isogeometric variational multiscale modeling of wall bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes abstract in this work we combine i nurbs based isogeometric analysis ii residual driven turbulence modeling and iii weak imposition of no slip and no penetration dirichlet boundary conditions on unstretched meshes to compute wall bounded turbulent flows while the first two ingredients were shown to be successful for turbulence computations at medium to high reynolds number i akkerman y bazilevs v m calo t j r hughes s hulshoff the role of continuity in residual based variational multiscale modeling of turbulence comput mech 41 2008 371 378 y bazilevs v m calo j a cottrell t j r hughes a reali g scovazzi variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows comput methods appl mech engrg 197 2007 173 201 it is the weak imposition of no slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher reynolds number y bazilevs t j r hughes weak imposition of dirichlet boundary conditions in fluid mechanics comput fluids 36 2007 12 26 y bazilevs c michler v m calo t j r hughes weak dirichlet boundary conditions for wall bounded turbulent flows comput methods appl mech engrg 196 2007 4853 4862 these three ingredients form a basis of a possible practical strategy for computing engineering flows somewhere between rans and les in complexity we demonstrate this by solving two challenging incompressible turbulent benchmark problems channel flow at friction velocity reynolds number 2003 and flow in a planar asymmetric diffuser we observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data this lends some credence to the proposed approach which we believe may become a viable engineering tool

a critical evaluation of the resolution properties of b spline and compact finite difference methods resolution properties of b spline and compact finite difference schemes are compared using fourier analysis in periodic domains and tests based on solution of the wave and heat equations in finite domains with uniform and nonuniform grids results show that compact finite difference schemes have a higher convergence rate and in some cases better resolution however b spline schemes have a more straightforward and robust formulation particularly near boundaries on nonuniform meshes

orthogonalized generalized iso geometric analysis ogiga and its applications to problems of fracture mechanics abstract ill conditioning of system matrices is one of the drawbacks of generalized extended isogeometric analysis giga xiga which results in increase in computational cost in the case of iterative solvers or erroneous results in the case of direct solvers linear dependency between the basis functions which can be measured in terms of smallest angle among all the bases is one of the attributes of ill conditioning in xiga in the present study a simplified method to find the smallest angle among all the bases is introduced also to reduce the problem of ill conditioning orthogonalized generalized isogeometric analysis ogiga is proposed in which the standard and the corresponding enriched basis functions are orthogonalized in order to study the performance of present method various fracture mechanics problems like 2 d homogenous cracks bi material interface cracks inclined cracks and 3 d crack problems are chosen the effect of crack position and the radius of enrichment zone on accuracy scaled condition number and smallest angle among all the bases is studied the results obtained from the proposed ogiga method are compared with results obtained from standard xiga and xiga with enrichment function orthogonalization oe xiga agathos et al 2019 in all the cases considered the conditioning of system matrices is significantly improved by employing present methodology and it can be easily extended to wide variety of problems

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

local refinement of analysis suitable t splines we develop a local refinement algorithm for analysis suitable t splines which does not produce excessive propagation of control points we then demonstrate its use as an adaptive framework for isogeometric analysis analysis suitable t splines are a class of t splines which are linearly independent and form a partition of unity these properties coupled with local refinement make this class of t splines appealing as a basis for isogeometric analysis

isogeometric divergence conforming variational multiscale formulation of incompressible turbulent flows a new residual based variational multiscale rbvms formulation for incompressible turbulent flows is proposed that is suitable for discretization using divergence conforming b splines the proposed methodology results in a pointwise satisfaction of the zero divergence constraint on the discrete velocity field the velocity fine scales are residual driven and constructed in a manner that is consistent with the divergence free constraint on the discrete velocity solution the resulting formulation is tested on laminar and turbulent flow benchmark problems showing excellent stability and accuracy characteristics in both regimes

discretizations in isogeometric analysis of navier stokes flow this paper deals with isogeometric analysis of 2 dimensional steady state incompressible navier stokes flow subjected to dirichlet boundary conditions we present a detailed description of the numerical method used to solve the boundary value problem numerical inf sup stability tests for the simplified stokes problem confirm the existence of many stable discretizations of the velocity and pressure spaces and in particular show that stability may be achieved by means of knot refinement of the velocity space error convergence studies for the full navier stokes problem show optimal convergence rates for this type of discretizations finally a comparison of the results of the method to data from the literature for the lid driven square cavity for reynolds numbers up to 10 000 serves as benchmarking of the discretizations and confirms the robustness of the method

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

hierarchically refined and coarsened splines for moving interface problems with particular application to phase field models of prostate tumor growth abstract moving interface problems are ubiquitous in science and engineering to develop an accurate and efficient methodology for this class of problems we present algorithms for local h adaptivity of hierarchical b splines to be utilized in isogeometric analysis we extend bezier projection an efficient quadrature free local projection technique to the hierarchical setting in this case extraction operators may not be invertible to address this issue we develop a multi level reconstruction operator which maintains the locality properties of the projection we also introduce a balance parameter to control the overlap of hierarchical functions leading to improved numerical conditioning we apply our algorithms to the simulation of localized prostate cancer growth we model this disease using the phase field method and a set of diffusion reaction equations to account for the dynamics of nutrients and a key biomarker termed prostate specific antigen our results include examples on simple 2d and 3d domains and a more compelling tissue scale patient specific simulation which is run over a prostate anatomy extracted from medical images our methods for local h adaptivity efficiently capture the evolving interface between the tumor and the neighboring healthy tissue with remarkable accuracy in all cases

an isogeometric design through analysis methodology based on adaptive hierarchical refinement of nurbs immersed boundary methods and t spline cad surfaces we explore hierarchical refinement of nurbs as a basis for adaptive isogeometric and immersed boundary analysis we use the principle of b spline subdivision to derive a local refinement procedure which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions we test hierarchical refinement of nurbs for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases using the b spline version of the finite cell method we illustrate the potential of immersed boundary methods as a seamless isogeometric design through analysis procedure for complex engineering parts defined by t spline cad surfaces specifically a ship propeller and an automobile wheel we show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features

isogeometric analysis of free surface flow abstract this paper presents the first application of isogeometric analysis a new computational technology built on higher order and higher continuity basis functions employed in computer aided design and computer graphics to the computation of free surface phenomena described using the level set approach the method is based on the variational framework that is suitable for discretization by standard finite elements as well as the basis functions employed in isogeometric analysis the underlying numerical formulation globally conserves mass and preserves a sharp air water interface for the entire length of the simulation the numerical tests indicate that the proposed methodology gives an accurate description of the free surface behavior in both quasi steady and dynamic regimes furthermore very good per degree of freedom accuracy is obtained when higher order and higher continuity isogeometric discretizations are employed in free surface computations

correct energy evolution of stabilized formulations the relation between vms supg and gls via dynamic orthogonal small scales and isogeometric analysis i the convective diffusive context this paper presents the construction of novel stabilized finite element methods in the convective diffusive context that exhibit correct energy behavior classical stabilized formulations can create unwanted artificial energy our contribution corrects this undesired property by employing the concepts of dynamic as well as orthogonal small scales within the variational multiscale framework vms the desire for correct energy indicates that the large and small scales should be h 0 1 orthogonal using this orthogonality the vms method can be converted into the streamline upwind petrov galerkin supg or the galerkin least squares gls method incorporating both large and small scales in the energy definition asks for dynamic behavior of the small scales therefore the large and small scales are treated as separate equations two consistent variational formulations which depict correct energy behavior are proposed i the galerkin least squares method with dynamic small scales glsd and ii the dynamic orthogonal formulation do the methods are presented in combination with an energy decaying generalized time integrator numerical verification shows that dissipation due to the small scales in classical stabilized methods can become negative on both a local and a global scale the results show that without loss of accuracy the correct energy behavior can be recovered by the proposed methods the computations employ nurbs based isogeometric analysis for the spatial discretization

isogeometric spline forests in this paper we present isogeometric spline forests an isogeometric spline forest is a hierarchical spline representation capable of representing surfaces or volumes of arbitrarily complex geometry and topological genus spline forests can accomodate arbitrary degree and smoothness in the underlying hierarchical basis as well as non uniform knot interval configurations we describe adaptive h refinement and coarsening algorithms for isogeometric spline forests and develop a bezier extraction framework which provides a simple and efficient single level finite element description of the complex multi level unstructured hierarchical spline basis we then demonstrate the potential of spline forests as a basis for analysis in the context of transient advection diffusion problems where fully integrated adaptivity is demonstrated for the first time in an isogeometric simulation in all cases the adaptive process remains local even in the case of moving fronts and preserves exact geometry at the coarsest level of the discretization the accuracy and robustness of the approach is demonstrated in all cases

goal adaptive isogeometric analysis with hierarchical splines abstract in this work a method of goal adaptive isogeometric analysis is proposed we combine goal oriented error estimation and adaptivity with hierarchical b splines for local h refinement the goal oriented error estimator is computed with a p refined discrete dual space which is adaptively refined alongside the primal space this discrete dual space is proven to be a strict superset of the primal space hierarchical refinements are introduced in marked regions that are formed as the union of chosen coarse level spline supports from the primal basis we present two ways of extracting localized refinement indicators suitable for the hierarchical refinement procedure one based on a partitioning of the dual weighted residual into contributions of basis function supports and one based on the combination of element indicators within a basis function support the proposed goal oriented adaptive strategy is exemplified for the poisson problem and a free surface flow problem numerical experiments on these problems show convergence of the adaptive method with optimal rates furthermore the corresponding goal oriented error estimators are shown to be accurate with effectivity indices in the range of 0 7 1 1

statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows abstract numerical simulations have proved that variational multiscale methods vmm perform well as pure numerical large eddy simulation les models in this paper we focus on the orthogonal subgrid scale oss finite element method and make an analysis of the statistical behavior of its stabilization terms in the quasi static approximation this is done by resorting to results from classical statistical fluid mechanics concerning two point velocity pressure and combined correlation functions of various orders given a fine enough mesh with characteristic element size h in the inertial subrange of a turbulent flow it is shown that the rate of transfer of subgrid kinetic energy provided by the oss stabilization terms does not depend on h and that it equals the molecular physical dissipation rate up to a dimensionless constant that only depends on the finite element shapes for a proper redesign of the standard parameters of the formulation this is a noteworthy fact taking into account that the subgrid stabilization terms do not arise from physical considerations but from the mathematical necessity to allow equal interpolation for the pressure and velocity fields as well as to control convection therefore the obtained results contribute somehow to the line of reasoning supporting that pure numerical approaches i e without introducing additional physical models could probably suffice in the les simulation of turbulent flows

velocity structure functions scaling and transitions in high reynolds number couette taylor flow flow between concentric cylinders with a rotating inner cylinder is studied for reynolds numbers in the range 2 ifmmode times else texttimes fi 10 3 lrl 10 6 taylor reynolds numbers 10l r ensuremath lambda l290 for a system with radius ratio ensuremath eta 0 724 even at the highest reynolds number studied the energy spectra do not show power law scaling i e there is no inertial range and the dissipation length scale is surprisingly large nevertheless the velocity structure functions calculated using extended self similarity exhibit clear power law scaling the structure function exponents ensuremath zeta p fit kolmogorov s log normal model within the experimental uncertainty ensuremath zeta p p 3 1 ensuremath mu 6 3 ensuremath p for pl 10 with ensuremath mu 0 27 these ensuremath zeta p values are close to those found in other flows measurements of torque scaling are presented that are an order of magnitude more accurate than those previously reported lathrop et al phys rev a 46 6390 1992 measurements of velocity in the fluid core reveal the presence of azimuthal traveling waves up to the highest reynolds numbers examined these waves show evidence of a transition at r t 1 3 ifmmode times else texttimes fi 10 4 this transition was observed previously in measurements of torque but our wave velocity and wall shear stress measurements provide the first evidence from local quantities of the transition at r t velocity measurements indicate that at r t there is a change in the coherent structures of the core flow this is consistent with our analyses of the scaling of the torque our measurements were made at two aspect ratios and no significant dependence on aspect ratio was observable for rg r t

variational multiscale analysis the fine scale green s function projection optimization localization and stabilized methods we derive an explicit formula for the fine scale green s function arising in variational multiscale analysis the formula is expressed in terms of the classical green s function and a projector which defines the decomposition of the solution into coarse and fine scales the theory is presented in an abstract operator format and subsequently specialized for the advection diffusion equation it is shown that different projectors lead to fine scale green s functions with very different properties for example in the advection dominated case the projector induced by the h 1 0 seminorm produces a fine scale green s function which is highly attenuated and localized these are very desirable properties in a multiscale method and ones that are not shared by the l 2 projector by design the coarse scale solution attains optimality in the norm associated with the projector this property combined with a localized fine scale green s function indicates the possibility of effective methods with local character for dominantly hyperbolic problems the constructs lead to a new class of stabilized methods and the relationship between h 1 0 optimality and the streamline upwind petrov galerkin supg method is described

an isogeometric variational multiscale method for large eddy simulation of coupled multi ion transport in turbulent flow electrochemical processes such as electroplating of large items in galvanic baths are often coupled to turbulent flow in this study we propose an isogeometric residual based variational multiscale finite element method for multi ion transport in dilute electrolyte solutions under turbulent flow conditions in other words this means that the concepts of isogeometric discretization and variational multiscale methods are successfully combined for developing a method capable of simulating the challenging problem of coupled multi ion transport in turbulent flow we present a comprehensive three dimensional computational method taking into account among others coupled convection diffusion migration equations subject to an electroneutrality constraint in combination with phenomenological electrode kinetics modeling the electrochemical subproblem is one way coupled to turbulent incompressible flow via convection ionic mass transfer in turbulent taylor couette flow is investigated representing an important model problem for rotating cylinder electrode configurations multi ion transport as considered here is an example for mass transport at high schmidt number sc 1389 an isogeometric discretization is especially advantageous for the present problem since i curved boundaries can be represented exactly and ii it has been proven to provide very accurate solutions for flow quantities when being applied in combination with residual based variational multiscale modeling we demonstrate that the method is robust and provides results which are in good agreement with direct numerical simulation results as well as empirical mass transfer correlations reported in literature

an improved nurbs based isogeometric analysis with enhanced treatment of essential boundary conditions the nurbs based isogeometric analysis offers a seamless integration between the cad and subsequent finite element analysis and has been shown to be very effective for wide classes of problems due to its accurate geometric description however similar to the moving least square or reproducing kernel meshfree shape functions the nurbs basis functions generally are not interpolatory functions in this work it is shown that the direct imposition of the inhomogeneous essential boundary conditions to the nurbs control points may lead to significant errors with deteriorated rates of convergence consequently an improved formulation for nurbs based isogeometric analysis is proposed this is fulfilled by employing a transformation method that relates the control variables to the collocated nodal values at the essential boundary by using open knot vectors the resulting nurbs basis functions associated with the interior control points vanish at the boundary thus unlike the meshfree approximation the nurbs control points can be clearly partitioned into boundary and interior groups therefore the transformation method can be only applied to the boundary control points via invoking collocation of physical values at a set of boundary points the nurbs approximation enhanced with transformed physical boundary variables is kinematically admissible and the essential boundary conditions can be enforced straightforwardly like the finite element method several potential and elasticity problems evince that much higher solution accuracy with optimal convergence rates can be achieved by the present improved formulation compared with the method with direct imposition of essential boundary conditions to control variables

isogeometric analysis of lagrangian hydrodynamics axisymmetric formulation in the rz cylindrical coordinates a recent isogeometric analysis iga formulation of lagrangian shock hydrodynamics 4 is extended to the 3d axisymmetric case the euler equations of compressible hydrodynamics are formulated using the rz cylindrical coordinates and are discretized in the weak form using nurbs based iga artificial shock viscosity and internal energy projection are added to stabilize the formulation the resulting discretization exhibits good accuracy and robustness properties it also gives exact symmetry preservation on the appropriately constructed meshes several benchmark examples are computed to examine the performance of the proposed formulation

existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis abstract isogeometric analysis is a numerical simulation method which uses the nurbs based representation of cad models nurbs stands for non uniform rational b splines and is a generalization of the concept of b splines the isogeometric method uses the tensor product structure of 2 or 3 dimensional nurbs functions to parameterize domains which are structurally equivalent to a rectangle or a hexahedron the special case of singularly parameterized nurbs surfaces and nurbs volumes is used to represent non quadrangular or non hexahedral domains without splitting which leads to a very compact and convenient representation if the parameterization of the physical domain is available the test functions for the isogeometric analysis are obtained by composing the inverse of the domain parameterization with the nurbs basis functions in the case of singular parameterizations however some of the resulting test functions are not well defined at the singular points and they do not necessarily satisfy the required integrability assumptions consequently the stiffness matrix integrals which occur in the numerical discretizations may not exist after summarizing the basics of the isogeometric method we discuss the existence of the stiffness matrix integrals for 1 2 and 3 dimensional second order elliptic partial differential equations we consider several types of singularities of nurbs parameterizations and derive conditions which guarantee the existence of the required integrals in addition we present cases with diverging integrals and show how to modify the test functions in these situations

isogeometric finite element data structures based on bezier extraction of t splines we develop finite element data structures for t splines based on bezier extraction generalizing our previous work for nurbs as in traditional finite element analysis the extracted bezier elements are defined in terms of a fixed set of polynomial basis functions the so called bernstein basis the bezier elements may be processed in the same way as in a standard finite element computer program utilizing exactly the same data processing arrays in fact only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same a byproduct of the extraction process is the element extraction operator this operator localizes the topological and global smoothness information to the element level and represents a canonical treatment of t junctions referred to as hanging nodes in finite element analysis and a fundamental feature of t splines a detailed example is presented to illustrate the ideas copyright 2011 john wiley sons ltd

isogeometric analysis of the cahn hilliard phase field model abstract the cahn hilliard equation involves fourth order spatial derivatives finite element solutions are not common because primal variational formulations of fourth order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally c 1 continuous there are a very limited number of two dimensional finite elements possessing c 1 continuity applicable to complex geometries but none in three dimensions we propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher order differential operators namely higher order accuracy robustness two and three dimensional geometric flexibility compact support and most importantly the possibility of c 1 and higher order continuity a nurbs based variational formulation for the cahn hilliard equation was tested on two and three dimensional problems we present steady state solutions in two dimensions and for the first time in three dimensions to achieve these results an adaptive time stepping method is introduced we also present a technique for desensitizing calculations to dependence on mesh refinement this enables the calculation of topologically correct solutions on coarse meshes opening the way to practical engineering applications of phase field methodology

two dimensional mesh embedding for b spline methods many factors motivate consideration of b splines as basis functions for solving partial differential equations these are arbitrary orders of accuracy and high resolving powers similar to those of compact schemes furthermore if one uses a galerkin scheme one gets in addition to conservation of the discretized quantities conservation of quadratic invariants such as energy this work develops another property namely the ability to treat semi structured embedded or zonal meshes for two dimensional geometries this can drastically reduce the number of grid points in many applications an algorithm is presented for constructing a global spline basis that automatically hasd 1 continuous derivatives at mesh block boundaries as everywhere else heredis the polynomial degree the basis functions are simply suitable products of one dimensional b splines both integer and noninteger refinement ratios are allowed across mesh blocks finally test cases for linear scalar equations such as the poisson and advection equation are presented

weak dirichlet boundary conditions for wall bounded turbulent flows abstract in turbulence applications strongly imposed no slip conditions often lead to inaccurate mean flow quantities for coarse boundary layer meshes to circumvent this shortcoming weakly imposed dirichlet boundary conditions for fluid dynamics were recently introduced in y bazilevs t j r hughes weak imposition of dirichlet boundary conditions in fluid mechanics comput fluids 36 2007 12 26 in the present work we propose a modification of the original weak boundary condition formulation that consistently incorporates the well known law of the wall to compare the different methods we conduct numerical experiments for turbulent channel flow at reynolds number 395 and 950 in the limit of vanishing mesh size in the wall normal direction the weak boundary condition acts like a strong boundary condition accordingly strong and weak boundary conditions give essentially identical results on meshes that are stretched to better capture boundary layers however on uniform meshes that are incapable of resolving boundary layers weakly imposed boundary conditions deliver significantly more accurate mean flow quantities than their strong counterparts hence weakly imposed boundary conditions present a robust technique for flows of industrial interest where optimal mesh design is usually not feasible and resolving boundary layers is prohibitively expensive our numerical results show that the formulation that incorporates the law of the wall yields an improvement over the original method

a generalized α method for integrating the filtered navier stokes equations with a stabilized finite element method abstract a generalized method is developed and analyzed for linear first order systems the method is then extended to the filtered navier stokes equations within the context of a stabilized finite element method the formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long transverse groove the method is formulated to obtain a second order accurate family of time integrators whose high frequency amplification factor is the sole free parameter such an approach allows the replication of midpoint rule zero damping gear s method maximal damping or anything in between

an interactive geometry modeling and parametric design platform for isogeometric analysis in this paper an interactive parametric design through analysis platform is proposed to help design engineers and analysts make more effective use of isogeometric analysis iga to improve their product design and performance we develop several rhinoceros rhino plug ins to take input design parameters through a user friendly interface generate appropriate surface and or volumetric models perform mechanical analysis and visualize the solution fields all within the same computer aided design cad program as part of this effort we propose and implement graphical generative algorithms for iga model creation and visualization based on grasshopper a visual programming interface to rhino the developed platform is demonstrated on two structural mechanics examples an actual wind turbine blade and a model of an integrally bladed rotor ibr in the latter example we demonstrate how the rhino functionality may be utilized to create conforming volumetric models for iga

novel higher order mass matrices for isogeometric structural vibration analysis abstract a set of novel higher order mass matrices are presented for isogeometric analysis of structural vibrations using nurbs the proposed method for the construction of higher order mass matrices contains two essential steps firstly based upon the standard consistent mass matrix a special reduced bandwidth mass matrix is designed this reduced bandwidth mass matrix meets the requirement of mass conservation while simultaneously preserves the same order of frequency accuracy as the corresponding consistent mass matrix subsequently a mixed mass matrix is formulated through a linear combination of the reduced bandwidth mass matrix and the consistent mass matrix the desired higher order mass matrix is then deduced from the mixed mass matrix by optimizing the linear combination parameter to achieve the most favorable order of accuracy both quadratic and cubic formulations are discussed in detail and it is shown that with regard to the vibration frequency the proposed higher order mass matrices have 6th and 8th orders of accuracy in contrast to the 4th and 6th orders of accuracy associated with the quadratic and cubic consistent mass matrices a generalization to two dimensional higher order mass matrix is further realized by the tensor product operation on the one dimensional reduced bandwidth and consistent mass matrices a series of benchmark examples congruously demonstrate that the proposed higher order mass matrices are capable of achieving the theoretically derived optimal accuracy orders for structural vibration analysis

three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs a three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs is presented in the finite deformation regime within a setting where the nurbs discretization of the contact surface is inherited directly from the nurbs discretization of the volume the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities the formulation delivers a non negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative lagrange discretizations independent of the discretization order these enable the achievement of improved smoothness in global contact forces and moments through higher order geometrical descriptions it is concluded that the presented mortar based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume

b spline method and zonal grids for simulations of complex turbulent flows a numerical technique for computations of turbulent flows is described the technique is based on b splines and allows grid embedding in physically significant flow regions numerical tests which include solutions of nonlinear advection diffusion equations and computations of flow over a circular cylinder at reynolds numbers up to 300 indicate that the method is accurate and efficient in computations of flow over a cylinder the lift drag and base suction coefficients agree well with existing experimental data and previous numerical simulations

a spectral numerical method for the navier stokes equations with applications to taylor couette flow a new spectral method for solving the incompressible navier stokes equations in a plane channel and between concentric cylinders is presented the method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step in addition the number of dependent variables is reduced resulting in a reduction in computer memory requirements several test problems have been computed for the channel flow and for flow between concentric cylinders including taylor couette flow with axisymmetric taylor vortices and wavy vortices in all cases agreement with available experimental and theoretical results is very good

variational multiscale modeling with discretely divergence free subscales abstract we introduce a residual based stabilized formulation for incompressible navier stokes flow that maintains discrete and for divergence conforming methods strong mass conservation for inf sup stable spaces with h 1 conforming pressure approximation while providing optimal convergence in the diffusive regime robustness in the advective regime and energetic stability the method is formally derived using the variational multiscale vms concept but with a discrete fine scale pressure field which is solved for alongside the coarse scale unknowns such that the coarse and fine scale velocities separately satisfy discrete mass conservation we show energetic stability for the full navier stokes problem and we prove convergence and robustness for a linearized model oseen flow under the assumption of a divergence conforming discretization numerical results indicate that all properties extend to the fully nonlinear case and that the proposed formulation can serve to model unresolved turbulence

the value of continuity refined isogeometric analysis and fast direct solvers abstract we propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers starting from a highly continuous isogeometric analysis iga discretization we introduce c 0 separators to reduce the interconnection between degrees of freedom in the mesh by doing so both the solution time and best approximation errors are simultaneously improved we call the resulting method refined isogeometric analysis riga to illustrate the impact of the continuity reduction we analyze the number of floating point operations flops computational times and memory required to solve the linear system obtained by discretizing the laplace problem with structured meshes and uniform polynomial orders theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between p 2 and p 3 with p being the polynomial order of the discretization numerical results indicate that our proposed refined isogeometric analysis delivers a speed up factor proportional to p 2 in a 2 d mesh with four million elements and p 5 the linear system resulting from riga is solved 22 times faster than the one from highly continuous iga in a 3 d mesh with one million elements and p 3 the linear system is solved 15 times faster for the refined than the maximum continuity isogeometric analysis

large eddy simulation of turbulent taylor couette flow using isogeometric analysis and the residual based variational multiscale method we present an application of the residual based variational multiscale turbulence modeling rbvms methodology to the computation of turbulent taylor couette flow at high reynolds number we show that the rbvms formulation globally conserves angular momentum a feature that is felt to be important for flows dominated by rotation and that is not shared by standard stabilized formulations of fluid flow weak imposition of dirichlet boundary conditions is employed to enhance the accuracy of the rbvms framework in the presence of thin turbulent boundary layers near solid walls calculation of conservative boundary forces and torques is also presented for the case of weakly enforced boundary conditions nurbs based isogeometric analysis is employed for the spatial discretization and mesh refinement is performed to assess the convergence characteristics of the proposed methodology numerical tests show that very accurate results are obtained on relatively coarse grids to the best of the authors knowledge this paper is the first to report large eddy simulation computations of this challenging test case

exact theory for the quantum eigenstates of a strongly chaotic system we present an exact theory for the quantum eigenstates of a strongly chaotic system which consists of a point particle sliding freely on a two dimensional compact surface of constant negative curvature the main result is a general sum rule which relates an almost arbitrarily smoothed sum over the quantum wavefunctions to a sum over the lengths of the classical orbits as an example we apply this formula to the gaussian smoothed sum over wavefunctions the question of scars as imprints of individual closed orbits is discussed and the connection with bogomolny s semiclassical theory is explicitly worked out the investigation of the amplitude distribution p reveals that the higher excited wavefunctions behave as gaussian random waves

isogeometric fluid structure interaction analysis with emphasis on non matching discretizations and with application to wind turbines abstract in this paper we develop a framework for fluid structure interaction fsi modeling and simulation with emphasis on isogeometric analysis iga and non matching fluid structure interface discretizations we take the augmented lagrangian approach to fsi as a point of departure here the lagrange multiplier field is defined on the fluid structure interface and is responsible for coupling of the two subsystems thus the fsi formulation does not rely on the continuity of the underlying function spaces across the fluid structure interface in order to produce the correct coupling conditions between the fluid and structural subdomains however in deriving the final fsi formulation the interface lagrange multiplier is formally eliminated and the formulation is written purely in terms of primal variables avoiding the use of lagrange multipliers adds efficiency to the proposed formulation as an added benefit the ability to employ non matching grids for multi physics simulations leads to significantly relaxed requirements that are placed on the geometry modeling and meshing tools for iga we show an application of the proposed fsi formulation to the simulation of the nrel 5 mw offshore wind turbine rotor where the aerodynamics domain is modeled using volumetric quadratic nurbs while the rotor structure is modeled using a cubic t spline based discretization of a rotation free kirchhoff love shell we conclude the article by showing fsi coupling of a t spline shell with a low order finite element method fem discretization of the aerodynamics equations this combined use of iga and fem is felt to be a good balance between speed robustness and accuracy of fsi simulations for this class of problems

geometric modeling isogeometric analysis and the finite cell method the advent of isogeometric analysis iga using the same basis functions for design and analysis constitutes a milestone in the unification of geometric modeling and numerical simulation however an important class of geometric models based on the csg constructive solid geometry concept such as trimmed nurbs surfaces do not fully support the isogeometric paradigm since basis functions do not explicitly represent the boundary the finite cell method fcm is a high order fictitious domain method which offers simple meshing of potentially complex domains into a structured grid of cuboid cells while still achieving exponential rates of convergence for smooth problems in the present paper we first discuss the possibility to directly couple the finite cell method to csg without any necessity for meshing the three dimensional domain and then explore a combination of the best of the two approaches iga and fcm closely following ideas of the recently introduced shell fcm the resulting finite cell extension to isogeometric analysis achieves a truly straightforward transfer of a trimmed nurbs surface into an analysis suitable nurbs basis while benefiting from the favorable properties of the high order and high continuity basis functions accuracy and efficiency of the new approach are demonstrated by a numerical benchmark and its versatility is outlined by the analysis of different trimmed design variants of a brake disk

modular generalized springer correspondence iii exceptional groups we complete the construction of the modular generalized springer correspondence for an arbitrary connected reductive group with a uniform proof of the disjointness of induction series that avoids the case by case arguments for classical groups used in previous papers in the series we show that the induction series containing the trivial local system on the regular nilpotent orbit is determined by the sylow subgroups of the weyl group under some assumptions we give an algorithm for determining the induction series associated to the minimal cuspidal datum with a given central character we also provide tables and other information on the modular generalized springer correspondence for quasi simple groups of exceptional type including a complete classification of cuspidal pairs in the case of good characteristic and a full determination of the correspondence in type g 2

finite element methods for first order hyperbolic systems with particular emphasis on the compressible euler equations a petrov galerkin finite element formulation is presented for first order hyperbolic systems of conservation laws with particular emphasis on the compressible euler equations applications of the methodology are made to one and two dimensional steady and unsteady flows with shocks results obtained suggest the potential of the type of methods developed

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

contact treatment in isogeometric analysis with nurbs abstract we study nurbs based isogeometric analysis of contact problems and compare with standard c 0 continuous lagrange finite elements a knot to surface kts algorithm is developed to treat the contact constraints with nurbs contact surface discretizations qualitative studies deliver satisfactory results for various finite deformation frictionless thermoelastic contact problems quantitative studies based on the hertz problem suggest the need for a relaxation of the mechanical contact constraints that appear in the standard kts approach the improved mortar based kts algorithm delivers robust and accurate results for nurbs discretizations based on numerical examples we conclude that nurbs based isogeometric analysis is a viable technology for contact problems and offers potential accuracy as well as convergence improvements over c 0 continuous finite elements

isogeometric collocation cost comparison with galerkin methods and extension to adaptive hierarchical nurbs discretizations abstract we compare isogeometric collocation with isogeometric galerkin and standard c 0 finite element methods with respect to the cost of forming the matrix and residual vector the cost of direct and iterative solvers the accuracy versus degrees of freedom and the accuracy versus computing time on this basis we show that isogeometric collocation has the potential to increase the computational efficiency of isogeometric analysis and to outperform both isogeometric galerkin and standard c 0 finite element methods when a specified level of accuracy is to be achieved with minimum computational cost we then explore an adaptive isogeometric collocation method that is based on local hierarchical refinement of nurbs basis functions and collocation points derived from the corresponding multi level greville abscissae we introduce the concept of weighted collocation that can be consistently developed from the weighted residual form and the two scale relation of b splines using weighted collocation in the transition regions between hierarchical levels we are able to reliably handle coincident collocation points that naturally occur for multi level greville abscissae the resulting method combines the favorable properties of isogeometric collocation and hierarchical refinement in terms of computational efficiency local adaptivity robustness and straightforward implementation which we illustrate by numerical examples in one two and three dimensions

continuity and convergence in rational triangular bezier spline based isogeometric analysis abstract this paper presents a method for isogeometric analysis using rational triangular bezier splines rtbs where optimal convergence rates are achieved in this method both the geometry and the physical field are represented by bivariate splines in bernstein bezier form over the triangulation of a domain from a given physical domain bounded by nurbs curves a parametric domain and its triangulation are constructed by imposing continuity constraints on bezier ordinates we obtain a set of global c r smooth basis functions convergence analysis shows that isogeometric analysis with such c r rtbs basis can deliver the optimal rate of convergence provided that the c r geometric map remains unchanged during the refinement process this condition can be satisfied by constructing a pre refinement geometric map that is sufficiently smooth numerical experiments verify that optimal rates of convergence are achieved for poisson and linear elasticity problems

isogeometric divergence conforming b splines for the unsteady navier stokes equations divergence conforming b splines are developed for application to the incompressible navier stokes equations on geometrically mapped domains these enable smooth pointwise divergence free solutions and thus satisfy mass conservation in the strongest possible sense semi discrete methods based on divergence conforming b splines are shown to conserve linear and angular momentum and satisfy balance laws for energy vorticity enstrophy and helicity these are geometric structure preserving quantities and numerical simulations that are sensitive to them are shown to be qualitatively correct and quantitatively accurate the methods developed are anticipated to open new doors to the practical calculation of complex flows and to studies of their physical behavior

refined isogeometric analysis for a preconditioned conjugate gradient solver david pardo has received funding from the project of the spanish ministry of economy and competitiveness with reference mtm2016 76329 r aei feder eu and mtm2016 81697 erc aei the bcam severo ocho accreditation of excellencesev 2013 0323 and the basque government through the berc 2014 2017 program and the consolidated research group grant it649 13 on mathematical modeling simulation and industrial applications m2si this publication was also made possible in part by the european union s horizon 2020 research and innovation programme under the marie sklodowska curie grant agreement no 644602 the csiro professorial chair in computational geoscience at curtin university the deep earth imaging enterprise future science platforms of the commonwealth scientific industrial research organisation csiro of australia the mega grant of the russian federation government n14 y26 31 0013 and the curtin institute for computation the j tinsley oden faculty fellowship research program at the institute for computational engineering and sciences ices of the university of texas at austin has partially supported the visits of vmc to ices the authors acknowledge the texas advanced computing center tacc at the university of texas at austin for providing hpc resources that have contributed to the research results reported within this paper

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100