robust and efficient discontinuous galerkin methods for under resolved turbulent incompressible flows abstract we present a robust and accurate discretization approach for incompressible turbulent flows based on high order discontinuous galerkin methods the dg discretization of the incompressible navier stokes equations uses the local lax friedrichs flux for the convective term the symmetric interior penalty method for the viscous term and central fluxes for the velocity pressure coupling terms stability of the discretization approach for under resolved turbulent flow problems is realized by a purely numerical stabilization approach consistent penalty terms that enforce the incompressibility constraint as well as inter element continuity of the velocity field in a weak sense render the numerical method a robust discretization scheme in the under resolved regime the penalty parameters are derived by means of dimensional analysis using penalty factors of order 1 applying these penalty terms in a postprocessing step leads to an efficient solution algorithm for turbulent flows the proposed approach is applicable independently of the solution strategy used to solve the incompressible navier stokes equations i e it can be used for both projection type solution methods as well as monolithic solution approaches since our approach is based on consistent penalty terms it is by definition generic and provides optimal rates of convergence when applied to laminar flow problems robustness and accuracy are verified for the orr sommerfeld stability problem the taylor green vortex problem and turbulent channel flow moreover the accuracy of high order discretizations as compared to low order discretizations is investigated for these flow problems a comparison to state of the art computational approaches for large eddy simulation indicates that the proposed methods are highly attractive components for turbulent flow solvers

flows in a tube structure equation on the graph the steady state navier stokes equations in thin structures lead to some elliptic second order equation for the macroscopic pressure on a graph at the nodes of the graph the pressure satisfies kirchoff type junction conditions in the non steady case the problem for the macroscopic pressure on the graph becomes nonlocal in time in the paper we study the existence and uniqueness of a solution to such one dimensional model on the graph for a pipe wise network we also prove the exponential decay of the solution with respect to the time variable in the case when the data decay exponentially with respect to time

lbb stability of a mixed galerkin finite element pair for fluid flow simulations we introduce a new mixed finite element for solving the 2 and 3 dimensional wave equations and equations of incompressible flow the element which we refer to as p1 d p2 uses discontinuous piecewise linear functions for velocity and continuous piecewise quadratic functions for pressure the aim of introducing the mixed formulation is to produce a new flexible element choice for triangular and tetrahedral meshes which satisfies the lbb stability condition and hence has no spurious zero energy modes the advantage of this particular element choice is that the mass matrix for velocity is block diagonal so it can be trivially inverted it also allows the order of the pressure to be increased to quadratic whilst maintaining lbb stability which has benefits in geophysical applications with coriolis forces we give a normal mode analysis of the semi discrete wave equation in one dimension which shows that the element pair is stable and demonstrate that the element is stable with numerical integrations of the wave equation in two dimensions an analysis of the resultant discrete laplace operator in two and three dimensions on various meshes which shows that the element pair does not have any spurious modes we provide convergence tests for the element pair which confirm that the element is stable since the convergence rate of the numerical solution is quadratic

approximate projection methods part i inviscid analysis the use of approximate projection methods for modeling low mach number flows avoids many of the numerical complications associated with exact projection methods but introduces additional design choices in developing a robust algorithm in this paper we first explore these design choices in the setting of inviscid incompressible flow using several computational examples we then develop a framework for analyzing the behavior of the different design variations and use that analysis to explain the features observed in the computations as part of this work we introduce a new variation of the approximate projection algorithm that combines the advantages of several of the previous versions

the use of explicit filters in large eddy simulation abstract explicit filtering is considered as a means of controlling the numerical errors that result when finite difference methods are used in large eddy simulation les the notion that the finite difference expressions themselves act as an effective filter is shown to be false for three dimensional simulations performed on nonuniform meshes for consistency the nonlinear terms in the navier stokes equations should be filtered explicitly at each time step in order to insure that the spectral content of the solution remains fixed at the desired filter level the explicit filtering operation allows a separation between the filter size and the mesh spacing and can be used to control the impact of the numerical errors numerical tests of the explicit filtering approach in turbulent channel flow are used to investigate the effectiveness of the explicit filtering approach and to assess its associated cost explicit filtering is shown to improve the computed results but this improvement comes at a rather high computational cost the explicitly filtered approach is also compared with straightforward mesh refinement as an alternative means of improving the computed results mesh refinement is also seen to increase the accuracy of the simulation but some traces of numerical error appear to persist in the solution

generalized minimum shift keying modulation techniques the simultaneous data demodulation and phase tracking of an msk signal using the viterbi algorithm is described and two variations of msk modulation are studied the msk with overlay is a dual rate modulation techniques in which low rate and high rate data are superimposed on an msk signal here the demodulator uses the viterbi algorithm to estimate both the low rate and high rate data simultaneously the msk with pseudorandom sequence spreading combats intentional or unintentional jamming a simplified receiver for these spread spectrum msk signals is found that takes into consideration the effect of random phase perturbations the performance of these demodulators is evaluated using transfer function bounds for the bit error probability for demodulation of the spread spectrum msk signal a simplified receiver is derived and its performance in the presence of continuous jamming is evaluated

dual phase continuous phase modulation for spread spectrum multiple access communication a new class of direct sequence spread spectrum multiple access ds ssma systems with continuous phase modulation cpm is defined the signals are unique in that the spreading is done by adding an extra phase term to the information phase while maintaining phase continuity constant envelope and efficient bandwidth usage the spreading phase is formed from the spreading code and is independent of the information phase which allows despreading to be done separately before data detection which in turn allows a simple cpm detector to be employed for data detection the information phase is considered in the minimum shift keying msk format and a serial msk type spread spectrum receiver is considered for performance analysis expressions for the signal to noise ratio the power spectral density and the probability of bit error are developed along with methods for computing their values to an arbitrarily close approximation numerical results show that the proposed system is an attractive alternative to the conventional ds ssma systems

a high order discontinuous galerkin method for 2d incompressible flows in this paper we introduce a high order discontinuous galerkin method for two dimensional incompressible flow in the vorticity stream function formulation the momentum equation is treated explicitly utilizing the efficiency of the discontinuous galerkin method the stream function is obtained by a standard poisson solver using continuous finite elements there is a natural matching between these two finite element spaces since the normal component of the velocity field is continuous across element boundaries this allows for a correct upwinding gluing in the discontinuous galerkin framework while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability the method is efficient for inviscid or high reynolds number flows optimal error estimates are proved and verified by numerical experiments

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

a spectral vanishing viscosity method for large eddy simulations a new simulation approach for high reynolds number turbulent flows is developed combining concepts of monotonicity in nonlinear conservation laws with concepts of large eddy simulation the spectral vanishing viscosity svv first introduced by e tadmor siam j numer anal 26 30 1989 is incorporated into the navier stokes equations for controlling high wavenumber oscillations unlike hyperviscosity kernels the svv approach involves a second order operator which can be readily implemented in standard finite element codes in the work presented here discretization is performed using hierarchical spectral hp methods accommodating effectively an ab initio intrinsic scale separation the key result is that monotonicity is enforced via svv leading to stable discretizations without sacrificing the formal accuracy i e exponential convergence in the proposed discretization several examples are presented to demonstrate the effectiveness of the new approach including a comparison with eddy viscosity spectral les of turbulent channel flow in its current implementation the svv approach for controlling the small scales is decoupled from the large scales but a procedure is proposed that will provide coupling similar to the classical les formulation

periodic in time flow in thin structure equation on the graph abstract the dimension reduction for the non stationary time periodic navier stokes equations in thin structures leads to a non local in time reynolds type equation on the graph with kirchhoff type junction conditions in the vertices the existence and uniqueness of a solution to this problem is proved

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

a model for the simulation of turbulent boundary layers in an incompressible stratified flow a model with several original physical and numerical features has been developed for direct numerical and large eddy simulations of a turbulent boundary layer in a stratified fluid the large scale flow for which the model was developed involves internal waves reflecting from a sloping boundary in the model the internal waves are generated by a new technique that forces monochromatic waves at specified wavelengths and frequencies a new analytic solution has been obtained representative of the forcing conditions in the model time discretization is based upon the projection method incorporating a third order adams bashforth scheme with variable time steps and spatial discretization employs fourth order compact differencing techniques on a variable grid that increases resolution close to the boundary the model is periodic in two dimensions and in the third dimension employs an open boundary and a solid sloping surface the pressure field is determined using a fast direct solution method of fourth order accuracy the model includes flow analysis aids such as tracking lagrangian particles and advected scalar quantities flow measurements are made of the integrated kinetic and potential energy balances local dissipation rates and the energy spectra the utility of the model is examined in a number of test problems it appears that the model is well suited for simulations of transitioning and turbulent boundary layers

a spectral multidomain penalty method model for the simulation of high reynolds number localized incompressible stratified turbulence a spectral multidomain penalty method model has been developed for the simulation of high reynolds number localized stratified turbulence this is the first time that a penalty method with a particular focus on subdomain interface treatment has been used with a multidomain scheme to simulate incompressible flows the temporal discretization ensures maximum temporal accuracy by combining third order stiffly stable and backward differentiation schemes with a high order boundary condition for the pressure in the non periodic vertical direction a spectral multidomain discretization is used and its stability for under resolved simulations at high reynolds numbers is ensured through use of penalty techniques spectral filtering and strong adaptive interfacial averaging the penalty method is implemented in different formulations for both the explicit non linear term advancement and the implicit treatment of the viscous terms the multidomain model is validated by comparing results of simulations of the mid to late time stratified turbulent wake with non zero net momentum to the corresponding laboratory data for a towed sphere the model replicates correctly the characteristic vorticity and internal wave structure of the stratified wake and exhibits robust agreement with experiments in terms of the temporal power laws in the evolution of mean profile characteristic velocity and lengthscales

on the stability of projection methods for the incompressible navier stokes equations based on high order discontinuous galerkin discretizations abstract the present paper deals with the numerical solution of the incompressible navier stokes equations using high order discontinuous galerkin dg methods for discretization in space for dg methods applied to the dual splitting projection method instabilities have recently been reported that occur for small time step sizes since the critical time step size depends on the viscosity and the spatial resolution these instabilities limit the robustness of the navier stokes solver in case of complex engineering applications characterized by coarse spatial resolutions and small viscosities by means of numerical investigation we give evidence that these instabilities are related to the discontinuous galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure integration by parts of these terms with a suitable definition of boundary conditions is required in order to obtain a stable and robust method since the intermediate velocity field does not fulfill the boundary conditions prescribed for the velocity a consistent boundary condition is derived from the convective step of the dual splitting scheme to ensure high order accuracy with respect to the temporal discretization this new formulation is stable in the limit of small time steps for both equal order and mixed order polynomial approximations although the dual splitting scheme itself includes inf sup stabilizing contributions we demonstrate that spurious pressure oscillations appear for equal order polynomials and small time steps highlighting the necessity to consider inf sup stability explicitly

a space time hybridizable discontinuous galerkin method for incompressible flows on deforming domains we present the first space time hybridizable discontinuous galerkin hdg finite element method for the incompressible navier stokes and oseen equations major advantages of a space time formulation are its excellent capabilities of dealing with moving and deforming domains and grids and its ability to achieve higher order accurate approximations in both time and space by simply increasing the order of polynomial approximation in the space time elements our formulation is related to the hdg formulation for incompressible flows introduced recently in e g n c nguyen j peraire b cockburn a hybridizable discontinuous galerkin method for stokes flow comput methods appl mech eng 199 2010 582 597 however ours is inspired in typical dg formulations for compressible flows which allow for a more straightforward implementation another difference is the use of polynomials of fixed total degree with space time hexahedral and quadrilateral elements instead of simplicial elements we present numerical experiments in order to assess the quality of the performance of the methods on deforming domains and to experimentally investigate the behavior of the convergence rates of each component of the solution with respect to the polynomial degree of the approximations in both space and time

an artificial compressibility flux for the discontinuous galerkin solution of the incompressible navier stokes equations discontinuous galerkin dg methods have proved to be well suited for the construction of robust high order numerical schemes on unstructured and possibly nonconforming grids for a variety of problems their application to the incompressible navier stokes ins equations has also been recently considered although the subject is far from being fully explored in this work we propose a new approach for the dg numerical solution of the ins equations written in conservation form the inviscid numerical fluxes both in the continuity and in the momentum equation are computed using the values of velocity and pressure provided by the exact solution of the riemann problem associated with a local artificial compressibility perturbation of the equations unlike in most of the existing methods artificial compressibility is here introduced only at the interface flux level therefore resulting in a consistent discretization of the ins equations irrespectively of the amount of artificial compressibility introduced the discretization of the viscous term follows the well established dg scheme named br2 the performance and the accuracy of the method are demonstrated by computing the kovasznay flow and the two dimensional lid driven cavity flow for a wide range of reynolds numbers and for various degrees of polynomial approximation

accuracy and speed in computing the chebyshev collocation derivative we study several algorithms for computing the chebyshev spectral derivative and compare their roundoff error for a large number of collocation points the elements of the chebyshev differentiation matrix if constructed in the usual way are not computed accurately a subtle cause is found to account for the poor accuracy when computing the derivative by the matrix vector multiplication method methods for accurately computing the elements of the matrix are presented and we find that if the entries of the matrix are computed accurately the roundoff error of the matrix vector multiplication is as small as that of the transform recursion algorithm furthermore results of the cpu time usage are shown for several different algorithms for computing the derivative by the chebyshev collocation method for a wide variety of two dimensional grid sizes on both an ibm mainframe and a cray 2 computer we find that which algorithm is fastest on a particular machine depends not only on the grid size but also on small

asymptotic analysis of the non steady navier stokes equations in a tube structure ii general case abstract the non steady navier stokes equations with dirichlet boundary conditions are considered in thin tube structures these domains are connected finite unions of thin finite cylinders in the 2 d case respectively thin rectangles the complete asymptotic expansion of the solution is constructed it contains a regular part and three types of the boundary layer correctors in space in time and in space and in time the estimates for the difference of the exact solution and its j th asymptotic approximation are proved

efficient estimation of continuous phase modulation with unknown carrier phase an efficient algorithm is presented for the estimation of continuous phase modulation cpm sequences over the gaussian channel with unknown carrier phase it operates on the excess phase trellis like the viterbi algorithm except that it is not a maximum likelihood ml estimator its decision metric for survivor selection at each node is chosen so that it achieves the node error event probability of coherent ml estimation in the limit as the carrier phase remains constant over a long interval so that the observation interval for forming the metric can be made large it is shown for the case of minimum shift keying msk that the bit error probability bep of perfectly coherent ml estimation is attained

a stable and high order accurate discontinuous galerkin based splitting method for the incompressible navier stokes equations abstract in this paper we consider discontinuous galerkin dg methods for the incompressible navier stokes equations in the framework of projection methods in particular we employ symmetric interior penalty dg methods within the second order rotational incremental pressure correction scheme the major focus of the paper is threefold i we propose a modified upwind scheme based on the vijayasundaram numerical flux that has favourable properties in the context of dg ii we present a novel postprocessing technique in the helmholtz projection step based on h div reconstruction of the pressure correction that is computed locally is a projection in the discrete setting and ensures that the projected velocity satisfies the discrete continuity equation exactly as a consequence it also provides local mass conservation of the projected velocity iii numerical results demonstrate the properties of the scheme for different polynomial degrees applied to two dimensional problems with known solution as well as large scale three dimensional problems in particular we address second order convergence in time of the splitting scheme as well as its long time stability

asymptotic analysis of the non steady navier stokes equations in a tube structure i the case without boundary layer in time abstract the non steady navier stokes equations with dirichlet boundary conditions are considered in thin tube structures these domains are connected finite unions of thin finite cylinders in the 2 d case respectively thin rectangles the complete asymptotic expansion of the solution is constructed in the case without boundary layer in time the estimates for the difference of the exact solution and its j th asymptotic approximation is proved the method of asymptotic partial domain decomposition is formulated and justified for the non steady navier stokes equations in a tube structure it gives the asymptotically exact interface conditions of coupling of the 1d and 3d models of the flow note that the obtained results hold true for the important in applications case of time periodic flows

short note a short note on the discontinuous galerkin discretization of the pressure projection operator in incompressible flow this note reports on the issue of spurious compressibility artifacts that can arise when the popular pressure projection pp method is used for unsteady simulations of incompressible flow using the symmetric interior penalty discontinuous galerkin sip dg method through a spectral analysis of the projection operator s sip dg discretization we demonstrate that the eigenfunctions of the operator do not form a basis that allows for the correct enforcement of the incompressibility constraint this short coming can cause numerical instabilities for inviscid advection dominated and density stratified flow simulations especially for long time integrations and or under resolved situations to remedy this problem we propose a local post processing projection that enforces incompressibility exactly to allow for stable and robust long time integrations

a high order discontinuous galerkin method for the unsteady incompressible navier stokes equations we present a high order discontinuous galerkin discretization of the unsteady incompressible navier stokes equations in convection dominated flows using triangular and tetrahedral meshes the scheme is based on a semi explicit temporal discretization with explicit treatment of the nonlinear term and implicit treatment of the stokes operator the nonlinear term is discretized in divergence form by using the local lax friedrichs fluxes thus local conservativity is inherent spatial discretization of the stokes operator has employed both equal order p k p k and mixed order p k p k 1 velocity and pressure approximations a second order approximate algebraic splitting is used to decouple the velocity and pressure calculations leading to an algebraic helmholtz equation for each component of the velocity and a consistent poisson equation for the pressure the consistent poisson operator is replaced by an equivalent in stability and convergence operator namely that arising from the interior penalty discretization of the standard poisson operator with appropriate boundary conditions this yields a simpler and more efficient method characterized by a compact stencil size we show the temporal and spatial behavior of the method by solving some popular benchmarking tests for an unsteady stokes problem second order temporal convergence is obtained while for the taylor vortex test problem on both semi structured and fully unstructured triangular meshes spectral convergence with respect to the polynomial degree k is obtained by studying the orr sommerfeld stability problem we demonstrate that the p k p k method yields a stable solution while the p k p k 1 formulation leads to unphysical instability the good performance of the method is further shown by simulating vortex shedding in flow past a square cylinder we conclude that the proposed discontinuous galerkin method with the p k p k formulation is an efficient scheme for accurate and stable solution of the unsteady navier stokes equations in convection dominated flows

a high order semi explicit discontinuous galerkin solver for 3d incompressible flow with application to dns and les of turbulent channel flow abstract we present an efficient discontinuous galerkin scheme for simulation of the incompressible navier stokes equations including laminar and turbulent flow we consider a semi explicit high order velocity correction method for time integration as well as nodal equal order discretizations for velocity and pressure the non linear convective term is treated explicitly while a linear system is solved for the pressure poisson equation and the viscous term the key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under resolved high reynolds number flows as well as small time steps this penalty method is similar to the grad div stabilization widely used in continuous finite elements we further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations the solver is specifically designed for large scale computations through matrix free linear solvers including efficient preconditioning strategies and tensor product elements which have allowed us to scale this code up to 34 4 billion degrees of freedom and 147 456 cpu cores we validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large eddy simulation of turbulent channel flow at r e 180 as well as 590

a dynamic programming algorithm for simultaneous phase estimation and data decoding on random phase channels the problem of simultaneously estimating phase and decoding data symbols from baseband data is posed the phase sequence is assumed to be a random sequence on the circle and the symbols are assumed to be equally likely symbols transmitted over a perfectly equalized channel a dynamic programming algorithm viterbi algorithm is derived for decoding a maximum em a posteriori map phase symbol sequence on a finite dimensional phase symbol trellis a new and interesting principle of optimality for simultaneously estimating phase and decoding phase amplitude coded symbols leads to an efficient two step decoding procedure for decoding phase symbol sequences simulation results for binary 8 ary phase shift keyed psk and 16 quadrature amplitude shift keyed qask symbol sets transmitted over random walk and sinusoidal jitter channels are presented and compared with results one may obtain with a decision directed algorithm or with the binary viterbi algorithm introduced by ungerboeck when phase fluctuations are severe and when occasional large phase fluctuations exist map phase symbol sequence decoding on circles is superior to ungerboeck s technique which in turn is superior to decision directed techniques