on a maximal lp lq approach to the compressible viscous fluid flow with slip boundary condition abstract in this paper we prove a local in time unique existence theorem for the compressible viscous fluids in the general domain with slip boundary condition for the purpose we use the contraction mapping principle based on the maximal l p l q regularity by means of the weis operator valued fourier multiplier theorem for the corresponding time dependent problem to obtain the maximal l p l q regularity we prove the sectorial r boundedness of the solution operator to the generalized stokes equations

a self contained automated methodology for optimal flow control this paper describes a self contained automated methodology for active flow control which couples the time dependent navier stokes system with an adjoint navier stokes system and optimality conditions from which optimal states i e unsteady flow fields and controls e g actuators may be determined the problem of boundary layer instability suppression through wave cancellation is used as the intital validation case to test the methodology here the objective of control is to match the stress vector along a portion of the boundary to a steady base flow control is effected through the injection or suction of fluid through a single orifice on the boundary the results demonstrate that instability suppression can be achieved without any a priori knowledge of the flow unsteadiness such as frequencies instability type etc the present methodology has been extended to three dimensions and may potentially be applied to separation control relaminarization and turbulence control applications using one to many sensors and actuators

a parallel two level domain decomposition based one shot method for shape optimization problems summary a two level domain decomposition method is introduced for general shape optimization problems constrained by the incompressible navier stokes equations the optimization problem is first discretized with a finite element method on an unstructured moving mesh that is implicitly defined without assuming that the computational domain is known and then solved by some one shot lagrange newton krylov schwarz algorithms in this approach the shape of the domain its corresponding finite element mesh the flow fields and their corresponding lagrange multipliers are all obtained computationally in a single solve of a nonlinear system of equations highly scalable parallel algorithms are absolutely necessary to solve such an expensive system the one level domain decomposition method works reasonably well when the number of processors is not large aiming for machines with a large number of processors and robust nonlinear convergence we introduce a two level inexact newton method with a hybrid two level overlapping schwarz preconditioner as applications we consider the shape optimization of a cannula problem and an artery bypass problem in 2d numerical experiments show that our algorithm performs well on a supercomputer with over 1000 processors for problems with millions of unknowns copyright 2014 john wiley sons ltd

computation of high order derivatives in optimal shape design in shape optimization problems each computation of the cost function by the finite element method leads to an expensive analysis the use of the second order derivative can help to reduce the number of analyses fujii 4 10 was the first to study this problem j simon 19 gave the second order derivative for the navier stokes problem and the authors describe in 8 11 a method which gives an intrinsic expression of the first and second order derivatives on the boundary of the involved domain in this paper we study higher order derivatives but one can ask the following questions are they expensive to calculate are they complicated to use are they imprecise are they useless medskip noindent at first sight the answer seems to be positive but classical results of v strassen 20 and j morgenstern 13 tell us that the higher order derivatives are not expensive to calculate and can be computed automatically the purpose of this paper is to give an answer to the third question by proving that the higher order derivatives of a function can be computed with the same precision as the function itself we prove also that the derivatives so computed are equal to the derivatives of the discrete problem see diagram 1 we call the discrete problem the finite dimensional problem processed by the computer this result allows the use of automatic differentiation 5 6 which works only on discrete problems furthermore the computations of taylor s expansions which are proposed at the end of this paper could be a partial answer to the last question

discontinuous galerkin multimodel methods for optimal control of aeroacoustics doi 10 2514 1 23798 a new multimodel computational framework for optimal control of aeroacoustic noise is presented using a nearfield compressible navier stokes solver coupled with a far field linearized euler solver both based on a discontinuous galerkin formulation in this approach the coupling of near and far field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources foroptimalcontrol gradientinformationisobtainedbythesolutionofanappropriateadjointproblemthat involves the propagationof adjoint information from the far fieldto the near field thiscomputational framework is applied to study optimal boundary control of blade vortex interaction which is a significant noise source for helicopters on approach to landing in the prototype problem presented here the noise propagated toward the ground is reduced by 12 db demonstrating the potential of an optimization based approach to blade vortexinteraction noise control

on some free boundary problem of the navier stokes equations in the maximal lp lq regularity class this paper concerns the free boundary problem for the navier stokes equations without surface tension in the lp in time and lq in space setting with 2 p and n q a local in time existence theorem is proved in a uniform wq2 1 q domain in the n dimensional euclidean space rn n 2 under the assumption that the weak dirichlet neumann problem is uniquely solvable moreover a global in time existence theorem is proved for small initial data under the additional assumption that is bounded this was already proved by solonnikov 25 by using the continuation argument of local in time solutions which are exponentially stable in the energy level under the assumption that the initial data is orthogonal to the rigid motion we also use the continuation argument and the same orthogonality condition for the initial data but our argument about the continuation of local in time solutions is based on some decay theorem for the linearized problem which is a different point than 25

an analytical comparison of the acoustic analogy and kirchhoff formulation for moving surfaces the lighthill acoustic analogy as embodied in the ffowcs williams hawkings fw h equation is compared with the kirchhoff formulation for moving surfaces a comparison of the two governing equations reveals that the main kirchhoff advantage namely nonlinear flow effects are included in the surface integration is also available to the fw h method if the integration surface used in the fw h equation is not assumed impenetrable the fw h equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation this means that the fw h equation is valid even if the integration surface is in the nonlinear region this is demonstrated numerically in the paper the kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region these errors may be hard to identify finally new metrics based on the sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and kirchhoff noise predictions

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

a reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks abstract in this paper we propose a reduced basis hybrid method rbhm for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent the rbhm is applied to stokes equations in domains which are decomposable into smaller similar blocks that are properly coupled the rbhm is built upon the reduced basis element method rbem and it takes advantage from both the reduced basis methods rb and the domain decomposition method we move from the consideration that the blocks composing the computational domain are topologically similar to a few reference shapes on the latter representative solutions corresponding to the same governing partial differential equations are computed for different values of some parameters of interest representing for example the deformation of the blocks a generalized transfinite mapping is used in order to produce a global map from the reference shapes of each block to any deformed configuration the desired solution on the given original computational domain is recovered as projection of the previously precomputed solutions and then glued across subdomain interfaces by suitable coupling conditions the geometrical parametrization of the domain by transfinite mapping induces non affine parameter dependence an empirical interpolation technique is used to recover an approximate affine parameter dependence and a subsequent offline online decomposition of the reduced basis procedure this computational decomposition yields a considerable reduction of the problem complexity results computed on some combinations of 2d and 3d geometries representing cardiovascular networks show the advantage of the method in terms of reduced computational costs and the quality of the coupling to guarantee continuity of both stresses pressure and velocity at subdomain interfaces

shape design in aorto coronaric bypass anastomoses using perturbation theory in this paper we present a new approach in the study of aorto coronaric bypass anastomoses configurations based on small perturbation theory the theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming branch of the bypass the toe into the coronary the aim is to provide design indications in the perspective of future development for prosthetic bypasses

shape topology optimization for navier stokes problem using variational level set method we consider the shape topology optimization of the navier stokes problem a new algorithm is proposed based on the variational level set method by this algorithm a relatively smooth evolution can be maintained without re initialization and drastic topology change can be handled easily finally the promising features of the proposed method are illustrated by two benchmark examples

shape reconstruction of an inverse stokes problem this paper deals with the shape reconstruction of a viscous incompressible fluid driven by the stokes flow for the approximate solution of the ill posed and nonlinear problem we propose a regularized newton method a theoretical foundation for the newton method is given by establishing the differentiability of the initial boundary value problem with respect to the interior boundary curve in the sense of a domain derivative the numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible

variational piecewise constant level set methods for shape optimization of a two density drum we apply the piecewise constant level set method to a class of eigenvalue related two phase shape optimization problems based on the augmented lagrangian method and the lagrange multiplier approach we propose three effective variational methods for the constrained optimization problem the corresponding gradient type algorithms are detailed the first uzawa type algorithm having applied to shape optimization in the literature is proven to be effective for our model but it lacks stability and accuracy in satisfying the geometry constraint during the iteration the two other novel algorithms we propose can overcome this limitation and satisfy the geometry constraint very accurately at each iteration moreover they are both highly initial independent and more robust than the first algorithm without penalty parameters the last projection lagrangian algorithm has less severe restriction on the time step than the first two algorithms numerical results for various instances are presented and compared with those obtained by level set methods the comparisons show effectiveness efficiency and robustness of our methods we expect our promising algorithms to be applied to other shape optimization and multiphase problems

on the free boundary problem for the oldroyd b model in the maximal lp lq regularity class abstract in the present work we prove the local well posedness of non newtonian compressible viscous barotropic fluid flow of oldroyd b type with free surface in a bounded domain of n dimensional euclidean space n 2 the key step is to prove the maximal l p l q regularity theorem for the linearized equation with the help of the r bounded solution operators for the corresponding resolvent problem and weis s operator valued fourier multiplier theorem

numerical solution of a flow control problem vorticity reduction by dynamic boundary action in order to laminarize an unsteady internal flow the vorticity field is minimized in a least squares sense using an optimal control approach the flow model is the navier stokes equation for a viscous incompressible fluid and the flow is controlled by suction and blowing on a part of the boundary a quasi newton method is used for the minimization of a quadratic objective function involving a measure of the vorticity and a regularization term the navier stokes equations are approximated using a finite difference scheme in time and finite element approximations in space accurate expressions for the gradient of the discrete objective function are needed to obtain a satisfactory convergence rate of the minimization algorithm therefore first order necessary conditions for a minimizer of the objective function are derived in the fully discrete case a memory saving device is discussed without which problems of any realistic size especially in three space dimensions would remain computationally intractable the feasibility of the optimal control approach for flow control problems is demonstrated by numerical experiments for a two dimensional flow in a rectangular cavity at a reynolds number high enough for nonlinear effects to be important

runge kutta methods in optimal control and the transformed adjoint system the convergence rate is determined for runge kutta discretizations of nonlinear control problems the analysis utilizes a connection between the kuhn tucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle this connection can also be exploited in numerical solution techniques that require the gradient of the discrete cost function

parametric free form shape design with pde models and reduced basis method we present a coupling of the reduced basis methods and free form deformations for shape optimization and design of systems modelled by elliptic pdes the free form deformations give a parameterization of the shape that is independent of the mesh the initial geometry and the underlying pde model the resulting parametric pdes are solved by reduced basis methods an important role in our implementation is played by the recently proposed empirical interpolation method which allows approximating the non affinely parameterized deformations with affinely parameterized ones these ingredients together give rise to an efficient online computational procedure for a repeated evaluation design environment like the one for shape optimization the proposed approach is demonstrated on an airfoil inverse design problem

convergence analysis of mixed finite element approximations to shape gradients in the stokes equation abstract eulerian derivatives of shape functionals in shape optimization can be written in two formulations of boundary and volume integrals the former is widely used in shape gradient descent algorithms the latter holds more generally although rarely being used numerically in literature for shape functionals governed by the stokes equation we consider the mixed finite element approximations to the two types of shape gradients from corresponding eulerian derivatives the standard mini and taylor hood elements are employed to discretize the state equation its adjoint and the resulting shape gradients we present thorough convergence analysis with a priori error estimates for the two approximate shape gradients the theoretical analysis shows that the volume integral formula has superconvergence property numerical results are presented to verify the theory and show that the volume formulation is more accurate