fully implicit methodology for the dynamics of biomembranes and capillary interfaces by combining the level set and newton methods abstract this framework is concerned with the numerical modeling of the dynamics of individual biomembranes and capillary interfaces in a surrounding newtonian fluid a level set approach helps to follow the interface motion our method features the use of high order fully implicit time integration schemes that enable to overcome stability issues related to the explicit discretization of the highly non linear bending force or capillary force at each time step the tangent systems are derived and the resulting nonlinear problems are solved by a newton raphson method based on the signed distance assumption several inexact newton strategies are employed to solve the capillary and vesicle problems and guarantee the second order convergence behavior we address in detail the main features of the proposed method and we report several experiments in the two dimensional case with the aim of illustrating its accuracy and efficiency comparative investigations with respect to the fully explicit scheme depict the stabilizing effect of the new method which allows to use significantly larger time step sizes

computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods the numerical simulation of the deformation of vesicle membranes under simple shear external fluid flow is considered in this paper a saddle point approach is proposed for the imposition of the fluid incompressibility and the membrane inextensibility constraints through lagrange multipliers defined in the fluid and on the membrane respectively using a level set formulation the problem is approximated by mixed finite elements combined with an automatic adaptive mesh procedure at the vicinity of the membrane boundary numerical experiments show that this combination of the saddle point and adaptive mesh method enhances the robustness of the method the effect of inertia on the stability of the vesicle in a shear flow is also investigated

asymptotic coefficients of hermite function series abstract by using complex variable methods steepest descent and residues to asymptotically evaluate the coefficient integrals the numerical analysis of hermite function series is discussed there are striking similarities and differences with the author s earlier work on chebyshev polynomial methods j comp phys 45 1982 45 49 for infinite or semi infinite domains like chebyshev series the hermite coefficients are asymptotically given by the sum of two types of terms i stationary point steepest descent contributions and ii residues at the poles of f z the function being expanded as a hermite series the stationary point term is determined solely by the asymptotic behavior of f z i e how rapidly f z decays as z along the real axis unlike chebyshev series however it is necessary to perform a separate analysis for functions which decay faster or slower than the gaussian function exp az2 singular functions too fall into two categories those that decay rapidly with z have asymptotic hermite coefficients which are dominated by the singularity but functions which decay as slowly as sech z or slower have hermite coefficients dominated by the stationary point terms and the singularity is irrelevant the end product of the analysis is the same as in the earlier work simple explicit formulas to optimize the efficiency of hermite methods and estimate a priori how many degrees of freedom are needed provided one knowns at least crudely i the asymptotic behavior of f z and ii its singularity nearest the real axis rather surprisingly one finds hermite functions superior to chebyshev polynomials for some classes of functions when the computational domain is infinite

a new code for electrostatic simulation by numerical integration of the vlasov and ampere equations using maccormack s method abstract we present a new simulation code for electrostatic waves in one dimension which uses the vlasov equation to integrate the distribution function and ampere s equation to integrate the electric field forward in time previous vlasov codes used the vlasov and poisson equations using ampere s equation has two advantages first boundary conditions do not have to be set on the electric field second it forms a logical basis for an electromagnetic code since the time integration of the electric and magnetic fields is treated in a similar way maccormack s method is used to integrate the vlasov equation which was found to be easy to implement and reliable a stability analysis is presented for the maccormack scheme applied to the vlasov equation conditions for stability are more stringent than the simple courant friedrich s lewy cfl conditions for the spatial and velocity grids we provide a simple linear function which when combined with the cfl conditions should ensure stability simulation results for landau damping are in excellent agreement with numerical solutions of the linear dispersion relation for a wide range of wavelengths the code is also able to retain phase memory as demonstrated by the recurrence effect and reproduce the effects of particle trapping the use of ampere s equation enables standing and traveling waves to be produced depending on whether the current is zero or non zero respectively in simulations where the initial current is non zero and maxwell s equations are satisfied initially additional standing waves may be set up which could be important when the coupling of wave fields from a transmitter to a plasma is considered

high order maximum principle preserving semi lagrangian finite difference weno schemes for the vlasov equation in this paper we propose the parametrized maximum principle preserving mpp flux limiter originally developed in 37 to the semi lagrangian finite difference weighted essentially non oscillatory scheme for solving the vlasov equation the mpp flux limiter is proved to maintain up to fourth order accuracy for the semi lagrangian finite difference scheme without any time step restriction numerical studies on the vlasov poisson system demonstrate the performance of the proposed method and its ability in preserving the positivity of the probability distribution function while maintaining the high order accuracy

a boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d we present a new method for the evolution of inextensible vesicles immersed in a stokesian fluid we use a boundary integral formulation for the fluid that results in a set of nonlinear integro differential equations for the vesicle dynamics the motion of the vesicles is determined by balancing the non local hydrodynamic forces with the elastic forces due to bending and tension numerical simulations of such vesicle motions are quite challenging on one hand explicit time stepping schemes suffer from a severe stability constraint due to the stiffness related to high order spatial derivatives and a milder constraint due to a transport like stability condition on the other hand an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step we present two semi implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme we discretize the equations by using a spectral method in space and a multistep third order accurate scheme in time we use the fast multipole method fmm to efficiently compute vesicle vesicle interaction forces in a suspension with a large number of vesicles we report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme

a convergent numerical scheme for integrodifferential kinetic models of angiogenesis abstract we study a robust finite difference scheme for integrodifferential kinetic systems of fokker planck type modeling tumor driven blood vessel growth the scheme is of order one and enjoys positivity features we analyze stability and convergence properties and show that soliton like asymptotic solutions are correctly captured we also find good agreement with the solution of the original stochastic model from which the deterministic kinetic equations are derived working with ensemble averages a numerical study clarifies the influence of velocity cut offs on the solutions for exponentially decaying data

towards an ultra efficient kinetic scheme part i basics on the bgk equation in this paper we present a new ultra efficient numerical method for solving kinetic equations in this preliminary work we present the scheme in the case of the bgk relaxation operator the scheme being based on a splitting technique between transport and collision can be easily extended to other collisional operators as the boltzmann collision integral or to other kinetic equations such as the vlasov equation the key idea on which the method relies is to solve the collision part on a grid and then to solve exactly the transport linear part by following the characteristics backward in time the main difference between the method proposed and semi lagrangian methods is that here we do not need to reconstruct the distribution function at each time step this allows to tremendously reduce the computational cost of the method and it permits for the first time to the author s knowledge to compute solutions of full six dimensional kinetic equations on a single processor laptop machine numerical examples up to the full three dimensional case are presented which validate the method and assess its efficiency in 1d 2d and 3d

a multiscale fast semi lagrangian method for rarefied gas dynamics in this paper we consider the extension of the method developed in dimarco and loubere 2013 22 23 with the aim of facing the numerical resolution of multi scale problems arising in rarefied gas dynamics the scope of this work is to consider situations in which the whole domain does not demand the use of a kinetic model everywhere this is the case of many realistic applications some regions of the computational domain require a microscopic description given by a kinetic model while the rest of the domain can be described by a coarser model of fluid type our aim is to show how the kinetic scheme developed in the pre cited articles is perfectly suited for building domain decomposition strategies which make the method more attractive with respect to classical numerical techniques for kinetic equations and multi scale realistic problems several numerical evidences are provided in this work in the two dimensional and three dimensional settings to assess the efficiency of the domain decomposition scheme

hermite spectral methods with a time dependent scaling for parabolic equations in unbounded domains hermite spectral methods are investigated for linear diffusion equations and nonlinear convection diffusion equations in unbounded domains when the solution domain is unbounded the diffusion operator no longer has a compact resolvent which makes the hermite spectral methods unstable to overcome this difficulty a time dependent scaling factor is employed in the hermite expansions which yields a positive bilinear form as a consequence stability and spectral convergence can be established for this approach the present method plays a similar role in the stability of the similarity transformation technique proposed by funaro and kavian math comp 57 1991 pp 597 619 however since coordinate transformations are not required the present approach is more efficient and is easier to implement in fact with the time dependent scaling the resulting discretization system is of the same form as that associated with the classical straightforward but unstable hermite spectral method numerical experiments are carried out to support the theoretical stability and convergence results

semi lagrangian schemes for the vlasov equation on an unstructured mesh of phase space a new scheme for solving the vlasov equation using an unstructured mesh for the phase space is proposed the algorithm is based on the semi lagrangian method which exploits the fact that the distribution function is constant along the characteristic curves we use different local interpolation operators to reconstruct the distribution function f some of which need the knowledge of the gradient of f we can use limiter coefficients to maintain the positivity and the l bound of f and optimize these coefficients to ensure the conservation of the l1 norm that is to say the mass by solving a linear programming problem several numerical results are presented in two and three axisymmetric case dimensional phase space the local interpolation technique is well suited for parallel computation

a numerical scheme for the integration of the vlasov poisson system of equations in the magnetized case we present a numerical algorithm for the solution of the vlasov poisson system of equations in the magnetized case the numerical integration is performed using the well known splitting method in the electrostatic approximation coupled with a finite difference upwind scheme finally the algorithm provides second order accuracy in space and time the cylindrical geometry is used in the velocity space in order to describe the rotation of the particles around the direction of the external uniform magnetic field using polar coordinates the integration of the vlasov equation is very simplified in the velocity space with respect to the cartesian geometry because the rotation in the velocity cartesian space corresponds to a translation along the azimuthal angle in the cylindrical reference frame the scheme is intrinsically symplectic and significatively simpler to implement with respect to a cartesian one the numerical integration is shown in detail and several conservation tests are presented in order to control the numerical accuracy of the code and the time evolution of the entropy strictly related to the filamentation problem for a kinetic model is discussed

on numerical methods for hamiltonian pdes and a collocation method for the vlasov maxwell equations abstract hamiltonian partial differential equations often have implicit conservation laws constants of the motion embedded within them it is not in general possible to preserve these conservation laws simply by discretization in conservative form because there is frequently only one explicit conservation law however by using weighted residual methods and exploiting the hamiltonian structure of the equations it is shown that at least some of the conservation laws are preserved in a method of lines continuous in time in particular the hamiltonian can always be exactly preserved as a constant of the motion other conservation laws in particular linear and quadratic casimirs and momenta can sometimes be conserved too depending on the details of the equations under consideration and the form of discretization employed collocation methods also offer automatic conservation of linear and quadratic casimirs some standard discretization methods when applied to hamiltonian problems are shown to be derived from a numerical approximation to the exact poisson bracket of the system a method for the vlasov maxwell equations based on legendre gauss lobatto collocation is presented as an example of these ideas

a semi lagrangian transport method for kinetic problems with application to dense to dilute polydisperse reacting spray flows abstract for sprays as described by a kinetic disperse phase model strongly coupled to the navier stokes equations the resolution strategy is constrained by accuracy objectives robustness needs and the computing architecture in order to leverage the good properties of the eulerian formalism we introduce a deterministic particle based numerical method to solve transport in physical space which is simple to adapt to the many types of closures and moment systems the method is inspired by the semi lagrangian schemes developed for gas dynamics we show how semi lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle particle coupling barely influences the transport i e when particle pressure is negligible the particle behavior is indeed close to free streaming the new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters which makes it robust it is a deterministic resolution method so that it does not require efforts on statistical convergence noise control or post processing all couplings are done among data under the form of eulerian fields which allows one to use efficient algorithms and to anticipate the computational load this makes the method both accurate and efficient in the context of parallel computing after a complete verification of the new transport method on various academic test cases we demonstrate the overall strategy s ability to solve a strongly coupled liquid jet with fine spatial resolution and we apply it to the case of high fidelity large eddy simulation of a dense spray flow a fuel spray is simulated after atomization at diesel engine combustion chamber conditions the large parallel strongly coupled computation proves the efficiency of the method for dense polydisperse reacting spray flows

coldice a parallel vlasov poisson solver using moving adaptive simplicial tessellation abstract resolving numerically vlasov poisson equations for initially cold systems can be reduced to following the evolution of a three dimensional sheet evolving in six dimensional phase space we describe a public parallel numerical algorithm consisting in representing the phase space sheet with a conforming self adaptive simplicial tessellation of which the vertices follow the lagrangian equations of motion the algorithm is implemented both in six and four dimensional phase space refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase space sheet at second order relying on additional tracers created when needed at runtime in order to preserve in the best way the hamiltonian nature of the system refinement is anisotropic and constrained by measurements of local poincare invariants resolution of poisson equation is performed using the fast fourier method on a regular rectangular grid similarly to particle in cells codes to compute the density projected onto this grid the intersection of the tessellation and the grid is calculated using the method of franklin and kankanhalli 65 66 67 generalised to linear order as preliminary tests of the code we study in four dimensional phase space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves we also perform a warm dark matter simulation in six dimensional phase space that we use to check the parallel scaling of the code

conservative numerical schemes for the vlasov equation abstract a new scheme for solving the vlasov equation using a phase space grid is proposed the algorithm is based on the conservation of the flux of particles and the distribution function is reconstructed using various techniques that allow control of spurious oscillations or preservation of the positivity several numerical results are presented in two and four dimensional phase space and the scheme is compared with the semilagrangian method this method is almost as accurate as the semilagrangian one and the local reconstruction technique is well suited for parallel computation

a numerical method for solving the vlasov poisson equation based on the conservative ido scheme we have applied the conservative form of the interpolated differential operator ido cf scheme in order to solve the vlasov poisson equation which is one of the multi moment schemes through numerical tests of the nonlinear landau damping and two stream instability we compared the present scheme with other schemes such as the spline and cip ones we mainly investigated the conservation property of the l1 norm energy entropy and phase space area for each scheme and demonstrated that the ido cf scheme is capable of performing stable long time scale simulation while maintaining high accuracy the scheme is based on an eulerian approach and it can thus be directly used for fokker planck high dimensional vlasov poisson and also guiding center drift simulations aiming at particular problems of plasma physics the benchmark tests for such simulations have shown that the ido cf scheme is superior in keeping the conservation properties without causing serious phase error

lyapunov stability of vlasov equilibria using fourier hermite modes we propose an efficient method to compute lyapunov exponents and lyapunov eigenvectors of long range interacting many particle systems whose dynamics is described by the vlasov equation we show that an expansion of a distribution function using hermite modes in velocity variable and fourier modes in configuration variable converges fast if an appropriate scaling parameter is introduced and identified with the inverse of the temperature as a consequence dynamics and linear stability properties of many particle states both in the close to and in the far from equilibrium regimes can be predicted using a small number of expansion coefficients as an example of a long range interacting system we investigate stability properties of stationary states the hamiltonian mean field model

block structured adaptive mesh refinement algorithms for vlasov simulation direct discretization of continuum kinetic equations like the vlasov equation are under utilized because the distribution function generally exists in a high dimensional 3d space and computational cost increases geometrically with dimension we propose to use high order finite volume techniques with block structured adaptive mesh refinement amr to reduce the computational cost the primary complication comes from a solution state comprised of variables of different dimensions we develop the algorithms required to extend standard single dimension block structured amr to the multi dimension case specifically algorithms for reduction and injection operations that transfer data between mesh hierarchies of different dimensions are explained in detail in addition modifications to the basic amr algorithm that enable the use of high order spatial and temporal discretizations are discussed preliminary results for a standard 1d 1v vlasov poisson test problem are presented results indicate that there is potential for significant savings for some classes of vlasov problems

nested iteration and first order system least squares for incompressible resistive magnetohydrodynamics this paper develops a nested iteration algorithm to solve time dependent nonlinear systems of partial differential equations for each time step newton s method is used to form approximate solutions from a sequence of nested spaces where the resolution of the approximations increases as the algorithm progresses nested iteration results in most of the iterations being performed on coarser grids where minimal work is needed to reduce error to the level of discretization error the approximate solution on a given coarse grid is interpolated to a refined grid and is used as an initial guess for the problem posed there the approximation is then already close enough to the solution on the current grid that a minimal amount of work is needed to solve the refined problem due to the rapid convergence of newton s method near a solution the paper develops an algorithm that attempts to optimize accuracy per computational cost on each grid so that essentially no unnecessary work is done on any grid the nested iteration algorithm is then applied to a reduced two dimensional model of the incompressible resistive magnetohydrodynamic mhd equations using this algorithm on the mhd equations in the context of a first order system least squares finite element discretization and algebraic multigrid to solve the linearized systems instabilities in a model tokamak fusion reactor are simulated numerical results show that this highly complex nonlinear problem is solved in an equivalent of 30 80 fine grid relaxation sweeps per time step

vlasov simulations using velocity scaled hermite representations the efficiency accuracy and stability of two different pseudo spectral methods using scaled hermite basis and weight functions applied to the nonlinear vlasov poisson equations in one dimension 1d 1v are explored and compared a variable velocity scaleuis introduced into the hermite basis and is shown to yield orders of magnitude reduction in errors as compared to linear kinetic theory with no increase in workload a set of fourier hermite coefficients representing a periodic gaussian distribution function are advanced through time with ano t2 accurate splitting method within this splitting scheme the advection and acceleration terms of the vlasov equation are solved separately using ano t4 accurate runge kutta method the asymmetrically weighted aw hermite basis which has been used previously by many authors conserves particles and momentum exactly and total energy too t3 however the aw hermite method doesnotconserve the square integral of the distribution and is in fact numerically unstable the symmetrically weighted sw hermite algorithm applied here to the vlasov system for the first time can either conserve particles and energy fornueven or momentum fornuodd as t 0 wherenuis the largest hermite mode number the sw hermite method conserves the square integral of the distribution and therefore remains numerically stable in addition careful velocity scaling improves the conservation properties of the sw hermite method damping and growth rates oscillation frequencies e field saturation levels and phase space evolution are seen to be qualitatively correct during simulations relative errors with respect to linear landau damping and linear bump on tail instability are shown to be less than 1 using only 64 velocity scaled hermite functions comparisons to particle in cell pic simulations show that as the number of particles increases to more than 106 the pic solutions converge to scaled sw hermite solutions that were found in only 1 10 of the run time the sw hermite method with velocity scaling is well suited to kinetic simulations of warm plasmas

arbitrarily high order convected scheme solution of the vlasov poisson system abstract the convected scheme cs is a forward trajectory semi lagrangian method for solution of transport equations which has been most often applied to the kinetic description of plasmas and rarefied neutral gases in its simplest form the cs propagates the solution forward in time by advecting the so called moving cells along their characteristic trajectories and by remapping them on the mesh at the end of the time step the cs is conservative positivity preserving simple to implement and it is not subject to time step restriction to maintain stability recently guclu and hitchon 2012 1 a new methodology was introduced for reducing numerical diffusion based on a modified equation analysis the remapping error was compensated by applying small corrections to the final position of the moving cells prior to remapping while the spatial accuracy was increased from 2nd to 4th order the new scheme retained the important properties of the original method and was shown to be extremely simple and efficient for constant advection problems here the cs is applied to the solution of the vlasov poisson system which describes the evolution of the velocity distribution function of a collection of charged particles subject to reciprocal coulomb interactions the vlasov equation is split into two constant advection equations one in configuration space and one in velocity space and high order time accuracy is achieved by proper composition of the operators the splitting procedure enables us to use the constant advection solver which we extend to arbitrarily high order of accuracy in time and space a new improved procedure is given which makes the calculation of the corrections straightforward focusing on periodic domains we describe a spectrally accurate scheme based on the fast fourier transform the proposed implementation is strictly conservative and positivity preserving the ability to correctly reproduce the system dynamics as well as resolving small scale features in the solution is shown in classical 1d 1v test cases both in the linear and the non linear regimes

convergence of a semi lagrangian scheme for the one dimensional vlasov poisson system a semi lagrangian scheme is proposed for solving the periodic one dimensional vlasov poisson system in phase space on unstructured meshes the distribution function f t x v and the electric field e t x are shown to converge to the exact solution values in the l infty norm the rate of convergence is in o h4 3

analysis of a new class of forward semi lagrangian schemes for the 1d vlasov poisson equations the vlasov equation is a kinetic model describing the evolution of a plasma which is a globally neutral gas of charged particles it is self consistently coupled with poisson s equation which rules the evolution of the electric field in this paper we introduce a new class of forward semi lagrangian schemes for the vlasov poisson system based on a cauchy kovalevsky ck procedure for the numerical solution of the characteristic curves exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the ck scheme as for a more classical verlet scheme a l 1 convergence of the schemes will be proved error estimates in o left delta t 2 h 2 frac h 2 delta t right for verlet are obtained where t and h max x v are the discretization parameters

a high order time splitting method based on integral deferred correction for semi lagrangian vlasov simulations semi lagrangian schemes with various splitting methods and with different reconstruction interpolation strategies have been applied to kinetic simulations for example the order of spatial accuracy of the algorithms proposed in qiu and christlieb 2010 29 is very high as high as ninth order however the temporal error is dominated by the operator splitting error which is second order for strang splitting it is therefore important to overcome such low order splitting error in order to have numerical algorithms that achieve higher orders of accuracy in both space and time in this paper we propose to use the integral deferred correction idc method to reduce the splitting error specifically the temporal order accuracy is increased by r with each correction loop in the idc framework where r 1 2r 1 2 for coupling the first order splitting and the strang splitting respectively the proposed algorithm is applied to the vlasov poisson system the guiding center model and two dimensional incompressible flow simulations in the vorticity stream function formulation we show numerically that the idc procedure can automatically increase the order of accuracy in time we also investigate numerical stability of the proposed algorithm via performing fourier analysis to a linear model problem

a new conservative unsplit method for the solution of the vlasov equation we have developed a new conservative method for solving the vlasov equation without using any splitting technique our goal is to maintain the positivity of the distribution function and to avoid un physical oscillations which might lead to numerical instabilities based on a finite volume conservative discretization of the conservative form of the vlasov equation we implemented a highly accurate second order upwind scheme in order to avoid un physical oscillations and their possible numerical instability we apply a flux limiter in the second order we validate our new vlasov solver by considering standard cases of one dimensional current driven ion acoustic instabilities solving a vlasov ampere set of equations

3d numerical simulations of vesicle and inextensible capsule dynamics vesicles are locally inextensible fluid membranes capsules are endowed with in plane shear elasticity mimicking the cytoskeleton of red blood cells rbcs but are extensible while rbcs are inextensible we use boundary integral bi methods based on the green function techniques to model and solve numerically their dynamics we regularize the single layer integral by subtraction of exact identities for the terms involving the normal and the tangential components of the force the stability and precision of bi calculation is enhanced by taking advantage of additional quadrature nodes located in vertices of an auxiliary mesh constructed by a standard refinement procedure from the main mesh we extend the partition of unity technique to boundary integral calculation on triangular meshes the proposed algorithm offers the same treatment of near singular integration regardless whether the source and the target points belong to the same surface or not bending forces are calculated by using expressions derived from differential geometry membrane incompressibility is handled by using two penalization parameters per suspended entity one for deviation of the global area from prescribed value and another for the sum of squares of local strains defined on each vertex extensible or inextensible capsules a model of rbc are studied by storing the position in the reference configuration for each vertex the elastic force is then calculated by direct variation of the elastic energy various nonequilibrium physical examples on vesicles and capsules will be presented and the convergence and precision tests highlighted overall a good convergence is observed with numerical error inversely proportional to the number of vertices used for surface discretization the highest order of convergence allowed by piece wise linear interpolation of the surface

stability of nonlinear vlasov poisson equilibria through spectral deformation and fourier hermite expansion we study the stability of spatially periodic nonlinear vlasov poisson equilibria as an eigenproblem in a fourier hermite basis in the space and velocity variables respectively of finite dimension n when the advection term in the vlasov equation is dominant the convergence with n of the eigenvalues is rather slow limiting the applicability of the method we use the method of spectral deformation introduced by crawford and hislop ann phys ny 189 265 1989 to selectively damp the continuum of neutral modes associated with the advection term thus accelerating convergence we validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear spatially homogeneous equilibria finally we study the stability of a periodic bernstein greene kruskal mode with multiple phase space vortices compare our results with numerical simulations of the vlasov poisson system and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed

outflow boundary conditions for the fourier transformed two dimensional vlasov equation in order to facilitate numerical simulations of plasma phenomena where kinetic processes are important we have studied the technique of fourier transforming the vlasov equation analytically in velocity space and solving the resulting equation numerically particular attention has been paid to the boundary conditions of the fourier transformed system by using outgoing wave boundary conditions in the fourier transformed space small scale information in velocity space is carried outside the computational domain and is removed representing a dissipative loss mechainsm thereby the so called recurrence phenomenon is reduced in the present article a previously developed method in one spatial and one velocity dimension plus time is generalised to two spatial and two velocity dimensions plus time different high order methods are used for computing derivatives as well as for the time stepping

a finite element code for the simulation of one dimensional vlasov plasmas i theory abstract the galerkin method is used to obtain a finite element solution to the vlasov poisson equations over the two dimensional x v phase plane using bilinear element shape functions a set of linear equations for updated values of the distribution function is obtained in which time dependent and time independent coefficients are separated to reduce the computation involved the noise levels are low and the energy conservation good the finite element approach offers certain advantages over alternative methods in applications to problems in plasma physics in particular the flexibility in using elements of different size allows problems in which regions of the plasma are characterized by often widely differing scale lengths to be treated efficiently

high order time discretization for backward semi lagrangian methods we introduce different high order time discretization schemes for backward semi lagrangian methods these schemes are based on multi step schemes like adams moulton and adams bashforth schemes combined with backward finite difference schemes we apply these methods to transport equations for plasma physics applications and for the numerical simulation of instabilities in fluid mechanics in the context of backward semi lagrangian methods this time discretization strategy is particularly efficient and accurate when the spatial error discretization becomes negligible and allows to use large time steps

arbitrary order time accurate semi lagrangian spectral approximations of the vlasov poisson system abstract the vlasov poisson system modeling the evolution of non collisional plasmas in the electrostatic limit is approximated by a semi lagrangian technique spectral methods of periodic type are implemented through a collocation approach groups of particles are represented by the fourier lagrangian basis and evolve for a single timestep along a high order accurate representation of the local characteristic lines the time advancing technique is based on truncated taylor series that can be in principle of any order of accuracy a variant is obtained by coupling the phase space discretization with high order accurate backward differentiation formulas bdf at each timestep particle displacements are reinterpolated and expressed in the original basis to guarantee the order of accuracy in all the variables at relatively low costs thus these techniques combine the excellent features of spectral approximations with high order time integration the resulting method has excellent conservation properties indeed it can be proven that the total number of particles proportional to the total mass and charge is conserved up to the machine precision series of numerical experiments are performed in order to assess the real performance in particular comparisons with standard benchmarks are examined

stabilized finite element methods for solving the level set equation without reinitialization new stabilized finite element methods are proposed for solving moving interface flow problems using the level set approach the formulations enhance the interface resolution without the need to resort to the reinitialization process these are established by adding a perturbation term that depends on the local residual of the eikonal equation to the supg variational formulation of the level set equation these methods are numerically evaluated for well known benchmark flow problems and compared with a modified variant of the penalty method of li et al 2005 the proposed stabilized finite element methods employing second order time and space approximations are promising simple and accurate techniques for solving complex moving interface flows

energy conserving discontinuous galerkin spectral element method for the vlasov poisson system abstract we propose a new energy conserving spectral element discontinuous galerkin method for the approximation of the vlasov poisson system in arbitrary dimension using cartesian grids the method is derived from the one proposed in 4 with two modifications energy conservation is obtained by a suitable projection operator acting on the solution of the poisson problem rather than by solving multiple poisson problems and all the integrals appearing in the finite element formulation are approximated with gauss lobatto quadrature thereby yielding a spectral element formulation the resulting method has the following properties exact energy conservation up to errors introduced by the time discretization stability thanks to the use of upwind numerical fluxes high order accuracy and high locality for the time discretization we consider both runge kutta methods and exponential integrators and show results for 1d and 2d cases 2d and 4d in phase space respectively

a deterministic solver for a hybrid quantum classical transport model in nanomosfets we model a nanomosfet by a mesoscopic time dependent coupled quantum classical system based on a sub band decomposition and a simple scattering operator we first compute the sub band decomposition and electrostatic force field described by a schrodinger poisson coupled system solved by a newton raphson iteration using the eigenvalue eigenfunction decomposition the transport in the classical direction for each sub band modeled by semiclassical boltzmann type equations is solved by conservative semi lagrangian characteristic based methods numerical results are shown for both the thermodynamical equilibrium and time dependent simulations in typical nowadays nanomosfets

solving the boltzmann equation in n log 2 n in c mouhot and l pareschi fast algorithms for computing the boltzmann collision operator math comp to appear c mouhot and l pareschi c r math acad sci paris 339 2004 pp 71 76 fast deterministic algorithms based on spectral methods were derived for the boltzmann collision operator for a class of interactions including the hard spheres model in three dimensions these algorithms are implemented for the solution of the boltzmann equation in two and three dimensions first for homogeneous solutions then for general nonhomogeneous solutions the results are compared to explicit solutions when available and to monte carlo methods in particular the computational cost and accuracy are compared to those of monte carlo methods as well as to those of previous spectral methods finally for inhomogeneous solutions we take advantage of the great computational efficiency of the method to show an oscillation phenomenon of the entropy functional in the trend to equilibrium which was suggested in the work l desvillettes and c villani invent math 159 2005 pp 245 316

time dependent hermite galerkin spectral method and its applications a time dependent hermite galerkin spectral method thgsm is investigated in this paper for the nonlinear convection diffusion equations in the unbounded domains the time dependent scaling factor and translating factor are introduced in the definition of the generalized hermite functions ghf as a consequence the thgsm based on these ghf has many advantages not only in theoretical proofs but also in numerical implementations the stability and spectral convergence of our proposed method have been established in this paper the korteweg de vries burgers kdvb equation and its special cases including the heat equation and the burgers equation as the examples have been numerically solved by our method the numerical results are presented and it surpasses the existing methods in accuracy our theoretical proof of the spectral convergence has been supported by the numerical results

asymptotically stable particle in cell methods for the vlasov poisson system with a strong external magnetic field this paper deals with the numerical resolution of the vlasov poisson system with a strong external magnetic field by particle in cell pic methods in this regime classical pic methods are subject to stability constraints on the time and space steps related to the small larmor radius and plasma frequency here we propose an asymptotic preserving pic scheme which is not subjected to these limitations our approach is based on first and higher order semi implicit numerical schemes already validated on dissipative systems s boscarino f filbet and g russo j sci comput 2016 doi 10 1007 s10915 016 0168 y additionally when the magnitude of the external magnetic field becomes large this method provides a consistent pic discretization of the guiding center equation that is an incompressible euler equation in vorticity form we propose several numerical experiments which provide a solid validation of the method and its underlying concepts

a high order semi lagrangian discontinuous galerkin method for vlasov poisson simulations without operator splitting abstract in this paper we develop a high order semi lagrangian sl discontinuous galerkin dg method for nonlinear vlasov poisson vp simulations without operator splitting in particular we combine two recently developed novel techniques one is the high order non splitting sldg transport method cai et al 2017 4 and the other is the high order characteristics tracing technique proposed in qiu and russo 2017 29 the proposed method with up to third order accuracy in both space and time is locally mass conservative free of splitting error positivity preserving stable and robust for large time stepping size the sldg vp solver is applied to classic benchmark test problems such as landau damping and two stream instabilities for vp simulations efficiency and effectiveness of the proposed scheme is extensively tested tremendous cpu savings are shown by comparisons between the proposed sl dg scheme and the classical runge kutta dg method

discontinuous galerkin methods for the vlasov maxwell equations discontinuous galerkin methods are developed for solving the vlasov maxwell system methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy such properties in general are hard to achieve within other numerical method frameworks for simulating the vlasov maxwell system the proposed scheme employs discontinuous galerkin discretizations for both the vlasov and the maxwell equations resulting in a consistent description of the distribution function and electromagnetic fields it is proven up to some boundary effects that charge is conserved and the total energy can be preserved with suitable choices of the numerical flux for the maxwell equations and the underlying approximation spaces error estimates are established for several flux choices the scheme is tested on the streaming weibel instability the order of accuracy and conservation properties of the proposed method are verified

a mass conservative scheme for solving the vlasov poisson equation using characteristic curve abstract in this paper we introduce a mass conservative scheme for solving the vlasov poisson equation this scheme is based on an eulerian approach and is constructed using an interpolation scheme with limiters in order to preserve the mass the difference in the values for numerical flux functions on each cell is used for this the flux functions are constructed by preserving both the solution along a characteristics and the mass in each cell we mainly investigate the conservation of l 1 and l 2 norms of the distribution function total energy entropy and minimum value in addition we show that this scheme is bounded on the total variation to demonstrate the efficiency of the proposed scheme this scheme is compared with the flux balance scheme positive and flux conservative scheme umeda s scheme and fifth order weno reconstruction finite volume scheme

a particle method for the semiclassical limit of the schrodinger equation and the vlasov poisson equations when using standard deterministic particle methods point values of the computed solutions have to be recovered from their singular particle approximations by using some smoothing procedure the choice of the smoothing procedure is rather flexible moreover there is always a parameter associated with the smoothing procedure if this parameter is too large the numerical solution loses its accuracy if it is too small oscillation appears no explicit formula has been given on how to choose this parameter in this paper we develop a particle method for the semiclassical limit of the schrodinger equation and the vlasov poisson equations in which we use the property of conservation of charge which was studied in d wei kinetic and related models 3 2010 pp 729 754 to construct the density this method avoids the recovery step of the particle methods thus it is simpler and more accurate in particular it gives more accurate field quantities consequently we apply this method to the vlasov poi

performance analysis and optimization of finite difference schemes for wave propagation problems in the present paper we gauge the performance of finite difference schemes with runge kutta time integration for wave propagation problems by rigorously defining appropriate cost and error metrics in a simple setting represented by the linear advection equation optimal values of the grid spacing and of the time step are obtained as a result of a cost minimization for given error level procedure the theory suggests superior performance of high order schemes when highly accurate solutions are sought for and in several space dimensions even more the analysis of the global discretization error shows the occurrence of two approximately independent sources of error associated with the space and time discretizations the improvement of the performance of finite difference schemes can then be achieved by trying to separately minimize the two contributions general guidelines for the design of problem tailored optimized schemes are provided suggesting that significant reductions of the computational cost are in principle possible the application of the analysis to wave propagation problems in a two dimensional environment demonstrates that the analysis carried out for the scalar case directly applies to the propagation of monochromatic sound waves for problems of sound propagation involving disparate length scales the analysis still provides useful insight for the optimal exploitation of computational resources however the actual advantage provided by optimized schemes is not as evident as in the single scale scalar case

a legendre fourier spectral method with exact conservation laws for the vlasov poisson system we present the design and implementation of an l 2 stable spectral method for the discretization of the vlasov poisson model of a collisionless plasma in one space and velocity dimension the velocity and space dependence of the vlasov equation are resolved through a truncated spectral expansion based on legendre and fourier basis functions respectively the poisson equation which is coupled to the vlasov equation is also resolved through a fourier expansion the resulting system of ordinary differential equation is discretized by the implicit second order accurate crank nicolson time discretization the non linear dependence between the vlasov and poisson equations is iteratively solved at any time cycle by a jacobian free newton krylov method in this work we analyze the structure of the main conservation laws of the resulting legendre fourier model e g mass momentum and energy and prove that they are exactly satisfied in the semi discrete and discrete setting the l 2 stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term the impact of the penalty term on the conservation properties is investigated theoretically and numerically an implementation of the penalty term that does not affect the conservation of mass momentum and energy is also proposed and studied a collisional term is introduced in the discrete model to control the filamentation effect but does not affect the conservation properties of the system numerical results on a set of standard test problems illustrate the performance of the method

compact implicit maccormack type schemes with high accuracy in this work the maccormack methodology is extended to implicit compact differencing schemes a prefactorization method is developed which splits the implicit matrix into two independent upper and lower matrices which are easier to invert using this method a new class of high order accurate compact maccormack type schemes is derived two fourth order schemes are described and results are shown for three linear and nonlinear caa benchmark problems

conservative semi lagrangian schemes for vlasov equations conservative methods for the numerical solution of the vlasov equation are developed in the context of the one dimensional splitting in the case of constant advection these methods and the traditional semi lagrangian ones are proven to be equivalent but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity in the non constant advection case they present an alternative to the traditional semi lagrangian schemes which can suffer from bad mass conservation in this time splitting setting

semi spectral method for the wigner equation we propose a numerical method to solve the wigner equation in quantum systems of spinless non relativistic particles the method uses a spectral decomposition into l 2 r d basis functions in momentum space to obtain a system of first order advection reaction equations the resulting equations are solved by splitting the reaction and advection steps so as to allow the combination of numerical techniques from quantum mechanics and computational fluid dynamics by identifying the skew hermitian reaction matrix as a generator of unitary rotations the method is validated for the case of particles subject to a one dimensional an harmonic and morse potential using finite differences for the advection part thereby we verify the second order of convergence and observe non classical behavior in the evolution of the wigner function

hamiltonian splitting for the vlasov maxwell equations a new splitting is proposed for solving the vlasov maxwell system this splitting is based on a decomposition of the hamiltonian of the vlasov maxwell system and allows for the construction of arbitrary high order methods by composition independent of the specific deterministic method used for the discretization of the phase space moreover we show that for a spectral method in space this scheme satisfies poisson s equation without explicitly solving it finally we present some examples in the context of the time evolution of an electromagnetic plasma instability which emphasizes the excellent behavior of the new splitting compared to methods from the literature

numerical study of the two species vlasov ampere system in this paper we propose energy conserving eulerian solvers for the two species vlasov ampere va system and apply the methods to simulate current driven ion acoustic instability the two species va systems are of practical importance in applications and they conserve many physical quantities including the particle number of each species and the total energy that is comprised of kinetic energy for both species and the electric energy the main goal of this paper is to generalize our previous work for the single species va system 9 and vlasov maxwell vm system 8 to the two species case the methodologies proposed involve careful design of temporal discretization and the use of the discontinuous galerkin dg spatial discretizations we show that the energy conserving time discretizations for single species equations 9 8 can also work for the two species case if extended properly compared to other high order schemes we emphasize that our schemes can preserve the total particle number and total energy on the fully discrete level regardless of mesh size making them very attractive for long time simulations we benchmark our algorithms on a test example to check the one species limit and the current driven ion acoustic instability to simulate the current driven ion acoustic instability a slight modification for the implicit method is necessary to fully decouple the split equations this is achieved by a gauss seidel type iteration technique numerical results verified the conservation and performance of our methods finally we remark that the schemes in this paper can be readily extended to applications when the models take more general form such as the multi species vm equations

edge stabilization for the generalized stokes problem a continuous interior penalty method in this note we introduce and analyze a stabilized finite element method for the generalized stokes equation stability is obtained by adding a least squares penalization of the gradient jumps acro

towards an ultra efficient kinetic scheme part ii in a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the boltzmann type dimarco and loubere 2013 17 the key idea on which the method relies is to solve the collision part on a grid and then to solve exactly the transport part by following the characteristics backward in time on the contrary to classical semi lagrangian methods one does not need to reconstruct the distribution function at each time step this allows to tremendously reduce the computational cost and to perform efficient numerical simulations of kinetic equations up to the six dimensional case without parallelization however the main drawback of the method developed was the loss of spatial accuracy close to the fluid limit in the present work we modify the scheme in such a way that it is able to preserve the high order spatial accuracy for extremely rarefied and fluid regimes in particular in the fluid limit the method automatically degenerates into a high order method for the compressible euler equations numerical examples are presented which validate the method show the higher accuracy with respect to the previous approach and measure its efficiency with respect to well known schemes direct simulation monte carlo finite volume muscl weno

multi dimensional fully implicit spectral method for the vlasov maxwell equations with exact conservation laws in discrete form a spectral method for the numerical solution of the multi dimensional vlasov maxwell equations is presented the plasma distribution function is expanded in fourier for the spatial part and hermite for the velocity part basis functions leading to a truncated system of ordinary differential equations for the expansion coefficients moments that is discretized with an implicit second order accurate crank nicolson time discretization the discrete non linear system is solved with a preconditioned jacobian free newton krylov method it is shown analytically that the fourier hermite method features exact conservation laws for total mass momentum and energy in discrete form standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically the whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities some preconditioning strategies are presented showing that the number of linear iterations of the krylov solver can be drastically reduced and a significant gain in performance can be obtained

a parallel deterministic solver for the schrodinger poisson boltzmann system in ultra short dg mosfets comparison with monte carlo abstract we present a parallel deterministic solver for the boltzmann schrodinger poisson system for partially confined dg mosfets our 2d model uses a dimensional coupling the electrons behave as particles along the longitudinal dimension and as waves along the transverse dimension in ben abdallah et al 2009 the authors validated in a simplified setting the solver for the eigenproblems in this paper we have focused on obtaining physically accurate results by introducing a realistic si conduction band and electron phonon interactions we have switched from cartesian to elliptic variables for the wave vector and consequently radically rebuilt the time integrator the code has been parallelized following a domain decomposition approach the results have been compared to those given by a monte carlo solver

a general strategy for the optimization of runge kutta schemes for wave propagation phenomena we analyze optimized explicit runge kutta schemes rk for computational aeroacoustics and wave propagation phenomena in general exploiting the analysis developed in s pirozzoli performance analysis and optimization of finite difference schemes for wave propagation problems j comput phys 222 2007 809 831 we rigorously evaluate the performance of several time integration schemes in terms of appropriate error and cost metrics and provide a general strategy to design runge kutta methods tailored for specific applications we present families of optimized second and third order runge kutta schemes with up to seven stages and describe their implementation in the framework of williamson s 2n storage formulation j h williamson low storage runge kutta schemes j comput phys 35 1980 48 56 numerical simulations of the 1d linear advection equation and of the 2d linearized euler equations are performed to demonstrate the validity of the theory and to quantify the improvement provided by optimized schemes

high order numerical methods for the space non homogeneous boltzmann equation in this paper we present accurate methods for the numerical solution of the boltzmann equation of rarefied gas the methods are based on a time splitting technique the transport is solved by a third order accurate in space positive and flux conservative pfc method the collision step is treated by a fourier approximation of the collision integral which guarantees spectral accuracy in velocity coupled with several high order integrators in time strang splitting is used to achieve second order accuracy in space and time several numerical tests illustrate the properties of the methods

a splitting algorithm for vlasov simulation with filamentation filtration a fourier fourier transformed version of the splitting algorithm for simulating solutions of the vlasov poisson system of equations is introduced it is shown that with the inclusion of filamentation filtration in this transformed algorithm it is both faster and more stable than the standard splitting algorithm it is further shown that in a scalar computer environment this new algorithm is approximately equal in speed and far less noisy than its particle in cell counterpart it is conjectured that in a multiprocessor environment the filtered splitting algorithm would be faster while producing more precise results

asymptotics on laguerre or hermite polynomial expansions and their applications in gauss quadrature abstract in this paper we present asymptotic analysis on the coefficients of functions expanded in forms of laguerre or hermite polynomial series which shows the decay of the coefficients and derives new error bounds on the truncated series moreover by applying the asymptotics new estimates on the errors for gauss laguerre radau laguerre and gauss hermite quadrature are deduced these results show that gauss laguerre type and gauss hermite type quadratures are nearly of same convergence rates

a parallel vlasov solver based on local cubic spline interpolation on patches a method for computing the numerical solution of vlasov type equations on massively parallel computers is presented in contrast with particle in cell methods which are known to be noisy the method is based on a semi lagrangian algorithm that approaches the vlasov equation on a grid of phase space as this kind of method requires a huge computational effort the simulations are carried out on parallel machines to that purpose we present a local cubic splines interpolation method based on a domain decomposition e g devoted to a processor hermite boundary conditions between the domains using ad hoc reconstruction of the derivatives provide a good approximation of the global solution the method is applied on various physical configurations which show the ability of the numerical scheme

a critical comparison of eulerian grid based vlasov solvers a common problem with direct vlasov solvers is ensuring that the distribution function remains positive a related problem is to guarantee that the numerical scheme does not introduce false oscillations in velocity space in this paper we use a variety of schemes to assess the importance of these issues and to determine an optimal strategy for eulerian split approaches to vlasov solvers from these tests we conclude that maintaining positivity is less important than correctly dissipating the fine scale structure which arises naturally in the solution to many vlasov problems furthermore we show that there are distinct advantages to using high order schemes i e third order rather than second a natural choice which satisfies all of these requirements is the piecewise parabolic method ppm which is applied here to vlasov s equation for the first time

optimized prefactored compact schemes the numerical simulation of aeroacoustic phenomena requires high order accurate numerical schemes with low dispersion and dissipation errors in this paper we describe a strategy for developing high order accurate prefactored compact schemes requiring very small stencil support these schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes the prefactorization strategy splits the central implicit schemes into forward and backward biased operators using fourier analysis we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components this ensures that when the forward and backward stencils are added the original central compact scheme is recovered to extend the resolution characteristic of the schemes an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh the resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth and eighth order compact schemes making them more suitable for high resolution numerical simulations in gas dynamics and computational aeroacoustics the efficiency accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems

the hermite spectral method for gaussian type functions although hermite functions were widely used for many practical problems numerical experiments with the standard normalized hermite functions psi n v worked poorly in the sense that too many hermite functions are required to solve differential equations in order to obtain accurate numerical solutions it is necessary to choose a scaling factor alpha and use psi n alpha v as the basis functions in this paper the scaling factors are given for functions that are of gaussian type which have finite supports m m the scaling factor used is max 0 leqq j leqq n gamma j m where gamma j j 0 n are the roots of psi n 1 v and n 1 is the number of the truncated terms used the numerical results show that after using this scaling factor only reasonable numbers of the hermite functions are required to solve differential equations

solving hyperbolic elliptic problems on singular mapped disk like domains with the method of characteristics and spline finite elements abstract a common strategy in the numerical solution of partial differential equations is to define a uniform discretization of a tensor product multi dimensional logical domain which is mapped to a physical domain through a given coordinate transformation by extending this concept to a multi patch setting simple and efficient numerical algorithms can be employed on relatively complex geometries the main drawback of such an approach is the inherent difficulty in dealing with singularities of the coordinate transformation this work suggests a comprehensive numerical strategy for the common situation of disk like domains with a singularity at a unique pole where one edge of the rectangular logical domain collapses to one point of the physical domain for example a circle we present robust numerical methods for the solution of vlasov like hyperbolic equations coupled to poisson like elliptic equations in such geometries we describe a semi lagrangian advection solver that employs a novel set of coordinates named pseudo cartesian coordinates to integrate the characteristic equations in the whole domain including the pole and a finite element elliptic solver based on globally c 1 smooth splines toshniwal et al 2017 27 the two solvers are tested both independently and on a coupled model namely the 2d guiding center model for magnetized plasmas equivalent to a vorticity model for incompressible inviscid euler fluids the numerical methods presented show high order convergence in the space discretization parameters uniformly across the computational domain without effects of order reduction due to the singularity dedicated tests show that the numerical techniques described can be applied straightforwardly also in the presence of point charges equivalently point like vortices within the context of particle in cell methods

flux corrected transport this paper describes a class of explicit eulerian finite difference algorithms for solving the continuity equation which are built around a technique called flux correction these flux corrected transport fct algorithms are of indeterminate order but yield realistic accurate results in addition to the mass conserving property of most conventional algorithms the fct algorithms strictly maintain the positivity of actual mass densities so steep gradients and inviscid shocks are handled particularly well this first paper concentrates on a simple one dimensional version of fct utilizing shasta a new transport algorithm for the continuity equation which is described in detail

high order fluid structure interaction in 2d and 3d application to blood flow in arteries this paper addresses the numerical approximation of fluid structure interaction fsi problems through the arbitrary lagrangian eulerian ale framework high order methods and a dirichlet newmann approach for the coupling the paper is divided into two main parts the first part concerns the discretization method for the fsi problem we introduce an improved ale map capable of handling curved geometries in 2d and 3d in a unified manner that is based on a local differential operator we also propose a minimal continuous interior penalty cip stabilization term for the fluid discretization that accounts for a smaller computational effort while stabilizing the flow regime the second part is dedicated to validating our numerical strategy through a benchmark and some applications to blood flow in arteries

a hybrid kinetic fluid model for solving the vlasov bgk equation our purpose is to derive a model for charged particles which combines a kinetic description of the fast particles with a fluid description of the slow ones in a previous paper a similar model was derived from a kinetic bgk equation that uses a constant relaxation time and does not include the effect of an electric field in this paper we consider a more general kinetic equation including an electric field and a varying relaxation time fast particles will be described through a collisional kinetic equation of vlasov bgk type while thermal particles will be modeled by a hydrodynamic model then we construct a numerical scheme for this model and validate the approach by presenting various numerical tests

combined hermite spectral finite difference method for the fokker planck equation the convergence of a class of combined spectral finite difference methods using hermite basis applied to the fokker planck equation is studied it is shown that the hermite based spectral methods are convergent with spectral accuracy in weighted sobolev space numerical results indicating the spectral convergence rate are presented a velocity scaling factor is used in the hermite basis and is shown to improve the accuracy and effectiveness of the hermite spectral approximation with no increase in workload some basic analysis for the selection of the scaling factors is also presented

convergence of a semi lagrangian scheme for the reduced vlasov maxwell system for laser plasma interaction the subject matter of this paper concerns the numerical approximation of reduced vlasov maxwell models by semi lagrangian schemes such reduced systems have been introduced recently in the literature for studying the laser plasma interaction we recall the main existence and uniqueness results on these topics we present the semi lagrangian scheme and finally we establish the convergence of this scheme

optimised prefactored compact schemes for linear wave propagation phenomena a family of space and time optimised prefactored compact schemes are developed that minimise the computational cost for given levels of numerical error in wave propagation phenomena with special reference to aerodynamic sound this work extends the approach of pirozzoli 1 to the maccormack type prefactored compact high order schemes developed by hixon 2 in which their shorter pade stencil from the prefactorisation leads to a simpler enforcement of numerical boundary conditions an explicit low storage multi step runge kutta integration advances the states in time theoretical predictions for spatial and temporal error bounds are derived for the cost optimised schemes and compared against benchmark schemes of current use in computational aeroacoustic applications in terms of computational cost for a given relative numerical error value one and two dimensional test cases are presented to examine the effectiveness of the cost optimised schemes for practical flow computations an effectiveness up to about 50 higher than the standard schemes is verified for the linear one dimensional advection solver which is a popular baseline solver kernel for computational physics problems a substantial error reduction for a given cost is also obtained in the more complex case of a two dimensional acoustic pulse propagation provided the optimised schemes are made to operate close to their nominal design points

electrohydrodynamics of three dimensional vesicles a numerical approach a three dimensional numerical model of vesicle electrohydrodynamics in the presence of dc electric fields is presented the vesicle membrane is modeled as a thin capacitive interface through the use of a semi implicit gradient augmented level set jet scheme the enclosed volume and surface area are conserved both locally and globally by a new navier stokes projection method the electric field calculations explicitly take into account the capacitive interface by an implicit immersed interface method formulation which calculates the electric potential field and the transmembrane potential simultaneously the results match well with previously published experimental analytic and two dimensional computational works

a level set projection model of lipid vesicles in general flows a new numerical method to model the dynamic behavior of lipid vesicles under general flows is presented a gradient augmented level set method is used to model the membrane motion to enforce the volume and surface incompressibility constraints a four step projection method is developed to integrate the full navier stokes equations this scheme is implemented on an adaptive non graded cartesian grid convergence results are presented along with sample two dimensional results of vesicles under various flow conditions

outflow boundary conditions for the fourier transformed three dimensional vlasov maxwell system a problem with the solution of the vlasov equation is its tendency to become filamented oscillatory in velocity space which in numerical simulations can give rise to unphysical oscillations and recurrence effects we present a three dimensional vlasov maxwell solver three spatial and velocity dimensions plus time in which the vlasov equation is fourier transformed in velocity space and the resulting equations solved numerically by designing absorbing outflow boundary conditions in the fourier transformed velocity space the highest fourier modes in velocity space are removed from the numerical solution this introduces a dissipative effect in velocity space and the numerical recurrence effect is strongly reduced the well posedness of the boundary conditions is proved analytically while the stability of the numerical implementation is assessed by long time numerical simulations well known wave modes in magnetized plasmas are shown to be reproduced by the numerical scheme

convergence of classes of high order semi lagrangian schemes for the vlasov poisson system abstract in this paper we present some classes of high order semi lagran gian schemes for solving the periodic one dimensional vlasov poisson system in phase space on uniform grids we prove that the distribution function f t x v and the electric field e t x converge in the l 2 norm with a rate of displaystyle mathcal o left delta t 2 h m 1 frac h m 1 delta t right where m is the degree of the polynomial reconstruction and delta t and h are respectively the time and the phase space discretization parameters

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

prefactored small stencil compact schemes abstract a new type of prefactored compact schemes is presented that obtains high order accuracy while using a very small stencil size these schemes require fewer boundary stencils and offer simpler boundary condition implementation than the existing compact schemes results are shown for linear and nonlinear 1 d benchmark problems and a 2 d linear benchmark problem boundary stencils for both exterior and interior multiblock boundaries are given and boundary condition specification is described and demonstrated

simulation of two fluid flows using a finite element level set method application to bubbles and vesicle dynamics a new framework for two fluid flows using a finite element level set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid this model is then enriched to deal with vesicles which mimic red blood cells mechanical behavior by introducing a lagrange multiplier to constrain the inextensibility of the membrane moreover high order polynomial approximation is used to increase the accuracy of the simulations a validation of this model is finally presented on known behaviors of vesicles under flow such as tank treading and tumbling motions