parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness we demonstrate that the cumulant lattice boltzmann model with optimized parameters captures the drag crisis for flows over a sphere no sub grid model and no wall function is required and the boundary layer is only marginally resolved it is observed that in the transition regime between the high and the low drag configuration the flow switches from one state to the other state

near wall treatment for the simulation of turbulent flow by the cumulant lattice boltzmann method abstract we present a new wall function implementation for the cumulant lattice boltzmann method that sets a partial slip velocity on the wall by computing a skin frictional coefficient our approach uses local information and is particularly appropriate for implementations on general purpose graphics processing units the validation of the model has been conducted by performing numerical simulations of the turbulent channel flow test case with different grid resolutions and for different reynolds numbers the results showed encouraging agreement with direct numerical simulation data for velocity profile reynolds shear and normal stresses

filter matrix lattice boltzmann simulation of lid driven deep cavity flows part i steady flows this paper seeks to make a systematic study over a series of lid driven flow in various deep cavities using the filter matrix lattice boltzmann fmlb model a concise description of the fmlb model is presented in this paper and important numerical considerations for effective use of the fmlb model are also clearly elucidated in particular the selection of a free parameter employed to appropriately control the weight of the third order terms in the fmlb solution vector is carefully examined resulting in some general suggestions that may render the fmlb stability consistently secured for simulations of different cavity flow scenarios employing the fmlb and the lattice bhatnagar gross krook lbgk methods for comparison purpose the first series of test cases correspond to the lid driven cavity flows with a low reynolds number re 0 01 at a variety of aspect ratios the simulation results demonstrate that the fmlb model is superior to the lbgk method in terms of numerical stability and particularly the fmlb result can reach quite good agreement with the benchmark solution even if the aspect ratio goes up to 15 then the fmlb model is used to compute the steady flows for deep cavities with aspect ratios ranging from 1 5 to 7 and elevated reynolds numbers ranging from 100 to 5000 a number of features of steady flows such as the locations strengths and sizes of the vortices as well as the effects of reynolds number and aspect ratio on the vortex structure are all predicted by the fmlb model with an obviously improved accuracy when compared to some other available numerical results

introducing a new kinetic model which admits an h theorem for simulating the nearly incompressible fluid flows we present a new kinetic model for simulating the nearly incompressible fluid flows the model uses constant speed particles which are free to move in all directions in the new model the maxwellian is replaced by a fractional form while the navier stokes and continuity equations are recovered it is known that the conventional lattice boltzmann model lbm with polynomial equilibrium distribution function cannot admit an h theorem wagner 1998 9 in the present work we show that the new model admits an h theorem and the numerical schemes which stem from the new model are more stable than the conventional lbm for the streaming stage two different approaches namely the lattice based and the discontinuous galerkin based schemes are introduced the former is more cost effective than the conventional lattice boltzmann models while it maintains their simplicity the latter is a higher order spectral element method using which one can employ non uniform triangular elements with high accuracy and geometrical flexibility unlike the conventional lbm the new model is derived from continuous relations hence it does not require a symmetric discrete velocity model the accuracy and stability of the model have been verified by simulating three benchmark problems the plane couette flow lid driven square cavity and flow around an impulsively started cylinder have been simulated the results of the present work are in excellent agreement with the exact solutions and with the results reported by others

regularity of the free boundary for the porous medium equation with r m 1 m 1 when u 0 then f 0 and both of the above equations become degenerate this degeneracy results in the interesting phenomenon of the finite speed of propagation if the initial data u is compactly supported in 1ztn the solution u t will remain compactly supported for all time t in this work we will show that under rather general assumptions on the initial data the free boundary

forward starting options pricing with double stochastic volatility stochastic interest rates and double jumps abstract we present an extension of double heston stochastic volatility model by introducing cir stochastic interest rate and double exponential jumps in the stock price process we derive the characteristic function and forward characteristic function of the log asset price and thereby forward starting options are well evaluated by the cos method we also provide efficient simulation of the proposed model and monte carlo solutions to forward starting options pricing based on the qe scheme numerical results show that the cos method is fast and efficient for pricing forward starting options

a nonlinearly preconditioned inexact newton algorithm for steady state lattice boltzmann equations most existing methods for calculating the steady state solution of the lattice boltzmann equations are based on pseudo time stepping which often requires a large number of time steps especially for high reynolds number problems to calculate the steady state solution directly without the time integration in this paper we propose and study a nonlinearly preconditioned inexact newton algorithm with a domain decomposition based linear solver for parallelization more precisely the proposed algorithmic framework involves an implicit second order discretization a two level inexact newton method and a nonlinear elimination preconditioner to accelerate the convergence of newton iteration a nonstandard pollution removing coarse space is introduced for the two level method numerical experiments are presented to demonstrate the robustness and efficiency of the algorithm especially for problems at a high reynolds number a comparison is also included to show the superiority of the proposed approach over o

grid refinement for lattice bgk models lattice boltzmann models proposed at the end of the 1980s as the noise free version of lattice gas models are based on gas kinetic representation of fluid flow their recent modifications the lattice bgk models provide especially simple effective and stable algorithms for the solution of hydrodynamical problems a local second order grid refinement scheme for the lattice bgk model is proposed in this work the refinement scheme and a boundary fitting scheme for complicated geometries are applied to simulate a benchmark problem of flow past a cylinder in a channel with small and moderate reynolds numbers

acceleration of steady state lattice boltzmann simulations on non uniform mesh using local time step method in this paper the local time step method is applied to the lattice boltzmann method lbm on non uniform grid generalized form of interpolation supplemented lbm gilbm for steady flow simulations the local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non uniform grid first code validation for global time step method is performed by solving flow around a cylinder at low reynolds numbers our results show good agreement with previous studies two dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions the pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement they are also consistent with the previous studies at the same time cpu time required to obtain the steady state solutions using the local time step are reduced by 70 80 compared with that using global time step

mixed fractional heston model and the pricing of american options this paper presents a fractional version of the heston model in which the volatility brownian and price brownian are replaced by mixed fractional brownian motions with hurst parameter h 34 1 so that the model exhibits a long range dependence then the existence and uniqueness of solution of mixed fractional heston model are discussed as well as the error of an euler scheme applied on this model finally some numerical illustrations are given in the last section by computing american put option prices

exact simulation of stochastic volatility and other affine jump diffusion processes the stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated discretization methods can be used for simulating security prices under these models however discretization introduces bias into the simulation results and a large number of time steps may be needed to reduce the discretization bias to an acceptable level this paper suggests a method for the exact simulation of the stock price and variance under hestons stochastic volatility model and other affine jump diffusion processes the sample stock price and variance from the exact distribution can then be used to generate an unbiased estimator of the price of a derivative security we compare our method with the more conventional euler discretization method and demonstrate the faster convergence rate of the error in our method specifically our method achieves an o s 1 2 convergence rate where s is the total computational budget the convergence rate for the euler discretization method is o s 1 3 or slower depending on the model coefficients and option payoff function

a novel pricing method for european options based on fourier cosine series expansions here we develop an option pricing method for european options based on the fourier cosine series and call it the cos method the key insight is in the close relation of the characteristic function with the series coefficients of the fourier cosine expansion of the density function in most cases the convergence rate of the cos method is exponential and the computational complexity is linear its range of application covers underlying asset processes for which the characteristic function is known and various types of option contracts we will present the method and its applications in two separate parts the first one is this paper where we deal with european options in particular in a follow up paper we will present its application to options with early exercise features

power concavity on nonlinear parabolic flows our object in this paper is to show that the concavity of the power of a solution is preserved in the parabolic p laplace equation called power concavity and that the power is determined by the homogeneity of the parabolic operator in the parabolic p laplace equation for the density u the concavity of u p 2 p is considered which indicates why the log concavity has been considered in heat flow p 2 in addition the long time existence of the classical solution of the parabolic p laplacian equation can be obtained if the initial smooth data has concavity and a nondegenerate gradient along the initial boundary 2004 wiley periodicals inc

semi lagrangian implicit bhatnagar gross krook collision model for the finite volume discrete boltzmann method in order to increase the accuracy of temporal solutions reduce the computational cost of time marching and improve the stability associated with collisions for the finite volume discrete boltzmann method an advanced implicit bhatnagar gross krook bgk collision model using a semi lagrangian approach is proposed in this paper unlike existing models in which the implicit bgk collision is resolved either by a temporal extrapolation or by a variable transformation the proposed model removes the implicitness by tracing the particle distribution functions pdfs back in time along their characteristic paths during the collision process an interpolation scheme is needed to evaluate the pdfs at the traced back locations by using the first order interpolation the resulting model allows for the straightforward replacement of f eq n 1 by f eq n no matter where it appears after comparing the proposed model with the existing models under different numerical conditions e g different flux schemes and time marching schemes and using the proposed model to successfully modify the variable transformation technique three conclusions can be drawn first the proposed model can improve the accuracy by almost an order of magnitude second it can slightly reduce the computational cost therefore the proposed scheme improves accuracy without extra cost finally the proposed model can significantly improve the t limit compared to the temporal interpolation model while having the same t limit as the variable transformation approach the proposed scheme with a second order interpolation is also developed and tested however that technique displays no advantage over the simple first order interpolation approach both numerical and theoretical analyses are also provided to explain why the developed implicit scheme with simple first order interpolation can outperform the same scheme with second order interpolation as well as the existing temporal extrapolation and variable transformation schemes

non extinction and critical exponent for a polytropic filtration equation abstract this paper is concerned with the homogeneous dirichlet boundary value problem of a polytropic filtration equation with reaction sources we will show the non extinction property of non trivial solutions and determine the critical fujita exponent for the problem

local continuity and asymptotic behaviour of degenerate parabolic systems abstract we study the local holder continuity and the asymptotic behaviour of solution u u 1 u k of the degenerate system u t i m u m 1 u i for m 1 and i 1 k which describes the population densities of k species whose diffusions are determined by their total population density u u 1 u k for the local holder continuity we adopt the intrinsic scaling and iteration arguments of degiorgi moser and dibenedetto under some regularity conditions we also prove that the population density of i th species with the population m i converges in c s to the function m i m b m x t as t where b m is the barenblatt profile of the standard porous medium equation with l 1 mass m m 1 m k as a consequence of asymptotic behaviour it is shown that each density becomes a concave function after a finite time

the number of peaks of nonnegative solutions to some nonlinear degenerate parabolic equations abstract we consider the cauchy problems for some nonlinear degenerate parabolic equations in r n for nonzero bounded nonnegative initial data having compact support and show that the set of peaks of the nonnegative solution consists of one point after a finite time

high order upwind compact finite difference lattice boltzmann method for viscous incompressible flows abstract in this work a high order upwind compact finite difference lattice boltzmann method ucdlbm is developed to efficiently solve viscous incompressible flow problems a fifth order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice boltzmann equation and the third order total variation diminishing runge kutta scheme is utilized for the discretization of the temporal term compared to the existing central compact finite difference lattice boltzmann method cfdlbm the present ucdlbm can prevent non physical oscillations without filtering due to the natural dissipative property of upwind schemes three benchmark problems involving the taylor green vortex problem the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method numerical results computed are in good agreement with the analytical solution or other available numerical results and the present ucdlbm is less time consuming than the cfdlbm without degenerating the order of accuracy of the numerical solutions

parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii application to flow around a sphere at drag crisis the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness

a fully implicit method for lattice boltzmann equations existing approaches for solving the lattice boltzmann equations with finite difference methods are explicit and semi implicit both have certain stability constraints on the time step size in this work a fully implicit second order finite difference scheme is developed we focus on a parallel highly scalable newton krylov ras algorithm for the solution of a large sparse nonlinear system of equations arising at each time step here ras is a restricted additive schwarz preconditioner based on a first order spatial discretization we show numerically that by using the fully implicit method the time step size is no longer constrained by the cfl condition and the newton krylov ras algorithm is scalable on a supercomputer with more than ten thousand processors moreover to calculate the steady state solution we investigate an adaptive time stepping strategy the total compute time required by the implicit method with adaptive time stepping is much smaller than that of an explicit method for several t

a simplified finite volume lattice boltzmann method for simulations of fluid flows from laminar to turbulent regime part ii extension towards turbulent flow simulation abstract in this paper the original finite volume lattice boltzmann method fvlbm on an unstructured grid part i of these twin papers is extended to simulate turbulent flows to model the turbulent effect the k sst turbulence model is incorporated into the present fvlbm framework and is also solved by the finite volume method based on the eddy viscosity hypothesis the eddy viscosity is computed from the solution of the k sst model and the total viscosity is modified by adding this eddy viscosity to the laminar kinematic viscosity given in the bhatnagar gross krook collision term because of solving for the collision term with the explicit method in the original fvlbm scheme the computational efficiency is much lower for simulating high reynolds number flow this is due to the fact that the largest time step decided by the stability condition of the collision term which is less than twice the relaxation time is much smaller than that decided by the cfl condition in order to enhance the computational efficiency the three stage second order implicit explicit imex runge kutta method is used for temporal discretization and the time step can be one or two orders of magnitude larger as compared with the explicit euler forward scheme although the computational cost is increased the final computational efficiency is enhanced by about one order of magnitude and good results can also be obtained at a large time step through the test case of a lid driven cavity flow two turbulent flow cases are carried out to validate the present method including flow over a backward facing step and flow around a naca0012 airfoil the numerical results are found to be in agreement with experimental data and numerical solutions demonstrating the applicability of the present fvlbm coupled with the k sst model to accurately predict the incompressible turbulent flows

high order finite elements applied to the discrete boltzmann equation a discontinuous galerkin approach for solving the discrete boltzmann equation is presented allowing to compute approximate solutions for fluid flow problems based on a two dimensional high order finite element and an explicit euler time stepping scheme the d2q9 model is discretized and the results are compared to the exact solution of the navier stokes equation four numerical examples are considered including stationary and instationary problems with curved boundaries it is demonstrated that the proposed method allows to obtain the desired highly efficient exponential convergence copyright 2006 john wiley sons ltd

equilibrium investment strategy for a defined contribution pension plan under stochastic interest rate and stochastic volatility abstract this paper aims to find the equilibrium investment strategy for a defined contribution pension plan under the mean variance criterion where both the interest rate and volatility are stochastic in the financial market the financial market consists of a risk free asset a bond and a risky asset specifically an affine model which includes the cox ingersoll ross model and the vasicek model as special cases is used to characterize the stochastic dynamics of the interest rate and the price process of the risky asset is described by the heston volatility model under the framework of nash equilibrium we first define the equilibrium strategy and the equilibrium value function then by solving an extended hamilton jacobi bellman equation we obtain both the equilibrium investment strategy and the corresponding equilibrium value function explicitly furthermore the effects of the stochastic interest rate and the stochastic volatility on the equilibrium investment strategy and the equilibrium efficient frontier are analyzed some numerical results and the economic meanings behind are also presented

consistent lattice boltzmann modeling of low speed isothermal flows at finite knudsen numbers in slip flow regime ii application to curved boundaries gaseous flows inside microfluidic devices often fall in the slip flow regime according to this theoretical description the navier stokes model remains applicable in bulk while at solid walls a slip velocity boundary model shall be considered physically it is well established that to properly account for the wall curvature the wall slip velocity must be determined by the shear stress rather than the normal component of the velocity derivative alone as commonly applied to planar surfaces it follows that the numerical transcription of this type of boundary condition is generally a challenging task for standard computational fluid dynamics cfd techniques this paper aims to show that the realization of the slip velocity condition on arbitrarily shaped boundaries can be accomplished in a natural way with the lattice boltzmann method lbm to substantiate this conclusion this work undertakes the following three studies first we examine the conditions under which the generic reflection type boundary rules used by lbm become consistent models for the slip velocity boundary condition this effort makes use of the second order chapman enskog expansion method where we address both planar and curved boundaries the analysis also clarifies the capabilities and limitations behind the considered reflection type slip schemes second we revisit the family of parabolic accurate lbm slip boundary schemes originally formulated in phys rev e 96 013311 2017 2470 004510 1103 physreve 96 013311 on the basis of the multireflection framework and discuss their characteristics when operating on curved boundaries as well as the limitations of other less accurate lbm slip boundary formulations such as the linearly accurate slip schemes and the widely popular kinetic based boundary schemes in addition we also discuss the numerical stability of the parabolic slip schemes previously developed providing an heuristic strategy to improve their stable range of operation third we evaluate the performance of the several slip boundary schemes debated in this paper the numerical tests correspond to two classical 2d benchmark flow problems of slip over non planar solid surfaces namely i the velocity profile of the cylindrical couette flow and ii the permeability of a slow rarefied gas over a periodic array of circular cylindrical obstacles the obtained numerical results confirm the competitiveness of the lbm when equipped with slip boundary schemes of parabolic accuracy as cfd tool to simulate slippage phenomena over arbitrarily non planar surfaces indeed although operating on a simple uniform mesh discretization the lbm yields a similar or even superior level of accuracy compared to state of the art fem simulations conducted on hardworking body fitted meshes this conclusion establishes the lbm as a very appealing cfd technique for simulating microfluidic flows in the slip flow regime a result that deserves further exploration in future studies

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

holder estimates for nonlinear degenerate parabolic sytems on etablit des estimations de holder pour le gradient d espace u des solutions locales faibles des systemes paraboliques degeneres on etablit la continuite de holder des solutions non negatives d une equation parabolique degeneree

on implementation of boundary conditions in the application of finite volume lattice boltzmann method a new implementation of boundary condition based on the half covolume and bounce back rule for the non equilibrium distribution function for the finite volume lbm is proposed here the numerical simulation results for the expansion channel flow and driven cavity problem indicate that this method is workable for arbitrary meshes in addition the fourth order runge kutta scheme is found to be a practical way in the lbm to accelerate the calculation speed

the cumulant lattice boltzmann equation in three dimensions theory and validation we propose analyze and validate a lattice boltzmann model with a cumulant collision operator the new model is analytically and numerically shown to poses smaller errors than a moment based multiple relaxation time lattice boltzmann model we demonstrate the usability of the cumulant lattice boltzmann model by simulations of flow around a sphere for reynolds numbers from 200 to 105

chebyshev collocation spectral lattice boltzmann method for simulation of low speed flows in this study the chebyshev collocation spectral lattice boltzmann method ccslbm is developed and assessed for the computation of low speed flows both steady and unsteady flows are considered here the discrete boltzmann equation with the bhatnagar gross krook approximation based on the pressure distribution function is considered and the space discretization is performed by the chebyshev collocation spectral method to achieve a highly accurate flow solver to provide accurate unsteady solutions the time integration of the temporal term in the lattice boltzmann equation is made by the fourth order runge kutta scheme to achieve numerical stability and accuracy physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used an iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows the main advantage of using the ccslbm over other high order accurate lattice boltzmann method lbm based flow solvers is the decay of the error at exponential rather than at polynomial rates note also that the ccslbm applied does not need any numerical dissipation or filtering for the solution to be stable leading to highly accurate solutions three two dimensional 2d test cases are simulated herein that are a regularized cavity the taylor vortex problem and doubly periodic shear layers the results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement the computational efficiency of the proposed solution methodology based on the ccslbm is also examined by comparison with those of the standard streaming collision classical lbm and two finite difference lbm solvers the study indicates that the ccslbm provides more accurate and efficient solutions than these lbm solvers in terms of cpu and memory usage and an exponential convergence is achieved rather than polynomial rates the solution methodology proposed the ccslbm is also extended to three dimensions and a 3d regularized cavity is simulated the corresponding results are presented and validated indications are that the ccslbm developed and applied herein is robust efficient and accurate for computing 2d and 3d low speed flows note also that high accuracy solutions obtained by applying the ccslbm can be used as benchmark solutions for the assessment of other lbm based flow solvers

a solution adaptive lattice boltzmann method for two dimensional incompressible viscous flows a stencil adaptive lattice boltzmann method lbm is developed in this paper it incorporates the stencil adaptive algorithm developed by ding and shu 26 for the solution of navier stokes n s equations into the lbm calculation based on the uniform mesh the stencil adaptive algorithm refines the mesh by two types of 5 points symmetric stencils which are used in an alternating sequence for increased refinement levels the two types of symmetric stencils can be easily combined to form a 9 points symmetric structure using the one dimensional second order interpolation recently developed by wu and shu 27 along the straight line and the d2q9 model the adaptive lbm calculation can be effectively carried out note that the interpolation coefficients are only related to the lattice velocity and stencil size hence the simplicity of lbm is not broken down and the accuracy is maintained due to the use of adaptive technique much less mesh points are required in the simulation as compared to the standard lbm as a consequence the computational efficiency is greatly enhanced the numerical simulation of two dimensional lid driven cavity flows is carried out accurate results and improved efficiency are reached in addition the steady and unsteady flows over a circular cylinder are simulated to demonstrate the capability of proposed method for handling problems with curved boundaries the obtained results compare well with data in the literature

an eulerian description of the streaming process in the lattice boltzmann equation this paper presents a novel strategy for solving discrete boltzmann equation dbe for simulation of fluid flows this strategy splits the solution procedure into streaming and collision steps as in the lattice boltzmann equation lbe method the streaming step can then be carried out by solving pure linear advection equations in an eulerian framework this offers two significant advantages over previous methods first the relationship between the relaxation parameter and the discretization of the collision term developed from the lbe method is directly applicable to the dbe method the resulting dbe collision step remains local and poses no constraint on time step second decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes an implicit unstructured dbe method is constructed based on this strategy and is evaluated using several test cases of flow over a backward facing step lid driven cavity flow and flow past a circular cylinder the speedup of convergence for some cases improves by a factor of about 20

long time existence of smooth solution for the porous medium equation in a bounded domain in this paper we are going to show the long time existence of the smooth solution for the porous medium equations in a smooth bounded domain 0 1 ut umin 0 u x 0 u0 0in u x t 0for x where m 1 is the permeability the proof is based on the short time existence of cs2 smooth solution the global cs1 estimate the holder estimate of divergence type degenerate equation with measurable coefficients and cs1 estimate of mixed type equation with lipschitz coefficients

a hybrid wavelet based adaptive immersed boundary finite difference lattice boltzmann method for two dimensional fluid structure interaction abstract a second generation wavelet based adaptive finite difference lattice boltzmann method fd lbm is developed in this paper in this approach the adaptive wavelet collocation method awcm is firstly to the best of our knowledge incorporated into the fd lbm according to the grid refinement criterion based on the wavelet amplitudes of density distribution functions an adaptive sparse grid is generated by the omission and addition of collocation points on the sparse grid the finite differences are used to approximate the derivatives to eliminate the special treatments in using the fd based derivative approximation near boundaries the immersed boundary method ibm is also introduced into fd lbm by using the adaptive technique the adaptive code requires much less grid points as compared to the uniform mesh code as a consequence the computational efficiency can be improved to justify the proposed method a series of test cases including fixed boundary cases and moving boundary cases are invested a good agreement between the present results and the data in previous literatures is obtained which demonstrates the accuracy and effectiveness of the present awcm ib lbm

lattice boltzmann method on quadtree grids for simulating fluid flow through porous media a new automatic algorithm abstract during the past two decades the lattice boltzmann lb method has been introduced as a class of computational fluid dynamic methods for fluid flow simulations in this method instead of solving the navier stocks equation the boltzmann equation is solved to simulate the flow of a fluid this method was originally developed based on uniform grids however in order to model complex geometries such as porous media it can be very slow in comparison with other techniques such as finite differences and finite elements to eliminate this limitation a number of studies have aimed to formulate the lattice boltzmann on the unstructured grids this paper deals with simulating fluid flow through a synthetic porous medium using the lb method and on the quadtree grid structure to this end the lb method was used on nonuniform grids coupled with a technique for image reconstruction which resulted in the quadtree grids for simulation of fluid flow through porous media accuracy and efficiency of this algorithm is compared against the conventional lb method based on uniform grids while the decrease in computational time in the proposed lb method on nonuniform grids is found to be significant regarding the size of the initial and reconstructed images the same level of accuracy is obtained when compared with the conventional lb method on uniform grids

worn stones with flat sides all time regularity of the interface we study the all time regularity of the free boundary problem associated to the deformation of a compact weakly convex surface in 3 with a flat side by its gaussian curvature we show that under certain necessary regularity and non degeneracy initial conditions the interface separating the flat from the strictly convex side remains smooth on 0 t tc up to the vanishing time tc of the flat side

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

an immersed boundary method for fluids using the xfem and the hydrodynamic boltzmann transport equation abstract this paper presents a stabilized finite element formulation of the hydrodynamic boltzmann transport equation hbte to predict nearly incompressible fluid flow the hbte is discretized with hermite polynomials in the velocity variable and a streamline upwind petrov galerkin formulation is used to discretize the spatial variable a nonlinear stabilization scheme is presented from which a simple linear stabilization scheme is constructed in contrast to the navier stokes ns equations the hbte is a first order equation and allows for conveniently enforcing dirichlet conditions along immersed boundaries a simple and efficient formulation for enforcing dirichlet boundary conditions is presented and its accuracy is studied for immersed boundaries captured by the extended finite element method xfem numerical experiments indicate that both the linear and non linear stabilization methods are sufficiently accurate and stable but the linear formulation reduces the computational cost significantly the accuracy of enforcing boundary conditions is satisfactory and shows second order convergence as the mesh is refined augmenting the boundary condition formulation with a penalty term increases the accuracy of enforcing the boundary condition constraints but may degrade the accuracy of the global solution comparisons with results of a single relaxation time lattice boltzmann method show that the proposed finite element method features greater robustness and lesser dependence of the computational costs on the level of mesh refinement

boundary estimates for solutions of nonlinear degenerate parabolic systems on etablit la regularite partout jusqu a la frontiere pour des solutions faibles de systemes paraboliques du type u l t div du p 2 du l f l x t u du dans t l 1 2 m u t r m m n p max 1 2n n 2 est un ouvert borne de r n n 2 0 t t 0 t

a spectral element discontinuous galerkin lattice boltzmann method for nearly incompressible flows we present a spectral element discontinuous galerkin lattice boltzmann method for solving nearly incompressible flows decoupling the collision step from the streaming step offers numerical stability at high reynolds numbers in the streaming step we employ high order spectral element discontinuous galerkin discretizations using a tensor product basis of one dimensional lagrange interpolation polynomials based on gauss lobatto legendre grids our scheme is cost effective with a fully diagonal mass matrix advancing time integration with the fourth order runge kutta method we present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous galerkin approach we show convergence studies for couette flows and demonstrate two benchmark cases with lid driven cavity flows for re 400 5000 and flows around an impulsively started cylinder for re 550 9500 computational results are compared with those of other theoretical and computational work that used a multigrid method a vortex method and a spectral element model

bond pricing under mixed generalized cir model with mixed wishart volatility process this paper proposes an extended version of the coxingersollross cir model with stochastic volatility and a pricing method on zero coupon bond under this model in this version we replace the standard brownian motion process with a semi martingale process named the mixed fractional brownian motion mfbm process which is a linear combination of a fractional brownian motion fbm and a standard brownian motion we assume that the part of the volatility process follows a mixed wishart process which defines by the square of the matrix valued mfbm process in order to evaluate the price of the zero coupon bond under the proposed model we use monte carlo simulation method the computed values of the zero coupon bond compare with the other interest rate models

finite volume versus streaming based lattice boltzmann algorithm for fluid dynamics simulations a one to one accuracy and performance study a finite volume fv discretization method for the lattice boltzmann lb equation which combines high accuracy with limited computational cost is presented in order to assess the performance of the fv method we carry out a systematic comparison focused on accuracy and computational performances with the standard streaming lattice boltzmann equation algorithm in particular we aim at clarifying whether and in which conditions the proposed algorithm and more generally any fv algorithm can be taken as the method of choice in fluid dynamics lb simulations for this reason the comparative analysis is further extended to the case of realistic flows in particular thermally driven flows in turbulent conditions we report the successful simulation of high rayleigh number convective flow performed by a lattice boltzmann fv based algorithm with wall grid refinement

large eddy simulation coupled with wall models for turbulent channel flows at high reynolds numbers with a lattice boltzmann method application to coriolis mass flowmeter abstract the numerical prediction of pressure drop within wall bounded flow domains at high reynolds numbers re using a large eddy simulation les approach is a challenging task for industrial applications because the fluid domain is usually underresolved a lattice boltzmann method lbm with bhatnagar gross and krook bgk collision operator coupled with the smagorinsky lilly turbulence model is used to model these wall bounded turbulent flows the near wall region is modelled using wall functions to decrease the required mesh resolution for high re the influence of different velocity boundary approaches and wall functions is investigated for the benchmark bi periodic fully developed turbulent channel flow for friction reynolds numbers re of 1000 2000 and 5200 this benchmark case is validated against direct numerical simulation dns results for turbulent statistics of 1st and 2nd order based on this validation the pressure drop of an industrial coriolis mass flowmeter is compared to experimental data for re up to 127 800 the error of the pressure drop calculation in underresolved grids is reduced by two orders of magnitude in comparison to a no slip approach for curved boundaries

the pricing of credit default swaps under a generalized mixed fractional brownian motion abstract in this paper we consider the pricing of the cds credit default swap under a gmfbm generalized mixed fractional brownian motion model as the name suggests the gmfbm model is indeed a generalization of all the fbm fractional brownian motion models used in the literature and is proved to be able to effectively capture the long range dependence of the stock returns to develop the pricing mechanics of the cds we firstly derive a sufficient condition for the market modeled under the gmfbm to be arbitrage free then under the risk neutral assumption the cds is fairly priced by investigating the two legs of the cash flow involved the price we obtained involves elementary functions only and can be easily implemented for practical purpose finally based on numerical experiments we analyze quantitatively the impacts of different parameters on the prices of the cds interestingly in comparison with all the other fbm models documented in the literature the results produced from the gmfbm model are in a better agreement with those calculated from the classical black scholes model

waiting time for a non newtonian polytropic filtration equation with convection abstract in this paper we study the waiting time phenomena for a class of non newtonian polytropic filtration equation with convection according to the nonlinearity in the diffusion and the convection terms some necessary and sufficient conditions on the initial data are given for the existence of waiting time

multiscale lattice boltzmann schemes with turbulence modeling abstract the viability of multiscale lattice boltzmann schemes for the numerical simulation of turbulent flows is discussed and numerically demonstrated for turboaxial machine applications the extension of boundary fitting formulas based on wall functions is proposed which enables the efficient computation of turbulent flows in complex curvilinear geometry using a simple cartesian grid examples of two dimensional turbulent flows in an axial compressor cascade are presented

the shape and term structure of the index option smirk why multifactor stochastic volatility models work so well state of the art stochastic volatility models generate a volatility smirk that explains why out of the money index puts have high prices relative to the black scholes benchmark these models also adequately explain how the volatility smirk moves up and down in response to changes in risk however the data indicate that the slope and the level of the smirk fluctuate largely independently although single factor stochastic volatility models can capture the slope of the smirk they cannot explain such largely independent fluctuations in its level and slope over time we propose to model these movements using a two factor stochastic volatility model because the factors have distinct correlations with market returns and because the weights of the factors vary over time the model generates stochastic correlation between volatility and stock returns besides providing more flexible modeling of the time variation in the smirk the model also provides more flexible modeling of the volatility term structure our empirical results indicate that the model improves on the benchmark heston stochastic volatility model by 24 in sample and 23 out of sample the better fit results from improvements in the modeling of the term structure dimension as well as the moneyness dimension

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

a characteristic galerkin method for discrete boltzmann equation abstract the characteristic galerkin finite element method for the discrete boltzmann equation is presented to simulate fluid flows in complex geometries the inherent geometric flexibility of the finite element method permits the easy use of simple cartesian variables on unstructured meshes and the mesh clustering near large gradients the characteristic galerkin procedure with appropriate boundary condition results in accurate solutions with little numerical diffusion several test cases are conducted including unsteady couette flows lid driven cavity flows and steady flow past a circular cylinder on unstructured meshes the numerical results are in good agreement with previous analytical if applicable numerical and experimental results

regularity in sobolev spaces for the fast diffusion and the porous medium equation abstract the degenerate parabolic equation u t u m 1 u m 0 is considered in a cylinder 0 t under homogeneous dirichlet boundary values the regularity of weak solutions for the fast diffusion equation m 1 and the porous medium equation m 1 are investigated regularity of u and u m 1 u in weighted sobolev spaces and in fractional order nikolskii spaces are proved

infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains we study the positivity and regularity of solutions to the fractional porous me dium equations ut sum 0 in 0 for m 1 and s 0 1 with dirichlet boundary data u 0 in 0 n and nonnegative initial condition u 0 u0 0 our first result is a quantitative lower bound for solutions that holds for all positive times t 0 as a consequence we find a global harnack principle stating that for any t 0 solutions are comparable to ds m where d is the distance to this is in sharp contrast with the local case s 1 where the equation has finite speed of propagation after this we study the regularity of solutions we prove that solutions are classical in the interior c in x and c1 in t and establish a sharp cxs m regularity estimate up to the boundary our methods are quite general and can be applied to wider classes of nonlocal parabolic equations of the form ut f u 0 in both in bounded and unbounded domains 2016 wiley periodicals inc

investigation of the les wale turbulence model within the lattice boltzmann framework turbulence models which can perform the transition from laminar flow to fully developed turbulent flow are of key importance in industrial applications a promising approach is the les wale model which can be used without wall functions or global damping functions the model produces an efficient and fast scheme due to its algebraic character additionally its prediction of the transition from laminar to turbulent regimes has shown promising results in this work the les wale model is investigated within the lattice boltzmann framework for validation purposes various test cases are presented first a channel flow at a reynolds number of 6876 is investigated secondly the flow around a wall mounted cube at various reynolds numbers is determined the flow regime varies from laminar to transitional to fully turbulent conditions at a reynolds number of 40 000 with respect to the cube height

least squares finite element scheme for the lattice boltzmann method on an unstructured mesh a numerical model of the lattice boltzmann method lbm utilizing least squares finite element method in space and the crank nicolson method in time is developed this method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite element method while employing accurate least squares optimization fourth order accuracy in space and second order accuracy in time are derived for a pure advection equation on a uniform mesh while high stability is implied from a von neumann linearized stability analysis implemented on unstructured mesh through an innovative element by element approach the proposed method requires fewer grid points and less memory compared to traditional lbm accurate numerical results are presented through two dimensional incompressible poiseuille flow couette flow and flow past a circular cylinder finally the proposed method is applied to estimate the permeability of a randomly generated porous media which further demonstrates its inherent geometric flexibility

equivalent partial differential equations of a lattice boltzmann scheme we show that when we formulate the lattice boltzmann equation with a small time step dt and an associated space scale dx a taylor expansion joined with the so called equivalent equation methodology leads to establishing macroscopic fluid equations as a formal limit we recover the euler equations of gas dynamics at the first order and the compressible navier stokes equations at the second order

non body fitted cartesian mesh simulation of highly turbulent flows using multi relaxation time lattice boltzmann method this paper presents a lattice boltzmann method lbm based study aimed at numerical simulation of highly turbulent and largely inclined flow around obstacles of curved geometry using non body fitted cartesian meshes the approach features 1 combining the interpolated bounce back scheme with the lbm of multi relaxation time mrt type to enable the use of simple cartesian mesh for the flow cases even with complex geometries and 2 incorporating the spalart allmaras sa turbulence model into lbm in order to represent the turbulent flow effect the numerical experiments are performed corresponding to flows around an naca0012 airfoil at re 5x10 5 and around a flat plate at re 2x10 4 respectively the agreement between all simulation results obtained from this study and the data provided by other literature demonstrates the reliability of the enhanced lbm proposed in this paper for simulating simply on cartesian meshes complex flows that may involve bodies of curved boundary high reynolds number and large angle of attack

three time integration methods for incompressible flows with discontinuous galerkin boltzmann method abstract this paper presents three time integration methods for incompressible flows with finite element method in solving the lattice bgk boltzmann equation the space discretization is performed using nodal discontinuous galerkin method which employs unstructured meshes with triangular elements and high order approximation degrees the time discretization is performed using three different kinds of time integration methods namely direct decoupling and splitting from the storage cost temporal accuracy numerical stability and time consumption we systematically compare three time integration methods then benchmark fluid flow simulations are performed to highlight efficient time integration methods numerical results are in good agreement with others or exact solutions

the asymptotic behaviour of solutions of a porous medium equation with bounded measurable coefficients abstract we prove the holder continuity of the interface of a solution of a porous medium equation with bounded measurable coefficients we also describe the asymptotic behaviour as time goes to infinity

wall model for large eddy simulation based on the lattice boltzmann method an original wall model for lattice boltzmann based large eddy simulation is presented it relies on either an analytical profile for the velocity profile within the first off wall cell or the solution of turbulent boundary layer equations the latter are solved thanks to a meshless approach to obtain a user friendly method the proposed method is observed to be both robust and accurate yielding very satisfactory results in plane channel flow up to re email protected 000 on uniform grids with dx email protected email protected 1000 the computed maximum error on skin friction is about 4 in most investigated cases on the coarsest grids 10 grid points across the half channel height it lies within 1 2 on finer grids with 20 60 uniformly distributed grid points in the channel half height

least squares finite element lattice boltzmann method a new numerical model of the lattice boltzmann method utilizing least squares finite element in space and crank nicolson method in time is presented the new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite element method s geometric flexibility and numerical stability while employing efficient and accurate least squares optimization for the pure advection equation on a uniform mesh the proposed method provides for fourth order accuracy in space and second order accuracy in time with unconditional stability in the time domain accurate numerical results are presented through two dimensional incompressible poiseuille flow and couette flow

finite volume lattice boltzmann method we present a finite volume formulation for the lattice boltzmann method fvlbm based on standard bilinear quadrilateral elements in two dimensions the accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the navier stokes equations for time dependent rotating couette flow and taylor vortex flow to demonstrate the flexibility of the scheme we have also simulated a modified rotating couette flow where the inner cylinder has an elliptical shape the results agree with those obtained from the traditional marker and cell method the fvlbm scheme is applicable to arbitrarily shaped two dimensional regions and thus the range of applicability of the lattice boltzmann method has been significantly extended

fully degenerate monge ampere equations abstract in this paper we consider the following nonlinear eigenvalue problem for the monge ampere equation find a non negative weakly convex classical solution f satisfying det d 2 f f p in f on for a strictly convex smooth domain r 2 and 0 p 2 when f 0 contains a convex domain we find a classical solution which is smooth on f 0 and whose free boundary f 0 is also smooth

multireflection boundary conditions for lattice boltzmann models we present a general framework for several previously introduced boundary conditions for lattice boltzmann models such as the bounce back rule and the linear and quadratic interpolations the objectives are twofold first to give theoretical tools to study the existing link type boundary conditions and their corresponding accuracy second to design boundary conditions for general flows which are third order kinetic accurate using these new boundary conditions couette and poiseuille flows are exact solutions of the lattice boltzmann models for a reynolds number mathrm re 0 stokes limit for arbitrary inclination with the lattice directions numerical comparisons are given for stokes flows in periodic arrays of spheres and cylinders linear periodic array of cylinders between moving plates and for navier stokes flows in periodic arrays of cylinders for mathrm re l200 these results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce back reflection up to an order of magnitude on the hydrodynamics fields further improvement is achieved with the new multireflection boundary conditions reaching a level of accuracy close to the quasianalytical reference solutions even for rather modest grid resolutions and few points in the narrowest channels more important the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions finally the good stability of these schemes is highlighted by some simulations of moving obstacles a cylinder between flat walls and a sphere in a cylinder

a short memory version of the vasicek model and evaluating european options on zero coupon bonds abstract this paper considers a fractional version of the vasicek interest rate model where the noise part of the model is modeled as fractional brownian motion with hurst index h 0 1 2 we first show that the increments of the model have short range dependence then the efficiency of the proposed model versus the classical interest rate models is examined by employing the mle calibration method and the akaike information criterion aic an analytic approximation formula for pricing zero coupon bond when the dynamics of the interest rate governed by the model is derived we also find a margin for the option price by using bid and ask formulas

perturbation solutions for bond pricing equations under a multivariate cir model with weak dependences abstract in this article we derive the explicit perturbation solutions for bond pricing equations under a multivariate cox ingersoll ross model whose factors have weak dependences between each other the error bounds of the perturbation approximations are demonstrated for the riccati equation and zero coupon bond price these results provide the accuracy order for the perturbation approximation since the perturbation approximations are constructed based on the exact solution of the riccati equation this computational approach can be applied to deal with the stiffness problem numerical results are presented to show that this computation approach is tractable and accurate for evaluating the bond price