fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations a new finite difference scheme on a non uniform staggered grid in cylindrical coordinates is proposed for incompressible flow the scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error provided that the discrete continuity equation is satisfied a novel pole treatment is also introduced where a discrete radial momentum equation with the fully conservative convection scheme is introduced at the pole the pole singularity is removed properly using analytical and numerical techniques the kinetic energy conservation property is tested for the inviscid concentric annular flow for the proposed and existing staggered finite difference schemes in cylindrical coordinates the pole treatment is verified for inviscid pipe flow mixed second and high order finite difference scheme is also proposed and the effect of the order of accuracy is demonstrated for the large eddy simulation of turbulent pipe flow

pathwise approximation of stochastic differential equations on domains higher order convergence rates without global lipschitz coefficients we study the approximation of stochastic differential equations on domains for this we introduce modified ito taylor schemes which preserve approximately the boundary domain of the equation under consideration assuming the existence of a unique non exploding solution we show that the modified ito taylor scheme of order has pathwise convergence order e for arbitrary e 0 as long as the coefficients of the equation are sufficiently differentiable in particular no global lipschitz conditions for the coefficients and their derivatives are required this applies for example to the so called square root diffusions

a three level average implicit finite difference scheme to solve equation obtained by coupling the rosenau kdv equation and the rosenau rlw equation in the present work a mathematical model to obtain the solution of the nonlinear wave by coupling the rosenau kdv equation and the rosenau rlw equation is proposed the solution properties are also derived a numerical tool is applied to the model by using a three level average implicit finite difference technique the fundamental conservative properties of the equation are preserved by the presented numerical scheme and the existence and uniqueness of the numerical solution are proved moreover the convergence and stability of the numerical solution are also shown the new method give second order accurate in time and space thus the presented results can be constructed to demonstrate the viability of the new model

decrypting a class of stream ciphers using ciphertext only pseudonoise sequences generated by linear feedback shift registers 1 with some nonlinear combining function have been proposed 2 5 for cryptographic applications as running key generators in stream ciphers in this correspondence it will be shown that the number of trials to break these ciphers can be significantly reduced by using correlation methods by comparison of computer simulations and theoretical results based on a statistical model the validity of this analysis is demonstrated rubin 6 has shown that it is computationally feasible to solve a cipher proposed by pless 2 in a known plaintext attack using as few as 15 characters here the number of ciphertext symbols is determined to perform a ciphertext only attack on the pless cipher using the correlation attack our conclusion from the analysis is that the pseudonoise generator s output sequence and the sequences generated by the linear feedback shift registers should be uncorrelated this leads to constraints for the nonlinear combining function to be used

effects of the computational time step on numerical solutions of turbulent flow effects of large computational time steps on the computed turbulence were investigated using a fully implicit method in turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined turbulence fluctuations could not be sustained if the computational time step was near or larger than the kolmogorov time scale

assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows in this work we study the performance of some variational multiscale models vms in the large eddy simulation les of turbulent flows we consider vms models obtained by different subgrid scale approximations which include either static or dynamic subscales linear or nonlinear multiscale splitting and different choices of the subscale space after a brief review of these models we discuss some implementation aspects particularly relevant to the simulation of turbulent flows namely the use of a skew symmetric form of the convective term and the computation of projections when orthogonal subscales are used we analyze the energy conservation and numerical dissipation of the alternative vms formulations which is numerically evaluated in the numerical study we have considered three well known problems the decay of homogeneous isotropic turbulence the taylor green vortex problem and the turbulent flow in a channel we compare the results obtained using different vms models paying special attention to the effect of using orthogonal subscale spaces the vms results are also compared against classical les scheme based on filtering and the dynamic smagorinsky closure altogether our results show the tremendous potential of vms for the numerical simulation of turbulence further we study the sensitivity of vms to the algorithmic constants and analyze the behavior in the small time step limit we have also carried out a computational cost comparison of the different formulations out of these experiments we can state that the numerical results obtained with the different vms formulations as far as they converge are quite similar however some choices are prone to instabilities and the results obtained in terms of computational cost are certainly different the dynamic orthogonal subscales model turns out to be best in terms of efficiency and robustness

strong convergence rates for cox ingersoll ross processes full parameter range abstract we study strong pathwise approximation of cox ingersoll ross processes we propose a milstein type scheme that is suitably truncated close to zero where the diffusion coefficient fails to be locally lipschitz continuous for this scheme we prove positive convergence rates for the full parameter range including the accessible boundary regime the error criterion is given by the maximal l p distance of the solution and its approximation on a compact interval in the particular case of a squared bessel process of dimension 0 the convergence rate is given by min 1 2 p

energy conserving runge kutta methods for the incompressible navier stokes equations energy conserving methods have recently gained popularity for the spatial discretization of the incompressible navier stokes equations in this paper implicit runge kutta methods are investigated which keep this property when integrating in time firstly a number of energy conserving runge kutta methods based on gauss radau and lobatto quadrature are constructed these methods are suitable for convection dominated problems such as turbulent flows because they do not introduce artificial diffusion and are stable for any time step secondly to obtain robust time integration methods that work also for stiff problems the energy conserving methods are extended to a new class of additive runge kutta methods which combine energy conservation with l stability in this class the radau iia b method has the best properties results for a number of test cases on two stage methods indicate that for pure convection problems the additive radau iia b method is competitive with the gauss methods however for stiff problems such as convection dominated flows with thin boundary layers both the higher order gauss and radau iia b method suffer from order reduction overall the gauss methods are the preferred method for energy conserving time integration of the incompressible navier stokes equations

a supra convergent finite difference scheme for the variable coefficient poisson equation on non graded grids we introduce a method for solving the variable coefficient poisson equation on non graded cartesian grids that yields second order accuracy for the solutions and their gradients we employ quadtree in 2d and octree in 3d data structures as an efficient means to represent the cartesian grid allowing for constraint free grid generation the schemes take advantage of sampling the solution at the nodes vertices of each cell in particular the discretization at one cell s node only uses nodes of two 2d or three 3d adjacent cells producing schemes that are straightforward to implement numerical results in two and three spatial dimensions demonstrate supra convergence in the l norm

suitability of upwind biased finite difference schemes for large eddy simulation of turbulent flows we have simulated flow past a circular cylinder at a reynolds number of 3 9 x 10 3 using a solver that employs an energy conservative second order central difference scheme for spatial discretization detailed comparisons of turbulence statistics and energy spectra in the downstream wake region 7 0 x d 10 0 have been made with the results of beaudan and moin and with experiments to assess the impact of numerical diffusion on the flowfield based on these comparisons conclusions are drawn on the suitability of higher order upwind schemes for les in complex geometries

a multi level dimension reduction monte carlo method for jump diffusion models abstract this paper develops and analyses convergence properties of a novel multi level monte carlo mlmc method for computing prices and hedging parameters of plain vanilla european options under a very general b dimensional jump diffusion model where b is arbitrary the model includes stochastic variance and multi factor gaussian interest short rate s the proposed mlmc method is built upon i the powerful dimension and variance reduction approach developed in dang et al 2017 for jump diffusion models which for certain jump distributions reduces the dimensions of the problem from b to 1 namely the variance factor and ii the highly effective multi level mc approach of giles 2008 applied to that factor using the first order strong convergence lamperti backward euler scheme we develop a multi level estimator with variance convergence rate o h 2 resulting in an overall complexity o 2 to achieve a root mean square error of the proposed mlmc can also avoid potential difficulties associated with the standard multi level approach in effectively handling simultaneously both multi dimensionality and jumps especially in computing hedging parameters furthermore it is considerably more effective than existing mlmc methods thanks to a significant variance reduction associated with the dimension reduction numerical results illustrating the convergence properties and efficiency of the method with jump sizes following normal and double exponential distributions are presented

multilevel monte carlo path simulation we show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using monte carlo path simulations in the simplest case of a lipschitz payoff and a euler discretisation the computational cost to achieve an accuracy of o e is reduced from o e 3 to o e 2 log e 2 the analysis is supported by numerical results showing significant computational savings

a linearly implicit conservative difference scheme for the generalized rosenau kawahara rlw equation this paper concerns the numerical study for the generalized rosenau kawahara rlw equation obtained by coupling the generalized rosenau rlw equation and the generalized rosenau kawahara equation we first derive the energy conservation law of the equation and then develop a three level linearly implicit difference scheme for solving the equation we prove that the proposed scheme is energy conserved unconditionally stable and second order accurate both in time and space variables finally numerical experiments are carried out to confirm the energy conservation the convergence rates of the scheme and effectiveness for long time simulation

a shift transformation for fully conservative methods turbulence simulation on complex unstructured grids abstract operator transformations are presented that allow matrix operators for collocated variables to be transformed into matrix operators for staggered variables while preserving symmetries these shift transformations permit conservative skew symmetric convective operators and symmetric positive definite diffusive operators to be obtained for staggered variables using collocated operators shift transformations are not limited to uniform or structured meshes and this formulation leads to a generalization of the works of perot j comput phys 159 2000 58 and verstappen and veldman j comput phys 187 2003 343 a set of shift operators have been developed for and applied to a time adaptive cartesian mesh method with a fractional step algorithm the resulting numerical scheme conserves mass to machine error and conserves momentum and energy to second order in time a mass conserving interpolation is used for the variables during mesh adaptation the interpolation conserves momentum and energy to second order in space turbulent channel flow simulations were conducted at re 180 using direct numerical simulation dns the dns results from the adaptive method compare favourably with spectral dns results despite the use of a formally second order accurate scheme

an euler type method for the strong approximation of the cox ingersoll ross process we analyse the strong approximation of the cox ingersoll ross cir process in the regime where the process does not hit zero by a positivity preserving drift implicit euler type method as an error criterion we use the p th mean of the maximum distance between the cir process and its approximation on a finite time interval we show that under mild assumptions on the parameters of the cir process the proposed method attains up to a logarithmic term the convergence of order 1 2 this agrees with the standard rate of the strong convergence for global approximations of stochastic differential equations with lipschitz coefficients despite the fact that the cir process has a non lipschitz diffusion coefficient

sharp interface immersed boundary level set method for wave body interactions a sharp interface cartesian grid method for the large eddy simulation of two phase turbulent flows interacting with moving bodies is presented the overall approach uses a sharp interface immersed boundary formulation and a level set ghost fluid method for solid fluid and fluid fluid interface treatments respectively a four step fractional step method is used for velocity pressure coupling and a lagrangian dynamic smagorinsky subgrid scale model is adopted for large eddy simulations a simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed a variety of test cases of different scales ranging from bubble dynamics water entry and exit landslide generated waves to ship hydrodynamics are performed for validation extensions for high reynolds number ship flows using wall layer models are also considered

a new correlation attack on nonlinear combining generators in this paper the correlation properties of a nonlinear combining function over its support or zero set are investigated based on this characterization a new attack on nonlinear combining generators is proposed our attack does not utilize traditional non linear statistics between the input and the output over the entire variable space as the distinguishing process is rather applied to the restricted input space the attack appears to be very efficient against nonlinear combining generators whose combining lfsrs are of relatively small input size in many cases our attack is a more favorable alternative than the known correlation attacks but also than algebraic attacks in certain cases to study the maximum correlation of a nonlinear combining function over its support or zero set the notion of maximum distinguishable correlation is introduced the relationship between the maximum distinguishable correlation and the nonlinearity of a combining function is then derived by using the normalized walsh transform finally we extend the usual notion of resiliency and discuss its implications towards the resistance against our attack

staggered grids for three dimensional convection of a multicomponent fluid in a porous medium convection in a porous medium may produce strong nonuniqueness of patterns we study this phenomena for the case of a multicomponent fluid and develop a mimetic finite difference scheme for the three dimensional problem discretization of the darcy equations in the primitive variables is based on staggered grids with five types of nodes and on a special approximation of nonlinear terms this scheme is applied to the computer study of flows in a porous parallelepiped filled by a two component fluid and with two adiabatic lateral planes we found that the continuous family of steady stable states exists in the case of a rather thin enclosure when the depth is increased only isolated convective regimes may be stable we demonstrate that the non mimetic approximation of nonlinear terms leads to the destruction of the continuous family of steady states

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

segregated runge kutta time integration of convection stabilized mixed finite element schemes for wall unresolved les of incompressible flows in this work we develop a high performance numerical framework for the large eddy simulation les of incompressible flows the spatial discretization of the nonlinear system is carried out using mixed finite element fe schemes supplemented with symmetric projection stabilization of the convective term and a penalty term for the divergence constraint these additional terms introduced at the discrete level have been proved to act as implicit les models in order to perform meaningful wall unresolved simulations we consider a weak imposition of the boundary conditions using a nitsche s type scheme where the tangential component penalty term is designed to act as a wall law next segregated runge kutta srk schemes recently proposed by the authors for laminar flow problems are applied to the les simulation of turbulent flows by the introduction of a penalty term on the trace of the acceleration these methods exhibit excellent stability properties for both implicit and explicit treatment of the convective terms srk schemes are excellent for large scale simulations since they reduce the computational cost of the linear system solves by splitting velocity and pressure computations at the time integration level leading to two uncoupled systems the pressure system is a darcy type problem that can easily be preconditioned using a traditional block preconditioning scheme that only requires a poisson solver at the end only coercive systems have to be solved which can be effectively preconditioned by multilevel domain decomposition schemes which are both optimal and scalable the framework is applied to the taylor green and turbulent channel flow benchmarks in order to prove the accuracy of the convection stabilized mixed fes as les models and srk time integrators the scalability of the preconditioning techniques in space only has also been proven for one step of the srk scheme for the taylor green flow using uniform meshes moreover a turbulent flow around a naca profile is solved to show the applicability of the proposed algorithms for a realistic problem

high order pole treatment in cylindrical coordinates for incompressible flow simulations with finite difference collocated schemes abstract a finite difference collocated scheme is proposed for the simulation of unsteady incompressible flows in cylindrical coordinates the rhie chow flux interpolation technique is used to avoid the odd even decoupling of the pressure field it is shown that the calculation of the coriolis and centrifugal acceleration terms based on the cell center values lead to numerical instabilities near the pole in the inviscid regime to avoid this issue a new formulation based on the combination of cell center and cell face velocity components is proposed for the calculation of these terms furthermore a new pole treatment methodology is introduced to calculate the viscous terms resulting single valued properties at the pole as regards the extensions of the present scheme to higher orders of accuracy a fourth order spatial discretization is also introduced and verified moreover it is shown that for higher order extensions the present pole treatment is able to preserve the order of accuracy and the l 2 norm and l norm errors are greatly improved in comparison with the previous schemes the robustness of the present method is assessed via five different numerical tests including laminar flows in a polar cavity vortex wall interaction evolution of a monopole vortex system to a tripole vortex system advection of the lamb dipole and large eddy simulation les of turbulent pipe flows compared to the previous les results for turbulent pipe flows significant improvement is obtained for the mean and fluctuating velocities especially at the core region of the channel similarly at the wall region the fluctuating axial and azimuthal velocities and the skewnesses of the axial and radial velocities are very close to the previous direct numerical simulation and experimental data

adaptive timestepping for pathwise stability and positivity of strongly discretised nonlinear stochastic differential equations abstract we consider the use of adaptive timestepping to allow a strong explicit euler maruyama discretisation to reproduce dynamical properties of a class of nonlinear stochastic differential equations with a unique equilibrium solution and non negative non globally lipschitz coefficients solutions of such equations may display a tendency towards explosive growth countered by a sufficiently intense and nonlinear diffusion we construct an adaptive timestepping strategy which closely reproduces the almost sure a s asymptotic stability and instability of the equilibrium and which can ensure the positivity of solutions with arbitrarily high probability our analysis adapts the derivation of a discrete form of the ito formula from appleby et al 2009 in order to deal with the lack of independence of the wiener increments introduced by the adaptivity of the mesh we also use results on the convergence of certain martingales and semi martingales which influence the construction of our adaptive timestepping scheme in a way proposed by liu mao 2017

boundary treatment for fourth order staggered mesh discretizations of the incompressible navier stokes equations harlow and welch phys fluids 8 1965 2182 2189 introduced a discretization method for the incompressible navier stokes equations conserving the secondary quantities kinetic energy and vorticity besides the primary quantities mass and momentum this method was extended to fourth order accuracy by several researchers 25 14 21 in this paper we propose a new consistent boundary treatment for this method which is such that continuous integration by parts identities including boundary contributions are mimicked in a discrete sense in this way kinetic energy is exactly conserved even in case of non zero tangential boundary conditions we show that requiring energy conservation at the boundary conflicts with order of accuracy conditions and that the global accuracy of the fourth order method is limited to second order in the presence of boundaries we indicate how non uniform grids can be employed to obtain full fourth order accuracy

convergence and stability of two classes of theta milstein schemes for stochastic differential equations abstract this paper examines convergence and stability of the two classes of theta milstein schemes for stochastic differential equations sdes with non global lipschitz continuous coefficients the split step theta milstein sstm scheme and the stochastic theta milstein stm scheme for 1 2 1 this paper concludes that the two classes of theta milstein schemes converge strongly to the exact solution with the order 1 for 0 1 2 under the additional linear growth condition for the drift coefficient these two classes of the theta milstein schemes are also strongly convergent with the standard order this paper also investigates exponential mean square stability of these two classes of the theta milstein schemes for 1 2 1 these two theta milstein schemes can share the exponential mean square stability of the exact solution for 0 1 2 similar to the convergence under the additional linear growth condition these two theta milstein schemes can also reproduce the exponential mean square stability of the exact solution

an improved optimal nearly analytical discretized method for 2d scalar wave equation in heterogeneous media based on the modified nearly analytical discrete operator abstractconventional finite difference methods will encounter strong numerical dispersion on coarse grids or when higher frequencies are used the nearly analytic discrete method nadm and its improved version developed recently can suppress numerical dispersion efficiently however the nadm is imperfect especially in long time seismic wave propagation simulation to overcome this limitation by minimizing the energy error function we have developed a modified optimal nearly analytical discretized mnad method the stencil of mnad for the 2d wave equation is a novel diamond stencil mnad has two major advantages the first one is that mnad can suppress numerical dispersion effectively on coarse grids which significantly improved computational efficiency and reduced memory demands the second advantage is that the energy error of mnad is much smaller after long time simulation the numerical dispersion analysis shows that the maximum phase velocity error was 5 92 even if only two sampling points w

high order accurate solution of the incompressible navier stokes equations on massively parallel computers the emergence of petascale supercomputers requires us to develop today s simulation codes for incompressible flows by codes which are using numerical schemes and methods that are better able to exploit the offered computational power in that spirit we present a massively parallel high order navier stokes solver for large incompressible flow problems in three dimensions the governing equations are discretized with finite differences in space and a semi implicit time integration scheme this discretization leads to a large linear system of equations which is solved with a cascade of iterative solvers the iterative solver for the pressure uses a highly efficient commutation based preconditioner which is robust with respect to grid stretching the efficiency of the implementation is further enhanced by carefully setting the adaptive termination criteria for the different iterative solvers the computational work is distributed to different processing units by a geometric data decomposition in all three dimensions this decomposition scheme ensures a low communication overhead and excellent scaling capabilities the discretization is thoroughly validated first we verify the convergence orders of the spatial and temporal discretizations for a forced channel flow second we analyze the iterative solution technique by investigating the absolute accuracy of the implementation with respect to the different termination criteria third orr sommerfeld and squire eigenmodes for plane poiseuille flow are simulated and compared to analytical results fourth the practical applicability of the implementation is tested for transitional and turbulent channel flow the results are compared to solutions from a pseudospectral solver subsequently the performance of the commutation based preconditioner for the pressure iteration is demonstrated finally the excellent parallel scalability of the proposed method is demonstrated with a weak and a strong scaling test on up to o 10 4 processing units and o 10 1 1 grid points

conservation properties of unstructured staggered mesh schemes classic cartesian staggered mesh schemes have a number of attractive properties they do not display spurious pressure modes and they have been shown to locally conserve mass momentum kinetic energy and circulation to machine precision recently a number of generalizations of the staggered mesh approach have been proposed for unstructured triangular or tetrahedral meshes these unstructured staggered mesh methods have been created to retain the attractive pressure aspects and mass conservation properties of the classic cartesian mesh method this work addresses the momentum kinetic energy and circulation conservation properties of unstructured staggered mesh methods it is shown that with certain choices of the velocity interpolation unstructured staggered mesh discretizations of the divergence form of the navier stokes equations can conserve kinetic energy and momentum both locally and globally in addition it is shown that unstructured staggered mesh discretizations of the rotational form of the navier stokes equations can conserve kinetic energy and circulation both locally and globally the analysis includes viscous terms and a generalization of the concept of conservation in the presence of viscosity to include a negative definite dissipation term in the kinetic energy equation these novel conserving unstructured staggered mesh schemes have not been previously analyzed it is shown that they are first order accurate on nonuniform two dimensional unstructured meshes and second order accurate on uniform unstructured meshes numerical confirmation of the conservation properties and the order of accuracy of these unstructured staggered mesh methods is presented

a co located incompressible navier stokes solver with exact mass momentum and kinetic energy conservation in the inviscid limit the incompressible navier stokes equations conserve mass momentum and kinetic energy in the inviscid limit therefore numerical methods should attempt to mimic these conservation properties as well there exists many well established methods with exact conservation properties based on staggered grids but existing methods based on co located grids introduce numerical dissipation in order to yield smooth pressure fields in the present work a novel method that utilizes null space vectors to yield a smooth pressure field is presented the method exactly preserves mass momentum and kinetic energy on co located grids

highly energy conservative finite difference method for the cylindrical coordinate system a highly energy conservative second order accurate finite difference method for the cylindrical coordinate system is developed it is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used this argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on cartesian coordinates numerical tests are undertaken for an inviscid flow with various schemes and it turns out that the proposed scheme offers a superior energy conservation property and greater stability than the intuitive and previously proposed methods for both equally spaced and unequally spaced meshes

an accurate numerical solver on second order pdes with variable coefficients in three dimensions in the present paper a numerical technique is developed for the approximate solution of second order partial differential equations pdes with variable coefficients in three dimensions with the temporary introduction of two unknown auxiliary functions of the coordinate system the initial equation is separated into three parts that are reduced to ordinary differential equations one for each dimension that are discretized with a finite difference scheme the use of suitable manipulations and the elimination of the unknown auxiliary functions gives finally a linear system of algebraic equations where the matrix of the coefficients of the unknowns is diagonally dominant a prerequisite for the rapid convergence of the iterative procedure the efficiency and accuracy of the proposed numerical scheme is validated by its application to two test problems of fluid mechanics which have exact solutions the numerical results based on the present technique are more accurate than those obtained by either the standard relaxation treatment with central differences or the adi method when the contribution of the first derivative terms in the initial equation is dominant in all cases the comparison of the numerical results with those of the analytical solution demonstrates the reliability of the presented numerical code

a fully conservative second order finite difference scheme for incompressible flow on nonuniform grids a second order accurate finite difference discretization of the incompressible navier stokes is presented that discretely conserves mass momentum and kinetic energy in the inviscid limit in space and time the method is thus completely free of numerical dissipation and potentially well suited to the direct numerical simulation or large eddy simulation of turbulent flow the method uses a staggered arrangement of velocity and pressure on a structured cartesian grid and retains its discrete conservation properties for both uniform and nonuniform gird spacing the predicted conservation properties are confirmed by inviscid simulations on both uniform and nonuniform grids the capability of the method to resolve turbulent flow is demonstrated by repeating the turbulent channel flow simulations of h choi and p moin 1994 j comput phys 113 1 where the effect of computational time step on the computed turbulence was investigated the present fully conservative scheme achieved turbulent flow solutions over the entire range of computational time steps investigated t tu2 0 4 to 5 0 little variation in statistical turbulence quantities was observed up to t 1 6 the present results differ significantly from those reported by choi and moin who observed significant discrepancies in the turbulence statistics above t 0 4 and the complete laminarization of the flow at and above t 1 6

stability of the drift implicit and double implicit milstein schemes for nonlinear sdes abstract this paper examines the stability of numerical solutions of nonlinear stochastic differential equations sdes with non global lipschitz continuous coefficients two implicit milstein schemes called drift implicit milstein scheme and double implicit milstein scheme are considered to simulate the underlying sdes it is proved that the schemes can preserve the stability and contractivity in mean square of the underlying systems

a fic based stabilized finite element formulation for turbulent flows abstract we present a new stabilized finite element fem formulation for incompressible flows based on the finite increment calculus fic framework onate 1998 in comparison to existing fic approaches for fluids this formulation involves a new term in the momentum equation which introduces non isotropic dissipation in the direction of velocity gradients we also follow a new approach to the derivation of the stabilized mass equation inspired by recent developments for quasi incompressible flows onate et al 2014 the presented fic fem formulation is used to simulate turbulent flows using the dissipation introduced by the method to account for turbulent dissipation in the style of implicit large eddy simulation

finite element methods and their error analysis for spdes driven by gaussian and non gaussian noises abstract in this paper we investigate the mean square error of numerical methods for spdes driven by gaussian and non gaussian noises the gaussian noise considered here is a hilbert space valued q wiener process and the non gaussian noise is defined through compensated poisson random measure associated to a levy process as the models consider the influences of gaussian and non gaussian noises simultaneously this makes the models more realistic when the models are also influenced by some randomly abrupt factors but more complicated as a consequence the numerical analysis of the problems becomes more involved we first study the regularity for the mild solution next we propose a semidiscrete finite element scheme in space and a fully discrete linear implicit euler scheme for the spdes and rigorously obtain their error estimates both the regularity results of the mild solution and error estimates obtained in the paper are novel

skew symmetric form of convective terms and fully conservative finite difference schemes for variable density low mach number flows the form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by morinishi et al y morinishi t s lund o v vasilyev p moin fully conservative higher order finite difference schemes for incompressible flow j comput phys 124 1998 90 and fully conservative finite difference schemes suitable for shock free unsteady compressible flow simulations are proposed commutable divergence advective and skew symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow these forms are analytically equivalent if the continuity is satisfied and the skew symmetric form is secondary conservative without the aid of the continuity while the divergence form is primary conservative the relations between the present and existing quasi skew symmetric forms are also revealed commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system and they are fully conservative provided that the corresponding discrete continuity is satisfied in addition a semi discrete convection scheme suitable for compact finite difference is presented based on the skew symmetric form the conservation properties of the present schemes are demonstrated numerically in a three dimensional periodic inviscid flow the proposed fully discrete fully conservative second order accurate scheme is also used to perform the dns of compressible isotropic turbulence and the simulation of open cavity flow

high order finite difference schemes on non uniform meshes with good conservation properties numerical simulation of turbulent flows dns or les requires numerical methods that are both stable and free of numerical dissipation one way to achieve this is to enforce additional constraints such as discrete conservation of mass momentum and kinetic energy the objective of this work is to generalize the high order schemes of morinishi et al to non uniform meshes while maintaining conservation properties of the schemes as much as possible this generalization is achieved by preserving symmetries of the uniform mesh case the proposed schemes do not simultaneously conserve mass momentum and kinetic energy however depending on the form of the convective term conservation of either momentum or energy in addition to mass can be achieved it is shown that the conservation properties of the generalized schemes are as good as those of the standard second order finite difference scheme on non uniform meshes while the accuracy of the new schemes is definitely superior the predicted conservation properties are demonstrated numerically in inviscid flow simulations

strong convergence of euler type methods for nonlinear stochastic differential equations traditional finite time convergence theory for numerical methods applied to stochastic differential equations sdes requires a global lipschitz assumption on the drift and diffusion coefficients in practice many important sde models satisfy only a local lipschitz property and since brownian paths can make arbitrarily large excursions the global lipschitz based theory is not directly relevant in this work we prove strong convergence results under less restrictive conditions first we give a convergence result for euler maruyama requiring only that the sde is locally lipschitz and that the pth moments of the exact and numerical solution are bounded for some p 2 as an application of this general theory we show that an implicit variant of euler maruyama converges if the diffusion coefficient is globally lipschitz but the drift coefficient satisfies only a one sided lipschitz condition this is achieved by showing that the implicit method has bounded moments and may be viewed as an euler maruyama approximation to a perturbed sde of the same form second we show that the optimal rate of convergence can be recovered if the drift coefficient is also assumed to behave like a polynomial

a note on strong approximation of sdes with smooth coefficients that have at most linearly growing derivatives abstract in the literature on strong approximation of sdes polynomial error rate results for numerical schemes are typically achieved under the assumption that the first order derivatives of the coefficients of the equation satisfy a polynomial growth condition in the present article we show that the latter condition is far from being sufficient for polynomial error rates we construct an sde with smooth coefficients that have first order derivatives of at most linear growth such that the solution at the final time can at best be approximated with a logarithmic rate whatever numerical method based on observations of the driving brownian motion at finitely many fixed times is used most interestingly it furthermore turns out that using a method that properly adjusts the number of evaluations of the driving brownian motion to its actual path the latter sde can in fact be approximated with polynomial rate 1 in terms of the average number of evaluations that are used to the best of our knowledge this is only the second example in the literature of an sde for which there exist adaptive methods that perform superior to non adaptive ones with respect to the convergence rate

finite difference method for incompressible navier stokes equations in arbitrary orthogonal curvilinear coordinates a finite difference method for solving three dimensional time dependent incompressible navier stokes equations in arbitrary curvilinear orthogonal coordinates is presented the method is oriented on turbulent flow simulations and consists of a second order central difference approximation in space and a third order semi implicit runge kutta scheme for time advancement spatial discretization retains some important properties of the navier stokes equations including energy conservation by the nonlinear and pressure gradient terms numerical tests cover cartesian cylindrical polar spherical cylindrical elliptic and cylindrical bipolar coordinate systems both laminar and turbulent flows are considered demonstrating reasonable accuracy and stability of the method

first order strong approximations of scalar sdes defined in a domain we are interested in strong approximations of one dimensional sdes which have non lipschitz coefficients and which take values in a domain under a set of general assumptions we derive an implicit scheme that preserves the domain of the sdes and is strongly convergent with rate one moreover we show that this general result can be applied to many sdes we encounter in mathematical finance and bio mathematics we will demonstrate flexibility of our approach by analyzing classical examples of sdes with sublinear coefficients cir cev models and wright fisher diffusion and also with superlinear coefficients 3 2 volatility ait sahalia model our goal is to justify an efficient multilevel monte carlo method for a rich family of sdes which relies on good strong convergence properties

the truncated milstein method for stochastic differential equations with commutative noise inspired by the truncated eulermaruyama method developed in mao 2015 we propose the truncated milstein method in this paper the strong convergence rate is proved to be close to 1 for a class of highly non linear stochastic differential equations with commutative noise numerical examples are given to illustrate the theoretical results

a staggered grid high order accurate method for the incompressible navier stokes equations a high order accurate finite difference method for the numerical solution of the incompressible navier stokes equations is presented fourth order accurate discretizations of the convective and viscous fluxes are obtained on staggered meshes using explicit or compact finite difference formulas high order accuracy in time is obtained by marching the solution with runge kutta methods the incompressibility constraint is enforced for each runge kutta stage iteratively either by local pressure correction or by a poisson equation based global pressure correction method local pressure correction is carried out on cell by cell basis using a local fourth order accurate discrete analog of the continuity equation the global pressure correction is based on the numerical solution of a poisson type equation which is discretized to fourth order accuracy and solved using gmres in both cases the updated pressure is used to recompute the velocities in order to satisfy the incompressibility constraint to fourth order accuracy the accuracy and efficiency of the proposed method is demonstrated in test problems

cryptanalysis of mir 1 a t function based stream cipher this correspondence describes the cryptanalysis of mir 1 a t function based stream cipher proposed at estream the ecrypt stream cipher project in 2005 this cipher uses a multiword t function with four 64 bit words as its basic structure mir 1 operations process the data in every 64 bits one word to generate a keystream the correspondence discusses a distinguishing attack against mir 1 that exploits the t function characteristics and the mir 1 initialization with merely three or four initial vector pairs this attack can distinguish a mir 1 output sequence from a truly random number sequence in this case the amount of data theoretically needed for cryptanalysis is only 210 words this correspondence also proposes a countermeasure that provides resistance against the attack described in this correspondence

a velocity divergence constraint for large eddy simulation of low mach flows the velocity divergence rate of fluid volumetric expansion is a flow field quantity of fundamental importance in low mach flows it directly affects the local mass density and therefore the local temperature through the equation of state in this paper starting from the conservative form of the sensible enthalpy transport equation we derive a discrete divergence constraint for use in large eddy simulation les of low mach flows the result accounts for numerical transport of mass and energy which is difficult to eliminate in relatively coarse engineering les calculations when total variation diminishing tvd scalar transport schemes are employed without the correction terms derived here unresolved numerical mixing of gas species with different heat capacities or molecular weights may lead to erroneous mixture temperatures and ultimately to an imbalance in the energy budget the new formulation is implemented in a publicly available les code called the fire dynamics simulator fds accuracy of the flow solver for transport is demonstrated using the method of manufactured solutions the conservation properties of the present scheme are demonstrated on two simple energy budget test cases one involving a small fire in a compartment with natural ventilation and another involving mixing of two gases with different thermal properties