and demonstrate how the first integral of the static version of the discrete model can be constructed from a jacobi elliptic function jef solution the first integral can be written in the form of a nonlinear map from which the static solution supported by the model can be constructed a set of jef solutions including the staggered ones is derived we also report on the stability analysis for the static bounded solutions and exemplify the dynamical behaviour of the unstable solutions this work provides a road map through this illustrative example on how to fully analyse translationally invariant models in terms of their static problem its first integral their full set of static solutions and associated conservation laws

computation of solid liquid phase fronts in the sharp interface limit on fixed grids a finite difference formulation is applied to track solid liquid boundaries on a fixed underlying grid the interface is not of finite thickness but is treated as a discontinuity and is explicitly tracked the imposition of boundary conditions exactly on a sharp interface that passes through the cartesian grid is performed using simple stencil readjustments in the vicinity of the interface attention is paid to formulating difference schemes that are globally second order accurate in x and t error analysis and grid refinement studies are performed for test problems involving the diffusion and convection diffusion equations and for stable solidification problems issues concerned with stability and change of phase of grid points in the evolution of solid liquid phase fronts are also addressed it is demonstrated that the field calculation is second order accurate while the position of the phase front is calculated to first order accuracy furthermore the accuracy estimates hold for the cases where there is a property jump across the interface unstable solidification phenomena are simulated and an attempt is made to compare results with previously published work the results indicate the need to begin an effort to benchmark computations of instability phenomena

an adaptive greedy technique for inverse boundary determination problem in this paper the method of fundamental solutions mfs is employed for determining an unknown portion of the boundary from the cauchy data specified on parts of the boundary we propose a new numerical method with adaptive placement of source points in the mfs to solve the inverse boundary determination problem since the mfs source points placement here is not trivial due to the unknown boundary we employ an adaptive technique to choose a sub optimal arrangement of source points on various fictitious boundaries afterwards the standard tikhonov regularization method is used to solve ill conditional matrix equation while the regularization parameter is chosen by the l curve criterion the numerical studies of both open and closed fictitious boundaries are considered it is shown that the proposed method is effective and stable even for data with relatively high noise levels

exact moving and stationary solutions of a generalized discrete nonlinear schrodinger equation we obtain exact moving and stationary spatially periodic and localized solutions of a generalized discrete nonlinear schrodinger equation more specifically we find two different moving periodic wave solutions and a localized moving pulse solution we also address the problem of finding exact stationary solutions and for a particular case of the model when stationary solutions can be expressed through the jacobi elliptic functions we present a two point map from which all possible stationary solutions can be found numerically we demonstrate the generic stability of the stationary pulse solutions and also the robustness of moving pulses in long term dynamics

on the order of accuracy of the immersed boundary method higher order convergence rates for sufficiently smooth problems the immersed boundary method is both a mathematical formulation and a numerical scheme for problems involving the interaction of a viscous incompressible fluid and a visco elastic structure in m c lai simulations of the flow past an array of circular cylinders as a test of the immersed boundary method ph d thesis courant institute of mathematical sciences new york university 1998 m c lai c s peskin an immersed boundary method with formal second order accuracy and reduced numerical viscosity j comput phys 160 2000 705 719 lai and peskin introduced a formally second order accurate immersed boundary method but the convergence properties of their algorithm have only been examined computationally for problems with nonsmooth solutions consequently in practice only first order convergence rates have been observed in the present work we describe a new formally second order accurate immersed boundary method and demonstrate its performance for a prototypical fluid structure interaction problem involving an immersed viscoelastic shell of finite thickness studied over a broad range of reynolds numbers we consider two sets of material properties for the viscoelastic structure including a case where the material properties of the coupled system are discontinuous at the fluid structure interface for both sets of material properties the true solutions appear to possess sufficient smoothness for the method to converge at a second order rate for fully resolved computations

a cut cell finite volume finite element coupling approach for fluid structure interaction in compressible flow we present a loosely coupled approach for the solution of fluid structure interaction problems between a compressible flow and a deformable structure the method is based on staggered dirichlet neumann partitioning the interface motion in the eulerian frame is accounted for by a conservative cut cell immersed boundary method the present approach enables sub cell resolution by considering individual cut elements within a single fluid cell which guarantees an accurate representation of the time varying solid interface the cut cell procedure inevitably leads to non matching interfaces demanding for a special treatment a mortar method is chosen in order to obtain a conservative and consistent load transfer we validate our method by investigating two dimensional test cases comprising a shock loaded rigid cylinder and a deformable panel moreover the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset finally we propose a three dimensional fluid structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations

an adaptive version of the immersed boundary method a computational setting for the immersed boundary method employing an adaptive mesh refinement is presented enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested progressively finer rectangular grid patches which dynamically follow the immersed boundary motion the set of equations describing the interaction between a non stationary viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method specially designed for locally refined meshes to an implicit formulation of the immersed boundary method the main contributions of this work concern the formulation and the implementation of a multilevel self adaptive version of the immersed boundary method on locally refined meshes this approach is tested for a particular two dimensional model problem for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary and on the associated uniform mesh built with the resolution of the finest level

exact stationary solutions for the translationally invariant discrete nonlinear schrodinger equations from a wide class of translationally invariant discrete nonlinear schrodinger dnls equations we extract a two parameter subclass corresponding to kerr nonlinearity for which any stationary solution can be derived recurrently from a quadratic equation this subclass which incorporates the integrable ablowitz ladik lattice as a special case admits exact stationary solutions that are derived in terms of the jacobi elliptic functions exact moving solutions for the discrete equations are also obtained in the continuum limit the constructed stationary solutions reduce to the exact moving solutions to the continuum nls equation with kerr nonlinearity numerical results are also presented for the special case of localized solutions including sech pulse or bright soliton tanh kink or dark soliton and 1 tanh called here inverted kink profiles for these solutions we discuss their linearization spectra and their mobility particularly we demonstrate that discrete dark solitons are dynamically stable for a wide range of lattice spacings contrary to what is the case for their standard dnls counterparts furthermore the bright and dark solitons in the non integrable translationally invariant lattices can propagate at slow speed without any noticeable radiation

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

accurate immersed boundary reconstructions for viscous flow simulations cells crossed by the immersed boundary is treated a novel interpolation method based on momentum balance and massconservationbasedon finitevolumemethodareintroducedtocorrectlypredictthevelocityandpressure fieldin the vicinity of the boundaries the assessment of the solution quality is based on calculations of taylor decaying vortices examples of laminar and turbulent flow calculations are also reported

translationally invariant discrete kinks from one dimensional maps for most discretizations of the phi4 theory the stationary kink can only be centered either on a lattice site or midway between two adjacent sites we search for exceptional discretizations that allow stationary kinks to be centered anywhere between the sites we show that this translational invariance of the kink implies the existence of an underlying one dimensional map phi n 1 f phi n a simple algorithm based on this observation generates three families of exceptional discretizations

an embedded boundary formulation for large eddy simulation of turbulent flows interacting with moving boundaries a non boundary conforming formulation for simulating complex turbulent flows with dynamically moving boundaries on fixed cartesian grids is proposed the underlying finite difference solver for the filtered incompressible navier stokes equations is based on a second order fractional step method on a staggered grid to satisfy the boundary conditions on an arbitrary immersed interface the velocity field at the grid points near the interface is reconstructed using momentum forcing without smearing the sharp interface the concept of field extension is also introduced to treat the points emerging from a moving solid body to the fluid laminar flow cases and large eddy simulations les are presented to demonstrate the formal accuracy and range of applicability of the method in particular simulations of laminar flow induced by the harmonic in line oscillation of a circular cylinder in quiescent fluid and from a transversely oscillating cylinder in a free stream are presented and compared to reference simulations and experiments les of turbulent flow over a traveling wavy wall and transitional flow through a bileaflet prosthetic heart valve are also shown all results are in very good agreement with reference results in the literature

high speed kinks in a generalized discrete phi 4 model we consider a generalized discrete ensuremath phi 4 model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity the constructed exact moving solutions are dependent on the specific value of the propagation velocity we demonstrate that in this class of models given a specific velocity the problem of finding the exact moving solution is integrable namely this problem originally expressed as a three point map can be reduced to a two point map from which the exact moving solutions can be derived iteratively it was also found that these high speed kinks can be stable and robust against perturbations introduced in the initial conditions

exceptional discretizations of the sine gordon equation the method of one dimensional maps was recently introduced as a means of generating exceptional discretizations of the phi 4 theory i e discrete phi 4 models which support kinks centered at a continuous range of positions relative to the lattice in this paper we employ this method to obtain exceptional discretizations of the sine gordon equation i e exceptional frenkel kontorova chains we also use one dimensional maps to construct a discrete sine gordon equation supporting kinks which move with arbitrary velocities without emitting radiation

standard nearest neighbour discretizations of klein gordon models cannot preserve both energy and linear momentum we consider nonlinear klein gordon wave equations and illustrate that standard discretizations thereof involving nearest neighbours may preserve either standardly defined linear momentum or standardly defined total energy but not both this has a variety of intriguing implications for the non potential discretizations that preserve only the linear momentum such as the self accelerating or self decelerating motion of coherent structures such as discrete kinks in these nonlinear lattices

immersed boundary method for flow around an arbitrarily moving body for the simulation of flow around an arbitrarily moving body an immersed boundary method is developed in a non inertial reference frame that is fixed to the body the navier stokes equation is formulated in a conservative form such that the force terms due to the rotation and the translational and rotational accelerations are included in the nonlinear term in order to satisfy the no slip condition on the body surface momentum forcing and mass source sink are applied on the body surface or inside the body the numerical method is based on a finite volume approach on a staggered mesh together with a fractional step method the present numerical method is applied to both the forced motion and fluid structure interaction problems in the latter we solve fully coupled navier stokes and dynamic equations for the moving body without introducing any iteration four different flow problems are tested and the results are in excellent agreements with previous numerical and experimental ones

on a class of discretizations of hamiltonian nonlinear partial differential equations abstract we present a new class of discretizations of partial differential equations pdes that preserve a momentum like integral of the motion this results in an effective translational invariance for the dynamical problem and the absence of a peierls nabarro barrier that is usually present in discretizations of hamiltonian pdes a general method to construct such discretizations for any nonlinearity is given and the properties of the resulting differential difference equations are analyzed in a number of different cases for nonlinear klein gordon as well for nonlinear schrodinger type systems while for the former nonintegrability of the dynamical problem is evident in the latter case numerical evidence suggests that the behavior is close to the one of integrable systems we also show how static solutions of the equations can be constructed for these discretizations and discuss the similarities and differences of the method with previously reported ones

meshless methods for the inverse problem related to the determination of elastoplastic properties from the torsional experiment abstract the problem of determining the elastoplastic properties of a prismatic bar from the given experimental relation between the torsional moment m and the angle of twist per unit length of the rod s length is investigated as an inverse problem the proposed method to solve the inverse problem is based on the solution of some sequences of the direct problem by applying the levenberg marquardt iteration method in the direct problem these properties are known and the torsional moment is calculated as a function of the angle of twist from the solution of a non linear boundary value problem this non linear problem results from the saint venant displacement assumption the ramberg osgood constitutive equation and the deformation theory of plasticity for the stress strain relation to solve the direct problem in each iteration step the kansa method is used for the circular cross section of the rod or the method of fundamental solutions mfs and the method of particular solutions mps are used for the prismatic cross section of the rod the non linear torsion problem in the plastic region is solved using the picard iteration

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 two dimensional conservation laws scheme for compressible flows with moving boundaries the generalized riemann problem grp scheme for the hydrodynamic conservation laws is extended to a two dimensional moving boundary tracking mbt configuration aimed at treating time dependent compressible flows with moving impermeable boundary surfaces a strang type operator splitting is employed for the integration of the conservation laws the boundary motion is also split into cartesian components that are taken with the respective operator split integration phases the conservation laws in boundary cells are integrated by a finite volume scheme that accounts for changing mesh geometry cell volume and side area through which mass momentum and energy fluxes are taken the central feature of the scheme is the algorithms for evaluating the changing mesh geometry at boundary cells these algorithms are based on a decomposition rule for evaluating polygon intersection area which has been used extensively for rezoning in hydrocodes over the past decades the decomposition rule is combined with the cartesian splitting of the boundary motion producing algorithms for the integration of conservation laws in boundary cells that are both consistent and simple consistency is taken to mean that the scheme produces an exact solution in the case of a uniform motion of the fluid and the boundary common velocity an illustrative example of shock lifting of a light weight cylinder is presented

an accurate moving boundary formulation in cut cell methods a cut cell method for cartesian meshes to simulate viscous compressible flows with moving boundaries is presented we focus on eliminating unphysical oscillations occurring in cartesian grid methods extended to moving boundary problems in these methods cells either lie completely in the fluid or solid region or are intersected by the boundary for the latter cells the time dependent volume fraction lying in the fluid region can be so small that explicit time integration schemes become unstable and a special treatment of these cells is necessary when the boundary moves a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level this causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme this temporally discontinuous alteration is shown to act like an unphysical source term which deteriorates the numerical solution i e it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary we develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut cell method which avoids these discontinuities results for canonical two and three dimensional test cases evidence the accuracy and robustness of the newly developed scheme

a versatile sharp interface immersed boundary method for incompressible flows with complex boundaries a sharp interface immersed boundary method for simulating incompressible viscous flow past three dimensional immersed bodies is described the method employs a multi dimensional ghost cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three dimensional stationary moving and or deforming bodies the complex immersed surfaces are represented by grids consisting of unstructured triangular elements while the flow is computed on non uniform cartesian grids the paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries simulations of a number of canonical two and three dimensional flows are used to verify the accuracy and fidelity of the solver over a range of reynolds numbers flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems finally two cases inspired from biology with highly complex three dimensional bodies are simulated in order to demonstrate the versatility of the method

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

exact static solutions of a two dimensional discrete ϕ4 model for a two dimensional scalar discrete 4 model we obtain several exact static solutions in the form of the jacobi elliptic functions jef with arbitrary shift along the lattice the quispel roberts thompson type quadratic maps are identified for the considered two dimensional model by using a jef solution we also show that many of the static solutions can be constructed iteratively from these quadratic maps by starting from an admissible initial value the kink solution having the form of tanh is numerically demonstrated to be generically stable

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

discrete klein gordon models with static kinks free of the peierls nabarro potential for the nonlinear klein gordon type models we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice these discrete models are therefore free of the peierls nabarro potential previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method a relevant physical consequence of our findings is the existence of a wide class of discrete klein gordon models where slow kinks practically do not experience the action of the peierls nabarro potential such kinks are not trapped by the lattice and they can be accelerated by even weak external fields