a new mixed basis navier stokes formulation for incompressible flows over complex geometries numerical modeling of complex geometries necessitates the use of curvilinear body fitted coordinates this article proposes a novel mixed basis formulation of the governing conservation equations for general curvilinear non orthogonal grids with the physical covariant velocity as the primary solution variable this results in an algorithm which has many advantages of orthogonal equations the conservation equations written in this form retains the diagonal dominance of the pressure equation the newly formed conservation equations are solved on a structured grid using the simpler algorithm and are shown to converge well for non orthogonal grids standard k model is used for the turbulence closure

active control and drag optimization for flow past a circular cylinder the main objective of this article is to investigate computational methods for the active control and drag optimization of incompressible viscous flow past cylinders using the two dimensional navier stokes equations as the flow model the computational methodology relies on the following ingredients space discretization of the navier stokes equations by finite element approximations time discretization by a second order accurate two step implicit explicit finite difference scheme calculation of the cost function gradient by the adjoint equation approach and minimization of the cost function by a quasi newton method a la bfgs the above methods have been applied to boundary control by rotation of the flow around a circular cylinder and show 30 to 60 drag reduction compared to the fixed cylinder configuration for reynolds numbers in the range from 200 to 1000

on the meaning of randomness in stochastic environmental models this paper describes and explains the differences between two different approaches toward stochastic water quality modeling two groups of models namely models based on differential equations with coefficients being either random variables random variable models or stochastic processes stochastic process models are analyzed the reasoning behind these two approaches is discussed and a numerical example illustrating the possible consequences in estimating stochastic characteristics of the solution process using either of these two approaches is presented and discussed

artificial boundary conditions for incompressible navier stokes equations a well posed result abstract numerical simulation of two dimensional incompressible viscous flows around an obstacle is considered two horizontal straight line artificial boundaries are introduced and the original flow is approximated by a flow in an infinite channel with slip boundary condition on the wall then two vertical segment artificial boundaries are introduced and a series of approximate artificial boundary conditions on them are derived by imposing the continuity of velocity and the normal stress thus the original problem is reduced to a problem defined in a bounded computational domain the well posedness of the reduced problem is proved the finite element approximation of this problem is given and error estimates are obtained furthermore numerical examples show the accuracy and efficiency of our artificial boundary conditions

optimization of the crystal surface temperature distribution in the single crystal growth process by the czochralski method the optimization of the crystal surface temperature distribution is performed for single crystal growth in the czochralski process in the optimization problem we seek an optimal solution in the sense that the index of crystalline defects is minimized while the single crystal growth rate is maximized in the objective function the von mises stress is considered a driving force that induces crystalline defects in order to solve the optimization problem with the equality constraints given by the governing partial differential equations the variational method is used based on the calculus of variations and the method of lagrange multiplier the euler lagrange equations are derived in the form of coupled partial differential equations they are solved by using the finite difference method and the iterative numerical scheme proposed in this work in order to handle inequality constraints the penalty function method is applied the optimal distributions of the crystal surface temperature obtained in this work may provide an insight into the optimal design of thermal surroundings such as thermal shield configurations and heater cooler positions

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

a numerical investigation into the steady flow past a rotating circular cylinder at low and intermediate reynolds numbers abstract numerical solutions have been obtained for steady uniform flow past a rotating circular cylinder results are presented for reynolds numbers based on the diameter of the cylinder 5 and 20 and the rotational parameters in the range of 0 3 to avoid the difficulties in satisfying the boundary conditions at large distances from the cylinder a new numerical technique is introduced further series expansion solutions are obtained which are valid at small values of but the results are found to be applicable over a wide range of values of the calculated values of the drag and lift coefficients and the general nature of the streamline patterns are in good agreement with the most recent time dependent calculations performed by badr and dennis

comparison of first order error analysis and monte carlo simulation in time dependent lake eutrophication models estimates of variance for a nonlinear seasonal food chain nutrient cycle eutrophication model of saginaw bay lake huron calculated by first order variance propagation and monte carlo analyses do not always agree a comparison of estimates of state variables indicates that monte carlo means are most like the measurements whereas monte carlo medians are most like the deterministic model output best agreement between monte carlo and first order estimates of both state variable values and their variances occurs when monte carlo output distributions are symmetric under these conditions both estimates are measures of variance associated with total populations i e all algae those distributions however change dramatically in time for most state variables for asymmetric distributions first order variance estimates measure variability about the typical component of the total population i e the typical algal species and monte carlo variance estimates measure variability of the mean component which is more reflective of the total one must be cognizant of these differences when estimating variance associated with model projections

solution of the div curl problem in generalized curvilinear coordinates we propose a method for solving the div curl problem on a structured nonorthogonal curvilinear grid the differential operators are discretized using a mac scheme for the unknowns in such a way that the discrete counterparts of the usual vector analysis relations are satisfied the derived discrete problem is then solved by performing a helmholtz type decomposition of the unknown vector field this allows us to obtain a vector field for which both divergence and curl are satisfied to within machine accuracy the method is validated for several configurations in two and three dimensions and its accuracy is numerically checked

numerical methods for the einstein equations in null quasi spherical coordinates we describe algorithms used in our construction of a fourth order in time evolution for the full einstein equations and assess the accuracy of some representative solutions the scheme employs several novel geometric and numerical techniques including a geometrically invariant coordinate gauge which leads to a characteristic transport formulation of the underlying hyperbolic system combined with a method of lines evolution convolution splines for radial interpolation regridding differentiation and noise suppression representations using spin weighted spherical harmonics and a spectral preconditioner for solving a class of first order elliptic systems on s2 initial data for the evolution is unconstrained subject only to a mild size condition for sample initial data of intermediate strength 19 of the total mass in gravitational energy the code is accurate to 1 part in 105 until null time z 55m when the coordinate condition breaks down

modeling of uncertainty for flood wave propagation induced by variations in initial and boundary conditions using expectation operator on explicit numerical solutions this study proposes a framework for uncertainty analysis by incorporating explicit numerical solutions of governing equations for flood wave propagation with the expectation operator it aims at effectively evaluating the effect of variations in initial and boundary conditions on the estimation of flood waves spatiotemporal semi variogram models are employed to quantify the correlation of the variables in time and space the 1 d nonlinear kinematic wave equation for the overland flow named evo ns kwe is applied in the model development model validation is made by comparison with the monte carlo simulation mcs model in the calculation of statistical properties of model outputs i e flow depths that is the mean standard deviation and coefficient of variation cv the results from the model validation show that the evo ns kwe model can produce excellent approximations of the mean and less satisfactory approximations of the standard deviation and cv compared with those obtained using the mcs model it concludes that the uncertainties of flow depths in the domain are significantly affected by variations in the boundary condition future application of the evo ns kwe model enable the evaluation of uncertainty in model outputs induced by the initial and boundary condition subject to uncertainty and will also provide corresponding probabilistic information for risk quantification method

a study of a numerical solution of the steady two dimensions navier stokes equations in a constricted channel problem by a compact fourth order method we present a numerical solution for the steady 2d navier stokes equations using a fourth order compact type method the geometry of the problem is a constricted symmetric channel where the boundary can be varied via a parameter from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular the set of non linear equations is solved by the newton method results have been obtained for reynolds number up to 500 estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method

pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations a calculation procedure for viscous flows at all mach numbers has been described the scheme has been developed for a nonorthogonal coordinate system in order to handle both incompressible and compressible flows pressure has been selected as a primary dependent variable in preference to density the pressure field is evaluated using the compressible form of the simpler algorithm the accuracy of the proposed scheme has been assessed by comparing the results with experimental data or other numerical results available in the literature

a cell boundary element method for viscous laminar flow solutions a cell boundary element method is developed to solve viscous fluid structure interaction problems modelled by navier stokes equations this is achieved through a hybrid approach incorporating boundary element and finite element methods in the proposed scheme cell equations are generated using the principles of the boundary element method with global equations derived following the procedures of the finite element method a primitive variable formulation with an unstructured mesh requirement forms the basis of the hybrid approach which can be applied to both two and three dimensional problems the validation of this numerical scheme of study involving analytical and numerical mathematical procedures is carried out using a number of well documented flow solutions and the accuracy and robustness of the method are demonstrated in these examples

numerical treatment of stochastic river quality models driven by colored noise 1 monte carlo simulation is a popular method of risk and uncertainty analysis in oceanographic atmospheric and environmental applications it is common practice to introduce a stochastic part to an already existing deterministic model and after many simulations to provide the user with statistics of the model outcome the underlying deterministic model is often a discretization of a set of partial differential equations describing physical processes such as transport turbulence buoyancy effects and continuity much effort is also put into deriving numerically efficient schemes for the time integration the resulting model is often quite large and complex in sharp contrast the stochastic extension used for monte carlo experiments is usually achieved by adding white noise unfortunately the order of time integration in the stochastic model is reduced compared to the deterministic model because white noise is not a smooth process instead of completely replacing the old numerical scheme and implementing a higher order scheme for stochastic differential equations we suggest a different approach that is able to use existing numerical schemes the method uses a smooth colored noise process as the driving force resulting in a higher order of convergence we show promising results from numerical experiments including parametric uncertainty

calculation of laminar separation bubbles in the wake inflation deflation regime a new interacting boundary layer method is developed for calculating two dimensional incompressible laminar separation bubbles the method relies on a completely consistent mixed boundary value treatment of the outer inviscid flow for attached flows the new method is found to converge as fast as the classical cauchy hilbert method and to yield the same solutions for separated flows the new method is found to converge two to three times faster than a comparable cauchy hilbert method the physical asymptotic theories that underlie this new numerical method will be discussed in so far as they motivate the method

optimal control of the cylinder wake in the laminar regime by trust region methods and pod reduced order models in this paper optimal control theory is used to minimize the total mean drag for a circular cylinder wake flow in the laminar regime re 200 the control parameters are the amplitude and the frequency of the time harmonic cylinder rotation in order to reduce the size of the discretized optimality system a proper orthogonal decomposition pod reduced order model rom is derived to be used as state equation we then propose to employ the trust region proper orthogonal decomposition trpod approach originally introduced by fahl m fahl trust region methods for flow control based on reduced order modeling ph d thesis trier university 2000 to update the reduced order models during the optimization process a lot of computational work is saved because the optimization process is now based only on low fidelity models a particular care was taken to derive a pod rom for the pressure and velocity fields with an appropriate balance between model accuracy and robustness the key enablers are the extension of the pod basis functions to the pressure data the use of calibration methods for the pod rom and the addition in the pod expansion of several non equilibrium modes to describe various operating conditions when the trpod algorithm is applied to the wake flow configuration this approach converges to the minimum predicted by an open loop control approach and leads to a relative mean drag reduction of 30 at reduced cost

direct solution of two dimensional navier stokes equations for static aeroelasticity problems a new method has been developed to calculate the steady flow and structural deformations for fluid structure interaction problems the discretized fluid dynamic and structural equations are regarded as a single set of coupled nonlinear algebraic equations the equilibrium solution is directly obtained using newton s method the governing equations used for the fluid flow are the two dimensional navier stokes equations and a finite element model is used to represent the structure this paper describes the analytical method and presents sample calculations demonstrating the technique the results show rapid convergence and good agreement with experimental data nomenclature bw half bandwidth of tangent matrix d set of structural displacement variables e set of governing equations for the aeroelastic system f flux vector in x direction g flux vector in y direction h distance from nozzle throat to centerline number of fluid dynamic control volumes in streamwise direction j number of fluid dynamic control volumes in cross stream direction l reference length total length of nozzle n total number of variables in system p pressure pe exit static pressure pt total pressure r system residual r magnitude of residual r radius at nozzle throat t tangent matrix system jacobian t wall thickness u set of fluid dynamic variables x set of variables for the aeroelastic system ax change in system variables during a newton iteration x streamwise coordinate y cross stream coordinate

the ls stag method a new immersed boundary level set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties this paper concerns the development of a new cartesian grid immersed boundary ib method for the computation of incompressible viscous flows in two dimensional irregular geometries in ib methods the computational grid is not aligned with the irregular boundary and of upmost importance for accuracy and stability is the discretization in cells which are cut by the boundary the so called cut cells in this paper we present a new ib method called the ls stag method which is based on the mac method for staggered cartesian grids and where the irregular boundary is sharply represented by its level set function this implicit representation of the immersed boundary enables us to calculate efficiently the geometry parameters of the cut cells we have achieved a novel discretization of the fluxes in the cut cells by enforcing the strict conservation of total mass momentum and kinetic energy at the discrete level our discretization in the cut cells is consistent with the mac discretization used in cartesian fluid cells and has the ability to preserve the five point cartesian structure of the stencil resulting in a highly computationally efficient method the accuracy and robustness of our method is assessed on canonical flows at low to moderate reynolds number taylor couette flow flows past a circular cylinder including the case where the cylinder has forced oscillatory rotations finally we will extend the ls stag method to the handling of moving immersed boundaries and present some results for the transversely oscillating cylinder flow in a free stream

water quality modeling a review of the analysis of uncertainty this paper reviews the role of uncertainty in the identification of mathematical models of water quality and in the application of these models to problems of prediction more specifically four problem areas are examined in detail uncertainty about model structure uncertainty in the estimated model parameter values the propagation of prediction errors and the design of experiments in order to reduce the critical uncertainties associated with a model the review is rather lengthy and it has therefore been prepared in effect as two papers there is a shorter largely nontechnical version which gives a quick impression of the current and future issues in the analysis of uncertainty in water quality modeling enclosed by this shorter discussion is the main body of the review dealing in turn with 1 identifiability and experimental design 2 the generation of preliminary model hypotheses under conditions of sparse grossly uncertain field data 3 the selection and evaluation of model structure 4 parameter estimation model calibration 5 checks and balances on the identified model i e model verification and model discrimination and 6 prediction error propagation much time is spent in discussing the algorithms of system identification in particular the methods of recursive estimation and in relating these algorithms and the subject of identification to the problems of prediction uncertainty and first order error analysis there are two obvious omissions from the review it is not concerned primarily with either the development and solution of stochastic differential equations or the issue of decision making under uncertainty although clearly some reference must be made to these topics in brief the review concludes not surprisingly that much work has been done on the analysis of uncertainty in the development of mathematical models of water quality and much remains to be done a lack of model identifiability has been an outstanding difficulty in the interpretation and explanation of past observed system behavior and there is ample evidence to show that the larger more comprehensive models are easily capable of generating highly uncertain predictions of future behavior for the future of the subject it is speculated that there is the possibility of progress in the development of novel algorithms for model structure identification a need for new questions to be posed in the problem of prediction and a distinct challenge to the conventional views of this review in the new forms of knowledge representation and manipulation now emerging from the field of artificial intelligence

modeling water table fluctuations by means of a stochastic differential equation the combined system of soil water and shallow groundwater is modeled with simple mass balance equations assuming equilibrium soil moisture conditions this results in an ordinary but nonlinear differential equation of water table depth at a single location if errors in model inputs errors due to model assumptions and parameter uncertainty are lumped and modeled as a wide band noise process a stochastic differential equation sde results a solution for the stationary probability density function is given through use of the fokker planck equation for the nonstationary case where the model inputs are given as daily time series sample functions of water table depth soil saturation and drainage discharge can be simulated by numerically solving the sde these sample functions can be used for designing drainage systems and to perform risk analyses the parameters and noise statistics of the sde are calibrated on time series of water table depths by embedding the sde in a kaiman filter algorithm and using the filter innovations in a filter type maximum likelihood criterion the stochastic model is calibrated and validated at two locations a peat soil with a very shallow water table and a loamy sand soil with a moderately shallow water table it is shown in both cases that sample functions simulated with the sde are able to reproduce a wide range of statistics of water table depth despite its unrealistic assumption of constant inputs the stationary solution derived from the fokker planck equation gives good results for the peat soil most likely because the characteristic response time of the water table is very small

newton s method applied to finite difference approximations for the steady state compressible navier stokes equations abstract newton s method is applied to finite difference approximations for the steady state compressible navier stokes equations in two spatial dimensions the finite difference equations are written in generalized curvilinear coordinates and strong conservation law form and a turbulence model is included we compute the flow field about a lifting airfoil for subsonic and transonic conditions we investigate both the requirements for an initial guess to insure convergence and the computational efficiency of freezing the jacobian matrices approximate newton method we consider the necessity for auxiliary methods to evaluate the temporal stability of the steady state solutions we demonstrate the ability of newton s method in conjunction with a continuation method to find nonunique solutions of the finite difference equations i e three different solutions for the same flow conditions

computations of boundary optimal control problems for an electrically conducting fluid we study four optimal control problems for an electrically conducting fluid the control is the normal electrical current on the boundary of the flow domain the objectives are to match a desired velocity field or to match a desired electrical potential field or to minimize the potential gradient or to minimize the vorticity in the flow domain we develop a systematic way to use the lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed mixed finite element methods are used to find approximate solutions for the optimality systems of equations that characterize the optimal controls a direct method and an iterative method are proposed for solving the discrete nonlinear optimality systems of equations numerical results for several examples are presented

a lagged implicit segregated data reconstruction procedure to treat open boundaries the problem of treating open boundaries is still a challenging one applying fully developed condition is constrained to long enough domains without having enough physical evidence about what happens on boundaries the domain extent could not be shortened and computational costs could not be reduced from the advent of free open boundary conditions they were confined to mixed finite element procedures recent works have extended their application to coupled finite volume solvers based on the shape function data reconstruction a wider class of flow solvers available however rely on the segregated procedure where the velocity components and pressure are solved in succession moreover many finite volume algorithms do not use the shape function reconstruction in this work by proposing a lagged implicit procedure we have extended the application of the open boundary condition to these wider classes of flow solvers the proposed extension is a combination of lagged implicit data reconstruction and overall mass conservation enforcement which is easily applicable to any segregated and coupled flow solver to validate the compatibility of this extension benchmark problem of backward facing step is solved on successively truncated domains where open boundary may pass through recirculation zones results show that the proposed extension works fine for that problem it reduced the computational domain length and hence memory by a factor of 4 6 and the required computational time by a factor of 21 flow passing a cylinder is also solved which proves that the method could be applied to external flow problems as well

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

buoyant flow calculations with non orthogonal curvilinear co ordinates for vertical and horizontal parallelepiped enclosures a control volume based finite difference formulation is developed for heat transfer and fluid flow in arbitrary three dimensional parallelepiped enclosures the governing equations in cartesian co ordinates are first transformed to those in non orthogonal curvilinear co ordinates by tensor transformations after introducing the properties of the parallelepiped geometry equations are obtained in the primitive variables for which all vectors and tensors are based on the curvilinear co ordinates with proper treatment of the heat flux and stress tensor terms the finite difference equations analogous to those in the cartesian coordinates are formed examples are utilized to show the validity of the methodology and the results are found to compare well with existing experimental data the differences in heat transfer and fluid flow inside parallelepiped enclosures and rectangular enclosures are delineated and discussed from a physical point of view

vorticity boundary conditions and boundary vorticity generation for two dimensional viscous incompressible flows abstract in this paper we present boundary conditions appropriate for the vorticity formulation of the two dimensional incompressible viscous navier stokes equations these boundary conditions are incorporated into a finite difference scheme and the resulting method is of the vorticity creation type i e vorticity is generated at the boundary to ensure that the tangential velocity boundary condition is satisfied the results of computations with this finite difference method are presented for flow past a circular cylinder a difference scheme and computational results for a model problem the prandtl boundary layer equations describing flow over a semi infinite flat plate are also presented

a transformation free hoc scheme for incompressible viscous flows past an impulsively started circular cylinder in this paper we present a higher order compact scheme for the unsteady two dimensional 2d navier stokes equations on nonuniform polar grids specifically designed for the incompressible viscous flows past a circular cylinder the scheme is second order accurate in time and at least third order accurate in space the scheme very efficiently computes both unsteady and time marching steady state flow for a wide range of reynolds numbers re ranging from 10 to 9500 for the impulsively started cylinder the robustness of the scheme is highlighted when it accurately captures the vortex shedding for moderate re represented by the von karman street and the so called and s phenomena for higher re comparisons are made with established numerical and experimental results and excellent agreement is found in all the cases both qualitatively and quantitatively

general strong conservation formulation of navier stokes equations in nonorthogonal curvilinear coordinates the selection of primary dependent variables for the solution of navier stokes equations in the curvilinear body fitted coordinates is still an unsettled issue reported formulations with primitive variables involve contravariant velocity components cartesian components and velocity projections also known as resolutes most of the formulations result in a weak conservation form of the momentum equations which contain grid line curvature and divergence related coriolis and centrifugal terms this paper presents a general strong conservation formulation of the momentum equations allowing the flexibility in choosing the various forms of the velocity components as the dependent variables ambiguous issues relating geometrical topology and forms of governing equations are discussed and clarified computational results obtained with both strong and weak forms are presented and compared to known analytical experimental data the results confirm the soundness of the formulation 19 refs

an adaptive residual based splitting approach for the penalized navier stokes equations the interest on immersed boundary methods ibm is increasing in computational fluid dynamics as they simplify the mesh generation problem in this work we consider an approach based on the addition of a penalty term to the navier stokes equations to account for the wall boundary conditions to discretize the resulting equations we use a residual distribution approach previously developed by some of the authors to adapt the method to the ibm considered we developed a new formulation of residual distribution based on a strang splitting method in time coupling an implicit asymptotic integration procedure of the penalization ode with a simplified explicit residual distribution for the navier stokes equations the first method provides an operator which is exact up to orders 2 with the penalty parameter assuming values of the order of 10 10 a modification of the solution gradient reconstruction necessary for the evaluation of the viscous fluxes is also introduced in the paper this guarantees that correct physical values of the viscous stresses are recovered in vicinity of the solid we show formally and numerically that the approach proposed is second order accurate for smooth solutions we evaluate its potential for ibm by coupling the resulting method with unstructured mesh adaptation on wall boundaries several steady and time dependent tests are used to show the promising features of the method proposed

numerical integration of stochastic differential equations in catchment modeling the paper discusses appropriate integration procedures for deriving solutions to stochastic differential equations sde s such sde s have been suggested as models for the generation of stochastic streamflows from catchments the sde s have been developed by expanding the nash cascade to include random inputs of rainfall and catchment abstractions the numerical integration of the sde provides sample functions that can be considered as representations of streamflows examples are given

an approximation technique for stochastic environmental modeling this paper describes the outline of an approximate mathematical technique capable of including stochastic components in environmental models based on ordinary differential equations the technique is based on the decomposition of the solution into additive components with the first component being the solution of a simplified deterministic equation and each of the other components being found in terms of those preceding it moments of the solution process can then be calculated by performing appropriate averaging the method provides natural statistical separability that is no truncations in the derivation stage or closure approximations are necessary the random quantities involved can be either random variables or stochastic processes no unrealistic assumptions like white noise behavior or small randomness are necessary solutions which are in the form of infinite but convergent series can be easily implemented into computer programs providing convenient support in management and decision analysis a demonstration application of a simple biochemical oxygen demand model for river waters illustrates the usefulness of the technique in environmental modeling

a high resolution pressure based algorithm for fluid flow at all speeds abstract a new collocated finite volume based solution procedure for predicting viscous compressible and incompressible flows is presented the technique is equally applicable in the subsonic transonic and supersonic regimes pressure is selected as a dependent variable in preference to density because changes in pressure are significant at all speeds as opposed to variations in density which become very small at low mach numbers the newly developed algorithm has two new features i the use of the normalized variable and space formulation nvsf methodology to bound the convective fluxes and ii the use of a high resolution scheme in calculating interface density values to enhance the shock capturing property of the algorithm the virtues of the newly developed method are demonstrated by solving a wide range of flows spanning the subsonic transonic and supersonic spectrum results obtained indicate higher accuracy when calculating interface density values using a high resolution scheme

steady state solutions of the euler equations in two dimensions rotating and translating v states with limiting cases i numerical algorithms and results new second and third order algorithms are presented for calculating translating and rotating steady state solutions of the 2d incompressible euler equations which we call v states these are piecewise constant regions of vorticity and the contours bounding them are obtained by solving iteratively a nonlinear integro differential equation new limiting contours with corners are obtained and compared with local analytical solutions the precise results correct mistakes for limiting contours that were previously given

first order system least squares methods for an optimal control problem by the stokes flow the least squares approximations of an optimal control problem governed by the stokes equations are considered which leads to an unconstrained coupled optimization problem by the lagrange multiplier method the least squares functionals for the two and three dimensional first order coupled optimality systems are employed by modifying those functionals in z cai t a manteuffel and s f mccormick siam j numer anal 34 1997 pp 1727 1741 the established ellipticity and continuity in a product h 1 norm yield the optimal discretization error estimates in the finite element spaces for numerical tests we apply v cycle multigrid methods to the whole discrete algebraic system

cauchy characteristic evolution and waveforms we investigate a new methodology for the computation of waves generated by isolated sources this approach consists of a global spacetime evolution algorithm based on a cauchy initial value formulation in a bounded interior region and based on characteristic hypersurfaces in the exterior we match the two schemes at their common interface the characteristic formulation allows accurate description of radiative infinity in a compactified finite coordinate interval so that our numerical solution extends to infinity and accurately models the free space problem the matching interface need not be situated far from the sources the wavefronts may have arbitrary nonspherical geometry and strong nonlinearity may be present in both the interior and the exterior regions stability and second order convergence of the algorithms to the exact solution of the infinite domain problem are established numerically in three space dimensions the matching algorithm is compared with examples of both local and nonlocal radiation boundary conditions proposed in the literature for linear problems matching outperformed the local radiation conditions chosen for testing and was about as accurate for the same grid resolution as the exact nonlocal conditions however since the computational cost of the nonlocal conditions is many times that of matching this algorithm may be used with higher grid resolutions yielding a significantly higher final accuracy for strongly nonlinear problems matching was significantly more accurate than all other methods tested this seems to be due to the fact that currently available local and nonlocal conditions are based on linearizing the governing equations in the far field while matching consistently takes nonlinearity into account in both interior and exterior regions

a reduced order method for simulation and control of fluid flows this article presents a reduced order modeling approach for simulation and control of viscous incompressible flows the reduced order models suitable for control and which capture the essential physics are developed using the reduced basis method the so called lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions the feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and in wall bounded channel flows control action is effected through boundary surface movement on a part of the solid wall our formulation of the reduced order method applied to flow control problems leads to a constrained minimization problem and is solved by applying newton like methods to the necessary conditions of optimality through our computational experiments we demonstrate the feasibility and applicability of the reduced order method for simulation and control of fluid flows

supg finite element method for adiabatic flows the purpose of this paper is to present the supg finite element method for adiabatic flows and to compare the results with those obtained via various computational methods the incompressibility assumption is often used to solve transient viscous flows on the other hand compressible flow analyses are also popular because natural flows include compressibility even if it is a negligible amount it is well known that incompressibility is a limit state of compressibility to solve compressible flows three kinds of governing equations are needed the conservation of mass momentum and energy in which density velocity and internal energy are independent variables if we assume that there is no heat transfer in or out of a system the energy equation can be eliminated from the governing equations density and velocity can be considered independent variables these kinds of flows are referred to as adiabatic flows in this paper the supg formulation is one of the most widely used methods in the finite element analyses of fluid flows in this paper the supg method for adiabatic flows is presented the polytropic law is introduced for the equation of state moreover the computational results obtained by four models of fluid flows are compared adiabatic flows compressible flows constant acoustic velocity flows and incompressible flows verifications are carried out using a lid driven cavity flow boundary effects are estimated using a wide computational domain drag forces are compared with those computed using incompressible flows the pressure coefficients over a surface of a circular cylinder located in fluid flows computed by the present method show good correspondence with the experimental measurement on the other hand significant discrepancies are observed between the pressure coefficients computed assuming constant density and the experimental results

a least squares penalty method for distributed optimal control problems for stokes equations the purpose of this paper is to construct an unconstrained optimal control problem by using a least squares approach for the constrained distributed optimal control problem associated with incompressible stokes equations the constrained equations are reformulated to the equivalent first order system by introducing vorticity and then the least squares functional corresponding to the system is enforced via a penalty term to the objective functional the existence of a solution of the unconstrained optimal control problem is proved and the convergence of this solution to that of unpenalized one is demonstrated as the penalty parameter tends to zero finite element approximations with error estimates are studied and the relevant computational experiments are presented

a cartesian ghost cell multigrid poisson solver for incompressible flows in this paper a simple cartesian ghost cell multigrid poisson solver is proposed for simulating incompressible fluid flows the flow field is discretized efficiently on a rectangular mesh in which solid bodies are immersed a small number of ghost mesh cells and their symmetric image cells are distributed in the vicinity of the solid boundary with the aid of the ghost and image cells the dirichlet and neumann boundary conditions can be implemented effectively chorin s fractional step projection method is adopted for the coupling of velocity and pressure for the solution of the navier stokes equations point wise gauss seidel iteration is used to solve the pressure poisson equation to speed up the convergence of the solution to the corresponding linear system sub level coarse meshes embedded with ghost and image cells are also introduced and operated in a sequential v cycle several test cases including the classical ideal incompressible flow around a cylinder a lid driven cavity flow and viscous flow past a fixed rotating cylinder are presented to demonstrate the accuracy and efficiency of the current approach 2010 john wiley sons ltd

does the stationary viscous flow around a circular cylinder exist for large reynolds numbers a numerical solution via variational imbedding we propose an approach to identifying the solutions of the steady incompressible navier stokes equations for large reynolds numbers these cannot be obtained as initial value problems for the unsteady system because of the instability of the latter our approach consists of replacing the original steady state problem for the navier stokes equations by a boundary value problem for the euler lagrange equations for minimization of the quadratic functional of the original equations this technique is called method of variational imbedding mvi and in this case it leads to a system of higher order partial differential equations which is solved by means of an operator splitting method as a featuring example we consider the classical flow around a circular cylinder which is known to lose stability as early as for re 40 we find a stationary solution with recirculation zone for reynolds numbers as large as re 200 thus new information about the possible hybrid flow regimes is obtained

evolution of scalar fields from characteristic data abstract we present a new algorithm for solving nonlinear wave equations when initial data is specified on characteristic surfaces the algorithm is directly applicable to hyperbolic systems such as maxwell yang mills and gravitational fields the basic principles should also be applicable to hydrodynamics it is an especially effective approach for studying radiation fields we show that this method is stable globally convergent to second order in the grid spacing and satisfies an energy conservation law we carry out numerical studies of scalar wave equations with nonlinear self interactions for some examples of physical interest we observe nonlinear phenomena such as backscattering radiative tail decay and approximate analogues to solitons in three dimensions

on the adoption of velocity variable and grid system for fluid flow computation in curvilinear coordinates abstract the issues of adopting the velocity components as dependent velocity variables including the cartesian and culvilinear ones for the navier stokes flow computations are investigated the viewpoint advocated is that a numerical algorithm should preferably honor both the physical conservation law in differential form and the geometric conservation law in discrete form it is demonstrated that with the curvilinear velocity vectors the curvatures of the grid lines introduce extra source terms into the governing equations with the cartesian velocity vector on the other hand the governing equations in curvilinear coordinates can retain the full conservation law form and honor the physical conservation laws the nonlinear combinations of the metric terms also cause the algorithms based on curvilinear velocity components to be more difficult to satisfy the geometric conservation law and hence more sensitive to grid skewness effect for the combined utilization of the cartesian velocity vector and the staggered grid arrangement the implications of spurious pressure oscillation arising from the 90 turning are discussed it is demonstrated that these spurious oscillations can possibly appear only under a very specific circumstance namely the meshes in the region with 90 turning must be parallel to the cartesian coordinates and of uniform spacing along coordinates otherwise no spurious oscillations can appear several flow solutions for domain with 90 and 360 turnings are presented to demonstrate that satisfactory results can be obtained by using the cartesian velocity components and the staggered grid arrangement

random differential equations in river water quality modeling a one dimensional steady state probabilistic river water quality model is developed to compute the joint and marginal probability density functions of bod and do at any point in a river the model can simultaneously consider randomness in the initial conditions inputs and coefficients of the water quality equations any empirical or known distribution can be used for the initial conditions randomness in each of the water quality equation inputs and coefficients is modeled as a gaussian white noise process the joint probability density function pdf of bod and do is determined by numerically solving the fokker plank random differential equation in addition moment equations are developed which allow the mean and variance of bod and do to be calculated independently of their joint pdf the probabilistic river water quality model is examined through sensitivity study and an application to a hypothetical river system

optimal control of two and three dimensional incompressible navier stokes flows the focus of this work is on the development of large scale numerical optimization methods for optimal control of steady incompressible navier stokes flows the control is affected by the suction or injection of fluid on portions of the boundary and the objective function represents the rate at which energy is dissipated in the fluid we develop reduced hessian sequential quadratic programming methods that avoid converging the flow equations at each iteration both quasi newton and newton variants are developed and compared to the approach of eliminating the flow equations and variables which is effectively the generalized reduced gradient method optimal control problems are solved for two dimensional flow around a cylinder and three dimensional flow around a sphere the examples demonstrate at least an order of magnitude reduction in time taken allowing the optimal solution of flow control problems in as little as half an hour on a desktop workstation

a coupled pressure based computational method for incompressible compressible flows pressure based flow solvers couple continuity and linearized truncated momentum equations to derive a poisson type pressure correction equation and use the well known simple algorithm momentum equations and the pressure correction equation are typically solved sequentially in many cases this method results in slow and often difficult convergence the current paper proposes a novel computational algorithm solving for pressure and velocity simultaneously within a pressure correction coupled solution approach using finite volume method on structured and unstructured meshes the method can be applied to both incompressible and subsonic compressible flows for subsonic compressible flows the energy equation is also coupled with flow field and the density of fluid is obtained by equation of state the procedure eliminates the pressure correction step the most expensive component of the simple like algorithms the proposed coupled continuity momentum energy equation method can be used to simulate steady state or transient flow problems the method has been tested on several cfd benchmark cases with excellent results showing dramatically improved numerical convergence and significant reduction in computational time

an analytic technique for stochastic analysis in environmental models this paper describes the development and application of a new mathematical technique to include stochasticity in environmental models the technique named the probability density function moment pdf m technique by the authors is based on a two tiered process first the basic governing equations are expanded to include stochastic terms stochastic terms are separated from nonfluctuating terms and the resulting set of equations is solved simultaneously solutions are used to calculate the moments of the output variables second the moments are used in conjunction with the fokker planck equation to produce an analytical solution for the probability density functions of the dependent variables because the approach produces analytical solutions it offers greater flexibility than a monte carlo approach in treating complex environmental situations unlike the stochastic differential equation approach it is not necessary to assume gaussian distributions in the solution technique complex random functions of time and space may be included and solutions are possible for higher dimensioned problems and cases with stochastic variations in stream velocity the pdf m technique represents a new and potentially powerful tool for extending the capabilities of computer models in management and decision analysis by providing analytical solutions for the probability density functions and associated moments of important environmental variables

steady viscous flow in a triangular cavity by efficient numerical techniques abstract accurate and efficient calculations of the flow inside a triangular cavity are presented for high reynolds numbers the navier stokes equations expressed in a stream function and vorticity formulation are solved numerically using finite differences on a transformed geometry second order numerical boundary conditions are derived and newton s iteration is employed to solve the nonlinear system resulting from the finite difference discretization aside from solving the equilateral triangular cavity problem we have also been able to compute numerical solutions for scalene triangular cavity problems our coarse mesh results for the equilateral triangular cavity problem are compared with finer mesh results in the literature and the agreement is good

output feedback boundary control of a ginzburg landau model of vortex shedding an exponentially convergent observer is designed for a linearized ginzburg landau model of vortex shedding in viscous flow past a bluff body measurements are restricted to be taken collocated with the actuation which is applied on the cylinder surface the observer is used in conjuction with a state feedback boundary controller designed in previous work to attenuate vortex shedding while the theoretical results apply to the linearized system under sufficiently smooth initial data that satisfy the boundary conditions simulations demonstrate the performance of the linear output feedback scheme on the nonlinear plant model

a unified mathematical framework and an adaptive numerical method for fluid structure interaction with rigid deforming and elastic bodies many problems of interest in biological fluid mechanics involve interactions between fluids and solids that require the coupled solution of momentum equations for both the fluid and the solid in this work we develop a mathematical framework and an adaptive numerical method for such fluid structure interaction fsi problems in which the structure may be rigid deforming or elastic we employ an immersed boundary ib formulation of the problem that permits us to avoid body conforming discretizations and to use fast cartesian grid solvers rigidity and deformational kinematic constraints are imposed using a formulation based on distributed lagrange multipliers and a conventional ib method is used to describe the elasticity of the immersed body we use cartesian grid adaptive mesh refinement amr to discretize the equations of motion and thereby obtain a solution methodology that efficiently captures thin boundary layers at fluid solid interfaces as well as flow structures shed from such interfaces this adaptive methodology is validated for several benchmark problems in two and three spatial dimensions in addition we use this scheme to simulate free swimming including the maneuvering of a two dimensional model eel and a three dimensional model of the weakly electric black ghost knifefish

an integral equation approach to the incompressible navier stokes equations in two dimensions we present a collection of methods for solving the incompressible navier stokes equations in the plane that are based on a pure stream function formulation the advantages of this approach are twofold first the velocity is automatically divergence free and second complicated nonlocal boundary conditions for the vorticity are avoided the disadvantage is that the solution of a nonlinear fourth order partial differential equation is required by recasting this partial differential equation as an integral equation we avoid the ill conditioning which hampers finite difference and finite element methods in this environment by using fast algorithms for the evaluation of volume integrals we are able to solve the equations using o m or o m log m operations where m is the number of points in the discretization of the domain

random evolution equations in hydrology a number of partial differential equations governing the dynamic behavior of different components of the hydrologic cycle in a region can be treated as abstract evolution equations in appropriate hilbert spaces when the source terms the boundary conditions the initial conditions and or the equation parameters are prescribed as stochastic processes the resulting random evolution equations may be solved in terms of the input stochastic processes if the semigroup associated with the partial differential operator is known this places in the hands of the modeler a very flexible tool to solve a large variety of problems several explicit examples of the methodology are illustrated finally applications of the ito s lemma in hilbert spaces to the numerical solution of stochastic partial differential equations in hydrology are presented

uncertainty analysis using corrected first order approximation method application of uncertainty and reliability analysis is an essential part of many problems related to modeling and decision making in the area of environmental and water resources engineering computational efficiency understandability and easier application have made the first order approximation foa method a favored tool for uncertainty analysis in many instances situations may arise where the accuracy of foa estimates becomes questionable often the foa application is considered acceptable if the coefficient of variation of the uncertain parameter s is 0 2 but this criterion is not correct in all the situations analytical as well as graphical relations for relative error are developed and presented for a generic power function that can be used as a guide for judging the suitability of the foa for a specified acceptable error of estimation further these analytical and graphical relations enable foa estimates for means and variances of model components to be corrected to their true values using these corrected values of means and variances for model components one can determine the exact values of the mean and variance of an output random variable this technique is applicable when an output variable is a function of several independent random variables in multiplicative additive or in combined multiplicative and additive forms two examples are given to demonstrate the application of the technique

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

steady viscous flow past a circular cylinder up to reynolds number 600 viscous flow past a circular cylinder becomes unstable around reynolds number re 40 with a numerical technique based on newton s method and made possible by the use of a supercomputer steady but unstable solutions have been calculated up to re 600 it is found that the wake bubble region with recirculating flow grows in length approximately linearly with re the width increases like re12 up to re 300 at which paint a transition to linear increase with re begins at the highest reynolds numbers we reached the wake resembles a pair of translating uniform vortices both touching the center line the cylinder moving in front with the same speed supplies the vorticity required to balance diffusion