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We address some of the computational challenges involved in fluid-structure interaction (FSI) modeling of clusters of ringsail parachutes. The geometric complexity created by the construction of the parachute from 'rings' and 'sails' with hundreds of gaps and slits makes this class of FSI modeling inherently challenging. There is still much room for advancing the computational technology for FSI modeling of a single raingsail parachute, such as improving the Homogenized Modeling of Geometric Porosity (HMGP) and developing special techniques for computing the reefed stages of the parachute and its disreefing. While we continue working on that, we are also developing special techniques targeting cluster modeling, so that the computational technology goes beyond the single parachute and the challenges specific to parachute clusters are addressed. The rotational-periodicity technique we describe here is one of such special techniques, and we use that for computing good starting conditions for FSI modeling of parachute clusters. In addition to reporting our preliminary FSI computations for parachute clusters, we present results from those starting-condition computations. In the category of more fundamental computational technologies, we discuss how we are improving the HMGP by increasing the resolution of the fluid mechanics mesh used in the HMGP computation and also by increasing the number of gores used. Also in that category, we describe how we use the multiscale sequentially coupled FSI techniques to improve the accuracy in computing the structural stresses in parts of the structure where we want to report more accurate values. All these special techniques are used in conjunction with the Stabilized Space-Time Fluid-Structure Interaction (SSTFSI) technique. Therefore, we also present in this paper a brief stability and accuracy analysis for the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, which is the core numerical technology of the SSTFSI technique.

We address the computational challenges related to the extraction of the arterial-lumen geometry, mesh generation and starting-point determination in the computation of arterial fluid―structure interactions (FSI) with patient-specific data. The methods we propose here to address those challenges include techniques for constructing suitable cutting planes at the artery inlets and outlets and specifying on those planes proper boundary conditions for the fluid mechanics, structural mechanics and fluid mesh motion and a technique for the improved calculation of an estimated zero-pressure arterial geometry. We use the stabilized space-time FSI technique, together with a number of special techniques recently developed for arterial FSI. We focus on three patient-specific cerebral artery segments with aneurysm, where the lumen geometries are extracted from 3D rotational angiography.

We focus on fluid-structure interaction (FSI) modeling and performance analysis of the ringsail parachutes to be used with the Orion spacecraft. We address the computational challenges with the latest techniques developed by the T*AFSM (Team for Advanced Flow Simulation and Modeling) in conjunction with the SSTFSI (Stabilized Space-Time Fluid-Structure Interaction) technique. The challenges involved in FSI modeling include the geometric porosity of the ringsail parachutes with ring gaps and sail slits. We investigate the performance of three possible design configurations of the parachute canopy. We also describe the techniques developed recently for building a consistent starting condition for the FSI computations, discuss rotational periodicity techniques for improving the geometric-porosity modeling, and introduce a new version of the HMGP (Homogenized Modeling of Geometric Porosity).

New special fluid-structure interaction (FSI) techniques, supplementing the ones developed earlier, are employed with the Stabilized Space-Time FSI (SSTFSI) technique. The new special techniques include improved ways of calculating the equivalent fabric porosity in Homogenized Modeling of Geometric Porosity (HMGP), improved ways of building a starting point in FSI computations, ways of accounting for fluid forces acting on structural components that are not expected to influence the flow, adaptive HMGP, and multiscale sequentially coupled FSI techniques. While FSI modeling of complex parachutes was the motivation behind developing some of these techniques, they are also applicable to other classes of complex FSI problems. We also present new ideas to increase the scope of our FSI and CFD techniques. .

We present a new space-time SUPG formulation of the shallow-water equations. In this formulation, we use a stabilization parameter that was introduced for compressible flows and a new shock-capturing parameter. In the context of two test problems, we evaluate the performance of the new shock-capturing parameter. We also evaluate the performance of the space-time SUPG formulation compared to the semi-discrete SUPG formulation, where the system of semi-discrete equations is solved with the central-difference (Crank-Nicolson) time-integration algorithm.

A stabilized finite element formulation for the computation of turbulent reacting flows and NOx emission is presented. The method is based on the Streamline-Upwind/Petrov–Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) formulations, complemented with directionally formulated diffusion for reaction-dominated flows (‘DRDJ’ stabilization). The stabilized formulation is applied to the advection–diffusion–reaction equations governing the turbulent combustion and the NOx emission equations based on the thermal and the N2O pathways. The simulation is carried out for a co-axial burner, with a non-premixed swirling flame. The burner is operated at high pressure to represent the take-off conditions for an aero-engine. The vortical patterns of the swirling flame are analyzed together with the temperature field and flame position. The NOx formation processes are discussed, providing insight into the features of thermal and N2O mechanisms. Copyright © 2010 John Wiley & Sons, Ltd.

We review and summarize our research activities in fluid-structure interaction (FSI) analysis of cerebral aneurysms using anatomically realistic geometry models based on medical images. Emphasis is placed on influencing factors in computational FSI, and their role and clinical implications are discussed in terms of the wall shear stress (WSS). The key factors are: (1) arterial and aneurysm geometries, (2) wall structure modeling, (3) blood pressure, (4) outflow conditions and (5) inflow conditions. Among these, we find the impact of the arterial and aneurysm geometries to be the most significant. Blood pressure also has a significant impact on the WSS distribution; a hypothetical hypertensive blood pressure condition could help estimate the rupture risk for an aneurysm. We find the other three factors to be minor compared with the arterial and aneurysm geometries and blood pressure, although the level of influence could be unique to the middle cerebral artery aneurysms that we have been focusing on in our studies.

Arterial fluid-structure interaction (FSI) computations involve a number of numerical challenges. Because blood flow is incompressible, iterative solution of the fluid mechanics part of the linear equation system at every nonlinear iteration of each time step is one of those challenges, especially for computations over slender domains and in the presence of boundary layer mesh refinement. In this paper we address that challenge. As test cases, we use equation systems from stabilized finite element computation of a bifurcating middle cerebral artery segment with aneurysm, with thin layers of elements near the arterial wall. We show how the preconditioning techniques, we propose for solving these large sparse nonsymmetric systems, perform at different time steps of the computation over a cardiac cycle. We also present a new hybrid parallel sparse linear system solver 'DD-Spike' and demonstrate its scalability. Copyright (C) 2010 John Wiley & Sons, Ltd.

In this two-part paper we present a collection of numerical methods combined into a single framework, which has the potential for a successful application to wind turbine rotor modeling and simulation. In Part 1 of this paper we focus on: 1. The basics of geometry modeling and analysis-suitable geometry construction for wind turbine rotors; 2. The fluid mechanics formulation and its suitability and accuracy for rotating turbulent flows; 3. The coupling of air flow and a rotating rigid body. In Part 2 we focus on the structural discretization for wind turbine blades and the details of the fluid–structure interaction computational procedures. The methods developed are applied to the simulation of the NREL 5MW offshore baseline wind turbine rotor. The simulations are performed at realistic wind velocity and rotor speed conditions and at full spatial scale. Validation against published data is presented and possibilities of the newly developed computational framework are illustrated on several examples. Copyright © 2010 John Wiley & Sons, Ltd.

We provide a brief chronological background on the deforming-spatial-domain/stabilized space–time (DSD/SST) formulation, its use in aerodynamic modeling of a paratrooper separating from an aircraft, and the fluid–object interactions subcomputation technique (FOIST). Copyright © 2010 John Wiley & Sons, Ltd.

Some comments are provided on the shock-capturing techniques and stabilization parameters used in a recent paper (B.S. Kirk, Int. J. Numer. Meth. Fluids 2009; DOI: 10.1002/fld.2195) in conjunction with the SUPG formulation of compressible flows. Copyright © 2010 John Wiley & Sons, Ltd.

We present applications of the stabilized finite element formulations developed for incompressible flows with thermal coupling to 2D and 3D test problems. The stabilized formulations are based on the streamline-upwind/Petrov–Galerkin and pressure-stabilizing/Petrov–Galerkin stabilizations and are supplemented with discontinuity capturing (DC), including the discontinuity-capturing directional dissipation. The stabilization and DC parameters associated with these formulations are also presented. The coupled fluid mechanics and temperature equations are solved with a direct coupling technique. The test problems computed include 2D and 3D natural convection, as well as a simplified 3D model of air circulation in a small data center. Copyright © 2008 John Wiley & Sons, Ltd.

We present an overview of how the arterial fluid mechanics problems can be modeled with the stabilized space–time fluid–structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM). The SSTFSI technique includes the enhancements introduced recently by the T★AFSM to increase the scope, accuracy, robustness and efficiency of this class of techniques. The SSTFSI technique is supplemented with a number of special techniques developed for arterial fluid mechanics modeling. These include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, and the sequentially coupled arterial FSI (SCAFSI) technique. The recipe for pre-FSI computations is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. The SCAFSI technique, which was introduced as an approximate FSI approach in arterial fluid mechanics, is also based on that assumption. The need for an estimated zero-pressure arterial geometry is based on recognizing that the patient-specific image-based geometries correspond to time-averaged blood pressure values. In our arterial fluid mechanics modeling the arterial walls can be represented with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element is made of hyperelastic (Fung) material. Test computations are presented for cerebral and abdominal aortic aneurysms, where the arterial geometries used in the computations are close approximations to the patient-specific image-based data. Copyright © 2007 John Wiley & Sons, Ltd.

The YZp shock-capturing technique was introduced recently for use in combination with the streamline-upwind/Petrov-Galerkin formulation of compressible flows in conservation variables. The YZβ shock-capturing parameter is much simpler than an earlier parameter derived from the entropy variables for use in conservation variables. In this paper, we propose to use the YZβ shock-capturing in combination with the variable subgrid scale (V-SGS) formulation of compressible flows in conservation variables. The V-SGS method is based on an approximation of the class of SGS models derived from the Hughes variational multiscale method. We evaluate the performance of the V-SGS and YZβ combination in a number of standard, 2D test problems. Compared to the earlier shock-capturing parameter derived from the entropy variables, in addition to being much simpler, the YZβ shock-capturing parameter yields better shock quality in these test problems.

We provide an overview of how fluid–solid and fluid–fluid interfaces can be computed successfully with the constrained interpolation profile/cubic interpolated pseudo-particle (CIP) method (J. Comput. Phys. 1985; 61:261–268; Comput. Phys. Commun. 1991; 66:219–232; Comput. Phys. Commun. 1991; 66:233–242; J. Comput. Phys. 2001; 169:556–593) based on adaptive Soroban grids (J. Comput. Phys. 2004; 194:57–77). In this approach, the CIP combined unified procedure (CCUP) technique (J. Phys. Soc. Jpn 1991; 60:2105–2108), which is based on the CIP method, is combined with the adaptive Soroban grid technique. One of the superior features of the approach is that even though the grid system is unstructured, it still has a simple data structure that renders remarkable computational efficiency. Another superior feature is that despite the unstructured and collocated nature of the grid, high-order accuracy and computational robustness are maintained. In addition, because the Soroban grid technique does not have any elements or cells connecting the grid points, the approach does not involve mesh distortion limitations. While the details of the approach and several numerical examples were reported in (Comput. Mech. 2006; published online), our objective in this paper is to provide an easy-to-follow description of the key aspects of the approach. Copyright © 2007 John Wiley & Sons, Ltd.

The stabilized space-time fluid-structure interaction (SSTFSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T*AFSM) are applied to FSI modelling in arterial fluid mechanics. Modelling of flow in arteries with aneurysm is emphasized. The SSTFSI techniques used are based on the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation and include the enhancements introduced recently by the T*AFSM to increase the scope, accuracy, robustness and efficiency of these techniques. The arterial structures can be modelled with the membrane or continuum elements, both of which are geometrically nonlinear, and the continuum element can be made of linearly elastic or hyperelastic material. Test computations are presented for cerebral and abdominal aortic aneurysms and carotid-artery bifurcation, where the arterial geometries used in the computations are close approximations to the patient-specific image-based data.

We propose a numerical model for computation of flow problems that involve both fluid-solid and fluid-fluid interfaces. The model is based on the mixed interface-tracking/interface-capturing technique (MITICT), which was introduced earlier for problems that involve both fluid-solid interfaces that are accurately tracked with a moving mesh method and fluid-fluid interfaces that are too complex to track and therefore treated with an interface-capturing technique. In our numerical model, fluid-solid interfaces are handled with the moving Lagrangian interface technique (MLIT) and fluid-fluid interfaces with the edge-tracked interface locator technique (ETILT). The mixed technique is tested in computation of a fluid-particle interaction problem in the presence of a fluid-fluid interface impacted by the particle.

The YZβ discontinuity-capturing operator, recently introduced in (Encyclopedia of Computational Mechanics, Vol. 3, Fluids. Wiley: New York, 2004) in the context of compressible flows, is applied to a time-dependent, scalar advection-diffusion equation with the purpose of modelling drug delivery processes in blood vessels. The formulation is recast in a residual-based form, which reduces to the previously proposed formulation in the limit of zero diffusion and source term. The NURBS-based isogeometric analysis method, proposed by Hughes et al. (Comput. Methods Appl. Mech. Eng. 2005; 194:4135-4195), was used for the numerical tests. Effects of various parameters in the definition of the FZβ operator are examined on a model problem and the better performer is singled out. While for low-order B-spline functions discontinuity capturing is necessary to improve solution quality, we find that high-order, high-continuity B-spline discretizations produce sharp, nearly monotone layers without the aid of discontinuity capturing. Finally, we successfully apply the YZβ approach to the simulation of drug delivery in patient-specific coronary arteries.

The constrained interpolation profile/cubic interpolated pseudo-particle (CIP) combined unified procedure (CCUP) method (J. Phys. Soc. Jpn. 1991; 60:2105-2108), which is based on the CIP method (J Comput. Phys. 1985; 61:261-268; J. Comput. Phys. 1987; 70:355-372; Comput. Phys. Commun. 1991; 66:219-232; J. Comput. Phys. 2001; 169:556-593) and the adaptive Soroban grid technique (J. Comput. Phys. 2004; 194:55-77) were combined in (Comput. Mech. 2006; published online) for computation of 3D fluid-object and fluid-structure interactions in the presence of free surfaces and fluid-fluid interfaces. Although the grid system is unstructured, it still has a very simple data structure and this facilitates computational efficiency. Despite the unstructured and collocated features of the grid, the method maintains high-order accuracy and computational robustness. Furthermore, the meshless feature of the combined technique brings freedom from mesh moving and distortion issues. In this paper, the combined technique is extended to ship hydrodynamics computations. We introduce a new way of computing the advective terms to increase the efficiency in that part of the computations. This is essential in ship hydrodynamics computations where the level of grid refinement needed near the ship surface and at the free surface results in very large grid sizes. The test cases presented are a test computation with a wave-making wedge and simulation of the hydrodynamics of a container ship.

Fluid-structure interaction (FSI) computations of two cerebral aneurysms are carried out under hypertensive and normotensive blood pressures. Hypertensive blood pressure is one of the major risk factors in subarachnoid hemorrhage, which is mostly caused by the rupture of cerebral aneurysm. Since hemodynamic wall shear stress (WSS) is known to play an important role in aneurysm progression, investigating the WSS distribution in conjunction with hypertensive blood pressure is expected to provide a better understanding of aneurysms. The WSS distributions obtained from the simulations show that hypertensive blood pressure considerably affects one of the subjects but not the other. The effect is a wider spreading of the high WSS region on the aneurysm wall, which prevents the wall from weakening. It is also shown that the deformation of the aneurysm wall can alter the flow patterns in the aneurysm to diminish the stagnant flow near the apex, which is linked to the weakening of the wall. The effect of hypertensive blood pressure and wall deformation is shown to be highly dependent on individual aneurysm geometry, and that stresses the importance of subject-specific simulations.

Soft landing of a payload with the aid of a retraction device is an important aspect in cargo parachute operations. Accurate simulation of this class of parachute operations with a computer model that takes into account the fluid–structure interactions involved would complement drop tests and support the design of cargo parachute systems. We describe the computational methods developed for this purpose, demonstrate how the computational model works in investigation of different soft-landing conditions, and show a good correlation between the data from our simulations and drop tests. Copyright © 2004 John Wiley & Sons, Ltd.

The enhanced-discretization successive update method (EDSUM) is a multi-level iteration method designed for computation of the flow behaviour at small scales. As an enhancement in iterative solution of non-linear and linear equation systems, the EDSUM is one of the enhanced discretization and solution techniques developed for more effective computation of complex flow problems. It complements techniques based on enhancement in spatial discretization and based on enhancement in time discretization in the context of a space-time formulation. It is closely related to the enhanced-discretization interface-capturing technique (EDICT), as the function spaces used in the EDSUM are very similar to those used in the EDICT. The EDSUM also has a built-in mechanism for transferring flow information between the large and small scales in a fashion consistent with the discretizations resulting from the underlying stabilized formulations. With a number of test computations for steady-state problems governed by the advection-diffusion equation, we demonstrate that the EDSUM has the potential to become a competitive technique for computation of flow behaviour at small scales

The interface-tracking and interface-capturing techniques we developed in recent years for computation of flow problems with moving boundaries and interfaces rely on stabilized formulations such as the streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) methods. The interface-tracking techniques are based on the deforming-spatial-domain/stabilized space-time formulation, where the mesh moves to track the interface. The interface-capturing techniques, typically used with non-moving meshes, are based on a stabilized semi-discrete formulation of the Navier-Stokes equations, combined with a stabilized formulation of the advection equation governing the time-evolution of an interface function marking the interface location. We provide an overview of the interface-tracking and interface-capturing techniques, and highlight how we determine the stabilization parameters used in the stabilized formulations

The application of a stabilized space-time finite element formulation to problems involving fluid-structure interactions and two-fluid interfaces is discussed. Two sample problems are presented and the method is validated by comparison with a test problem.

SUMMARY We present our numerical methods for the solution of large-scale incompressible flow applications with complex geometries. These methods include a stabilized finite element formulation of the Navier‐Stokes equations, implementation of this formulation on parallel architectures such as the Thinking Machines CM-5 and the CRAY

Massively parallel finite element methods for large-scale computation of storm surges and tidal flows are discussed here. The finite element computations, carried out using unstructured grids, are based on a three-step explicit formulation and on an implicit space-time formulation. Parallel implementations of these unstructured grid-based formulations are carried out on the Fujitsu Highly Parallel Computer AP1000 and on the Thinking Machines CM-5. Simulations of the storm surge accompanying the Ise-Bay typhoon in 1959 and of the tidal flow in Tokyo Bay serve as numerical examples. The impact of parallelization on this type of simulation is also investigated. The present methods are shown to be useful and powerful tools for the analysis of storm surges and tidal flows.

SUMMARY Massively parallel finite element computations of 3D, unsteady incompressible flows, including those involving fluid-structure interactions, are presented. The computations with time-varying spatial domains are based on the deforming spatial domaidstabilized spacetime (DSD/SST) finite element formulation. The capability to solve 3D problems involving fluid-structure interactions is demonstrated by investigating the dynamics of a flexible cantilevered pipe conveying fluid. Computations of flow past a stationary rectangular wing at Reynolds number 1000, 2500 and lo7 reveal interesting flow patterns. In these computations, at each time step approximately 3 x lo6 non-linear equations are solved to update the flow field. Also, preliminary results are presented for flow past a wing in flapping motion. In this case a specially designed mesh moving scheme is employed to eliminate the need for remeshing. All these computations are canied out on the Amy High Performance Computing Research Center supercomputers CM-200 and CM-5, with major speed-ups compared with traditional supercomputers. The coupled equation systems arising from the finite element discretizations of these large-scale problems are solved iteratively with diagonal preconditioners. In some cases, to reduce the memory requirements even further, these iterations are carried out with a matrix-fiee strategy. The finite element formulations and their parallel implementations assume unstructured meshes.

Massively parallel finite element strategies for large-scale computations of shallow water flows and contaminant transport are presented. The finite element discretizations, carried out on unstructured grids, are based on a three-step explicit formulation both for the shallow water equations and for the advection-diffusion equation governing the contaminant transport. Parallel implementations of these unstructured-grid-based formulations are carried out on the Army High Performance Computing Research Center Connection Machine CM-5. It is demonstrated with numerical examples that the strategies presented are applicable to large-scale computations of various shallow water flow problems.

A numerical simulation capability for the injector flow of a regenerative liquid propellant gun (RLPG) is presented. The problem involves fairly complex geometries and two pistons in relative motion ; therefore a stabilized space-time finite element formulation developed earlier and capable of handling flows with moving mechanical components is used. In addition to the specifics of the numerical method, its application to a 30 mm RLPG test firing is discussed. The computational data from the simulation of this test case are interpreted to provide information on flow characteristics, with emphasis on the tendency of the flow to separate from the injection orifice boundary of the test problem. In addition, the computations provided insight into the behaviour of the flow entering the combustion chamber.

Massively parallel finite element computations of the compressible Euler and Navier-Stokes equations using parallel supercomputers are presented. The finite element formulations are based on the conservation variables and the streamline-upwind/Petrov-Galerkin (SUPG) stabilization method is used to prevent potential numerial oscillations due to dominant advection terms. These computations are based on both implicit and explicit methods and their parallel implementation assumes that the mesh is unstructured. The implicit computations are based on iterative strategies. Large-scale 3D problems are solved using a matrix-free iteration technique which reduces the memory requirements significantly. The flow problems we consider typically come from aerospace applications, including those in 3D and those involving moving boundaries interacting with boundary layers and shocks. Problems with fixed boundaries are solved using a semidiscrete formulation and the ones involving moving boundaries are solved using the deformable-spatial-domain/stabilized-space-time (DSD/SST) formulation.

The influence of the location of the outflow computational boundary on the unsteady incompressible flow past a circular cylinder at Reynolds number 100 is examined. The vorticity-streamfunction formulation of the Navier-Stokes equations is used in all computations. Two types of outflow boundary conditions are subjected to a series of tests in which the domain length is gradually reduced. The traction-free condition performs well in most cases and allows the outflow boundary to be located as close as 6.5 cylinder diameters from the body. The other boundary condition type is not as forgiving, but has the advantage of being simpler to implement and can still provide reasonably accurate solutions. It is also observed that both condition types can influence the flow field strongly and globally when the boundary is brought closer than 2.5 diameters from the body. In such cases the temporal periodicity of the solution is lost.

SUMMARY Iterative versions of the adaptive implicit-xplicit method are presented for the finite element computation of flow problems with particular reference to incompressible flows and advection-diffusion problems. The iterative techniques employed are the grouped element-by-element and generalized minimum residual methods. For most flow problems of practical interest, especially in three dimensions, methods involving direct solution of linear equation systems give rise to massive global coefficient matrices. Storage and inversion of these matrices place a heavy demand on the computational resources in terms of the CPU time and memory. Iterative, explicit and semi-explicit methods, on the other hand, require storage and inversion of much simpler matrices, if at all. Properly implemented, these methods can substantially reduce the demand for memory and CPU time while retaining most of the desirable properties of the direct methods. In this paper we present the adaptive implicit-explicit (AIE) procedures’ which are employed in combination with iterative techniques such as the grouped element-by-element (GEBE)’ and generalized minimum residual (GMRES)3 methods. Although the description of the concepts and the numerical demonstrations are based on incompressible flows and convection4iffusion problems, the approach presented here is applicable to a wider class of problems in computational fluid dynamics. In the AIE method the elements are dynamically grouped into implicit and explicit subsets. The selection of the implicit elements is determined, at a given instant in time, by the element level Courant number and some measure of the local variations in the solution. Since the computational cost associated with the explicit elements is much smaller than that of the implicit elements, by placing the implicit elements only where and when they are needed, substantial savings in the CPU time and memory can be achieved. The GEBE iteration method, on the other hand, is based on static (i.e. one-time) arrangement of the elements into groups, with the condition that no two elements in the same group can share a common node. In the GEBE method the preconditioning matrix is chosen to be a sequential product of the element group matrices; this approach is a variation of the one taken in the regular EBE methods employed in computational fluid and solid mechanics.’ The GEBE approach eliminates the need for the formation, storage and factorization of large global matrices.

Heterogeneous equation systems in a pair of coupled co-ordinate systems are solved by a finite element method. The specific physical application studied is the effect of temperature on single-well chemical tracer (SWCT) tests to measure residual oil saturation (volume fraction of immobile oil phase) remaining after waterflooding of an oil reservoir. Since temperature effects are caused by injecting cooler surface fluid down a well into a warm reservoir, the vertical temperature profile in the wellbore as well as the temperature distribution in the porous oil-bearing layer must be considered. The entire system is modelled to account for the different transport mechanisms. However, it is expedient to divide the connected geometrical region into two model domains. The equations for each submodel are expressed in an appropriate set of co-ordinates. The variational formulation of each model is then discussed. A significant temperature effect on the estimation of residual oil saturation occurs when the radial temperature and concentration wave propagation speeds in the porous formation are about the same. In this case the temperature gradient is located across the chemical tracer bank, causing the chemical reaction rate to vary radially. The temperature effects are demonstrated for two actual field tests in complex reservoirs.

A review of the solution techniques of Tezduyar et al. (1988 and 1989) for the vorticity-streamfunction formulation of two-dimensional incompressible flows is presented. While both the viscous and inviscid cases are considered, the derivation of the proper finite-element formulations for multiply connected domains is emphasized. In all formulations associated with the vorticity transport equation, the streamline upwind/Petrov-Galerkin method is used. The adaptive implicit-explicit and grouped element-by-element solution strategies are employed to maximize the computational efficiency. The solutions obtained in all test cases compare well with solutions from previously published investigations. The convergence and benchmark studies performed in this paper show that the solution techniques presented are accurate, reliable, and efficient.

Some comments are provided on the citations offered in a recent paper (M. Behr, Int. J. Numer. Meth. Fluids 2008; 57:1421–1434) that describes space–time finite element computations of advection of ‘Gaussian hills’, including computations with mesh refinement in the time direction. Copyright © 2008 John Wiley & Sons, Ltd.

SUMMARY In this paper we present streamline-upwind/Petrov-Galerkin finite element procedures for two-dimensional fluid dynamics computations based on the vorticity-stream function formulation of the incompressible Navier-Stokes equations. We address the difficulties associated with the convection term in the vorticity transport equation, lack of boundary condition for the vorticity at no-slip boundaries, and determination of the value of the stream function at the internal boundaries for multiply connected domains. The proposed techniques, implemented within the framework of block-iteration methods, have successfully been applied to various problems involving simply and multiply connected domains. There are some advantages in using the vorticity-stream function formulation of the incompressible Navier-Stokes equations for two-dimensional computations. Compared to the velocity-pressure formulation, the vorticity-stream function formulation leads to computed flow fields which satisfy the incompressibility condition automatically; also the number of unknown functions is reduced from three to two and the vorticity field is computed directly instead of being obtained by differentiation of the velocity field. The last advantage becomes important if one needs to study the vorticity field and therefore wants that this field be represented as accurately as possible. We propose suitable finite element procedures for the solution of the time-dependent vorticity transport equation and the Poisson’s equation which relates the stream function to the vorticity. The difficulties associated with the convection term in the vorticity transport equation, lack of