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Poisson equation lies in the heart of the numerical solutions of incompressible Navier–Stokes equations (NSEs) based on the popular projection methods, which decouple the pressure and velocities fields. This paper presents enhanced numerical solutions of the 2D incompressible NSEs inspired by a newly-developed Generalized Harmonic Polynomial Cell (GHPC) method for the Poisson equation, which has a fourth-order spatial accuracy. To achieve that, the original GHPC method is adapted to accommodate immersed boundaries, necessary when a staggered grid for velocities and pressure is applied. The finite difference method (FDM) is used in the spatial discretization of the diffusion and advection terms. Numerical analyses of lid-driven cavity flow, a Taylor–Green vortex, and flow around a smooth circular cylinder all show encouraging results, confirming the accuracy and efficiency of the new solver. Through comparison with an NSEs solver which applies second-order FDM for the Poisson equation, we demonstrate that the accuracy of the pressure solution can be greatly improved by applying the more accurate GHPC method for the Poisson equation, even though the accuracy of the velocities solutions are limited by the numerical schemes for advection–diffusion equations. The accuracy in the pressure solution can also be translated into CPU time saving to achieve a predefined accuracy. The present immersed-boundary GHPC Poisson equation solver can easily be ‘plugged’ into other existing NSEs solvers utilizing staggered grids.

A novel two-dimensional numerical wave tank based on the two-phase Navier–Stokes equations (NSEs) is presented. The popular projection method is applied to decouple the pressure and velocity fields, while the solutions are uniquely enhanced by a newly-developed immersed-boundary generalized harmonic polynomial cell (IB-GHPC) method for the pressure Poisson equation, which lies at the heart of the projection method. The GHPC method, originally proposed for the constant-coefficient Poisson equation, has been employed in solving the single-phase NSEs with success, though it cannot be directly applied for two-phase flows. In this paper, we show that the GHPC method can still be used in solving two-phase flow problems by introducing a pressure-correction method. By considering wave generation and propagation, the accuracy and convergence rate of the present numerical model is demonstrated. The solver is further validated against model tests for wave propagation over a submerged breakwater, and a perforated plate in oscillatory flows and incident waves. Excellent agreement with benchmark results confirms the accuracy and the validity of the new numerical wave tank towards more general wave–structure-interaction problems. The free-surface effect on the wave loads of a perforated plate is further investigated through applications of the present numerical model.

We consider a boundary value problem for the stationary Stokes problem and the corresponding pressure-Poisson equation. We propose a new formulation for the pressure-Poisson problem with an appropriate additional boundary condition. We establish error estimates between solutions to the Stokes problem and the pressure-Poisson problem in terms of the additional boundary condition. As boundary conditions for the Stokes problem, we use a traction boundary condition and a pressure boundary condition introduced in C. Conca et al (1994).

The solution of the pressure Poisson equation arising in the numerical solution of incompressible Navier–Stokes equations (INSE) is by far the most expensive part of the computational procedure, and often the major restricting factor for parallel implementations. Improvements in iterative linear solvers, e.g. deploying Krylov-based techniques and multigrid preconditioners, have been successfully applied for solving the INSE on CPU-based parallel computers. These numerical schemes, however, do not necessarily perform well on GPUs, mainly due to differences in the hardware architecture. Our previous work using many P100 GPUs of a flagship supercomputer showed that porting a highly optimized MPI-parallel CPU-based INSE solver to GPUs, accelerates significantly the underlying numerical algorithms, while the overall acceleration remains limited (Zolfaghari et al., Comput. Phys. Commun., 244, 132-142, 2019). The performance loss was mainly due to the Poisson solver, particularly the V-cycle geometric multigrid preconditioner. We also observed that the pure compute time for the GPU kernels remained nearly constant as grid size was increased. Motivated by these observations, we present herein an algebraically simpler, yet more advanced parallel implementation for the solution of the Poisson problem on large numbers of distributed GPUs. Data parallelism is achieved by using the classical Jacobi method with successive over-relaxation and an optimized iterative driver routine. Task parallelism is enhanced via minimizing GPU-GPU data exchanges as iterations proceed to reduce the communication overhead. The hybrid parallelism results in nearly 300 times less time-to-solution and thus computational cost (measured in node-hours) for the Poisson problem, compared to our best-case scenario CPU-based parallel implementation which uses a preconditioned BiCGstab method. The Poisson solver is then embedded in a flow solver with explicit third-order Runge-Kutta scheme for time-integration, which has been previously ported to GPUs. The flow solver is validated and computationally benchmarked for the transition and decay of the Taylor-Green Vortex at R e = 1600 and the flow around a solid sphere at R e D = 3700 . Good strong scaling is demonstrated for both benchmarks. Further, nearly 70% lower electrical energy consumption than the CPU implementation is reported for Taylor-Green vortex case. We finally deploy the solver for DNS of systolic flow in a bileaflet mechanical heart valve, and present new insight into the complex laminar-turbulent transition process in this prosthesis.

Compressibility effects on pressure fluctuations in wall-bounded turbulent flows at various Mach numbers are investigated by deriving a pressure Poisson equation that allows splitting pressure fluctuations into rapid and slow terms, as in incompressible flows, and into additional mass-flux and viscous terms. The rapid and slow terms are further split into their solenoidal and dilatational components by using Helmholtz decomposition. The solenoidal components are found to be independent of Mach number and similar to incompressible flows, whereas the dilatational components increase quadratically with Mach number.

The moving particle semi-implicit method is a meshless particle method for incompressible fluid and has proven useful in a wide variety of engineering applications of free-surface flows. Despite its wide applicability, the moving particle semi-implicit method has the defects of spurious unphysical pressure oscillation. Three various divergence approximation formulas, including basic divergence approximation formula, difference divergence approximation formula, and symmetric divergence approximation formula are proposed in this paper. The proposed three divergence approximation formulas are then applied for discretization of source term in pressure Poisson equation. Two numerical tests, including hydrostatic pressure problem and dam-breaking problem, are carried out to assess the performance of different formulas in enhancing and stabilizing the pressure calculation. The results demonstrate that the pressure calculated by basic divergence approximation formula and difference divergence approximation formula fluctuates severely. However, application of symmetric divergence approximation formula can result in a more accurate and stabilized pressure.

In the community of computational fluid dynamics, pressure Poisson equation with Neumann boundary condition is usually encountered when solving the incompressible Navier–Stokes equations in a segre...

Open Boundary treatment is a well-known issue in the Smoothed Particle Hydrodynamics (SPH) method, mainly when the truly Incompressible (ISPH) approach is employed. In the paper a novel method is proposed to set pressure boundary conditions in the computational domain inlets and outlets, without requiring the velocity profile assignment. The new technique allows to treat in the same way inflow and outflow sections, effectively dealing with the release of new particles at inlets and the deactivation of the ones leaving the domain through the outlets. Several 3D numerical tests, both in the laminar and turbulent regimes, are carried out to validate the proposed numerical scheme considering steady and oscillating pressure boundary conditions.

In recent years, Lattice Boltzmann Methods (LBM’s) have emerged as a popular class of paradigms for the simulation of multiphase flows. These methods rely on discretized Boltzmann equations to represent the individual multiphase species. Among LBM’s advantages is its ability to explicitly account for interfacial physics and its local streaming/collision operations which make it ideally suited for parallelization. However, one drawback of LBM is in the simulation of incompressible multiphase flow, whereby the density should remain constant along material characteristics. Because LBM uses a state equation to relate pressure and density, incompressibility cannot be enforced directly. This is true even for incompressible single-phase LBM calculations, in which a finite density drop is needed to drive through the flow. This is also the case for compressible Navier-Stokes algorithms when applied to low Mach number flow. To mitigate compressibility effects, LBM can be used in low Mach regimes which should keep material density variation small. In this work, we demonstrate that the assumption of low Mach number is not sufficient in multiphase internal flows. In such flows, in the absence of a Pressure Poisson constraint to enforce incompressibility, LBM predicts a compressible solution whereby a density gradient must develop to conserve mass. Imposition of inflow/outflow boundary conditions or a mean body force can ensure that mass is conserved globally, thereby quelling density variation. The primary numerical problem we study is the deformation of a liquid droplet immersed in another fluid. Though LBM is not typically conducted with a pressure Poisson equation, we incorporate one in this work and demonstrate that its inclusion can significantly lower the density variation in view of maintaining an incompressible flow.

Turbulent boundary layer and metamaterial properties were explored to initiate the viability of controlling acoustic waves driven by pressure fluctuations from flow. A turbulent boundary layer scaling analysis was performed on zero-pressure-gradient turbulent boundary layers over rough surfaces, for 30,000≤〖Re〗_θ≤100,000. Relationships between fluctuating pressures and velocities were explored through the pressure Poisson equation. Certain scaling laws were implemented in attempts to collapse velocity spectra and turbulence profiles. Such analyses were performed to justify a proper scaling of the low-frequency region of the wall-pressure spectrum. Such frequencies are commonly associated with eddies containing the largest length scales. This study compared three scaling methods proposed in literature: The low-frequency classical scaling (velocity scale U_τ, length scale δ), the convection velocity scaling (U_e-U ̅_c, δ), and the Zagarola-Smits scaling (U_e-U ̅, δ). A default scaling (U_e, δ) was also selected as a baseline case for comparison. At some level, the classical scaling best collapsed rough and smooth wall Reynolds stress profiles. Low-pass filtering of the scaled turbulence profiles improved the rough-wall scaling of the Zagarola-Smits and convection velocity laws. However, inconsistent scaled results between the pressure and velocity requires a more rigorous pressure Poisson analysis. The selection of a proper scaling law gives insight into turbulent boundary layers as possible sources for acoustic metamaterials. A quiescent (no flow) experiment was conducted to measure the capabilities of a metamaterial in retaining acoustic surface waves. A point source speaker provided an acoustic input while the resulting sound waves were measured with a probe microphone. Acoustic surface waves were found via Fourier analysis in time and space. Standing acoustic surface waves were identified. Membrane response properties were measured to obtain source condition characteristics for turbulent boundary layers once the metamaterial is exposed to flow. Master of Science Aerodynamicists are often concerned with interactions between fluids and solids, such as an aircraft wing gliding through air. Due to frictional effects, the relative velocity of the air on the solid-surface is negligible. This results in a layer of slower moving fluid near the surface referred to as a boundary layer. Boundary layers regularly occur in the fluid-solid interface, and account for a sufficient amount of noise and drag on aircraft. To compensate for increases in drag, engines are required to produce increased amounts of power. This leads to higher fuel consumption and increased costs. Additionally, most boundary layers in nature are turbulent, or chaotic. Therefore, it is difficult to predict the exact paths of air molecules as they travel within a boundary layer. Because of its intriguing physics and impacts on economic costs, turbulent boundary layers have been a popular research topic. This study analyzed air pressure and velocity measurements of turbulent boundary layers. Relationships between the two were drawn, which fostered a discussion of future works in the field. Mainly, the simultaneous measurements of pressure on the surface and boundary layer velocity can be performed with understanding of the Pressure Poisson equation. This equation is a mathematical representation of the boundary layer pressure on the surface. This study also explored the possibility of turbulent-boundary-layer-driven-acoustic-metamaterials. Acoustic metamaterials contain hundreds of cavities which can collectively manipulate passing sound waves. A facility was developed at Virginia Tech to measure this effect, with aid from a similar laboratory at Exeter University. Microphone measurements showed the reduction of sound wave speed across the metamaterial, showing promise in acoustic manipulation. Applications in metamaterials in the altering of sound caused by turbulent boundary layers were also explored and discussed.

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier-Stokes equations. The key feature of this approach is the seamless integration of a reduced order model (ROM) in the framework of an industrially validated computational fluid dynamics software. This is of special importance in an industrial environment because in the online phase of the PGD ROM the description of the flow for a specific set of parameters is obtained simply via interpolation of the generalised solution, without the need of any extra solution step. On the one hand, the spatial problems arising from the PGD separation of the unknowns are treated using the classical solution strategies of OpenFOAM, namely the semi-implicit method for pressure linked equations (SIMPLE) algorithm. On the other hand, the parametric iteration is solved via a collocation approach. The resulting ROM is applied to several benchmark tests of laminar incompressible Navier-Stokes flows, in two and three dimensions, with different parameters affecting the flow features. Eventually, the capability of the proposed strategy to treat industrial problems is verified by applying the methodology to a parametrised flow control in a realistic geometry of interest for the automotive industry., Comment: 35 pages, 17 figures

China and India Award of Royal Academy of Engineering, UK to Drs Eldad Avital and Krishna M. Singh. Grant Numbers: Grant No. SEMF1A4R, Grant No. EP/L000261/1

In a recent work by Gui et al. [13], an incompressible SPH model was presented that employs a mixed pressure Poisson equation (PPE) source term combining both the density-invariant and velocity divergence-free formulations. The present work intends to apply the model to a wider range of fluid impact situations in order to quantify the numerical errors associated with different formulations of the PPE source term in incompressible SPH (ISPH) models. The good agreement achieved between the model predictions and the documented data is taken as a further demonstration that the mixed source term formulation can accurately predict the fluid impact pressures and forces, both in the magnitude and in the spatial and temporal patterns. Furthermore, an in-depth numerical analysis using either the pure density-invariant or velocity divergence-free formulation has revealed that the pure density-invariant formulation can lead to relatively large divergence errors while the velocity divergence-free formulation may cause relatively large density errors. As compared with these two approaches, the mixed source term formulation performs much better having the minimum total errors in all test cases. Although some recent studies found that the weakly compressible SPH models perform somewhat better than the incompressible SPH models in certain fluid impact problems, we have shown that this could be largely caused by the particular formulation of PPE source term in the previous ISPH models and a better formulation of the source term can significantly improve the accuracy of ISPH models.

Zheng, X.; Ma, Q.; Shao, S.; Hu, Z., and Gui, Q., 2019. An improved 2D + t incompressible smoothed particle hydrodynamics approach for high-speed vessel waves. Journal of Coastal Research,...

In this study, numerical analysis of viscous flows is carried out based on the unstructured grid. There exist some difficulties in expressing and computing numerical derivatives on the unstructured grid due to lack of the structured characteristics. The general computer algorithms are developed to perform numerical derivatives easily and extended to be applicable to various geometries composed of hybrid meshes. And the optimal method of strongly implicit procedure is newly contrived to accelerate the rate of convergence in solving the pressure Poisson equation. To verify numerical schemes, the driven cavity problems of 2 and 3 dimension are simulated. The numerical results are compared with others and our numerical schemes are shown to be valid.

To evaluate a multigrid-based solver for the pressure Poisson equation (PPE) with Galerkin coarsening, which works directly on the specified domain, for the computation of relative pressure fields from velocity MRI data.We compared the proposed structure-defined Poisson solver to other popular Poisson solvers working on unmodified rectangular and modified quasirectangular domains using synthetic and in vitro phantoms in which the mathematical solution of the pressure field is known, as well as on in vivo MRI velocity measurements of aortic blood flow dynamics.All three PPE solvers gave accurate results for convex computational domains. Using a rectangular or quasirectangular domain on a more complicated domain, like a c-shape, revealed a systematic underestimation of the pressure amplitudes, while the proposed PPE solver, working directly on the specified domain, provided accurate estimates of the relative pressure fields.Popular iterative approaches with quasirectangular computational domains can lead to significant systematic underestimation of the pressure amplitude. We suggest using a multigrid-based PPE solver with Galerkin coarsening, which works directly on the structure-defined computational domain. This solver provides accurate estimates of the relative pressure fields for both simple and complex geometries with additional significant improvements with respect to execution speed.

In this paper, a parallel monolithic method for shell-fluid interaction based on the consistent Pressure Poisson Equation (PPE) is developed and its parallel computational efficiency is demonstrated. The Conjugate Gradient (CG) method without any preconditioner works well to solve the consistent PPE, even though the coefficient matrix of the original coupled equation system becomes ill-conditioned due to (a) the inhomogeneity of submatrix elements between the fluid and the structure and (b) the ill-conditioned submatrix of shell structure. Thus our parallel monolithic method using the consistent PPE and the CG method without any preconditioner is efficient for parallel analyses of shell-fluid interaction problems. The present parallel solution procedure is based on the mesh decomposition. To demonstrate the performances of the developed method, it is applied to simulate the vibration of an elastic plate situated in the wake of a rectangular prism and a flapping elastic wing in quiescent fluid.

In Sani et al. (Int. J. Numer. Meth. Fluids 2006; 50:673–682), the authors claim to provide a proof of well-posedness for certain formulations of the Navier–Stokes equations for incompressible flow. We consider the proof of their main Theorem 1 incomplete, and point out some inconsistencies in the above paper. Copyright © 2008 John Wiley & Sons, Ltd.

In this paper, a parallel monolithic method for shell-fluid interaction based on the consistent Pressure Poisson Equation (PPE) is developed and its parallel computational efficiency is demonstrated. The previous and present studies show that iterative solvers without preconditioning work well to solve the PPE, even though the coefficient matrix of the original linearized coupled equations becomes to be ill-conditioned. As a consequence, combining with the iterative solvers without preconditioning parallelized based on the mesh decomposition, the developed method can archive efficient parallel computation. To demonstrate the performances of the developed method, it is applied to simulate the vibration of an elastic plate situated in the wake of a rectangular cylinder and a flapping elastic wing in fluid.

The characteristics of fluid forces on a rotationally oscillating circular cylinder in a uniform flow are studied experimentally at various forcing frequencies and rotational amplitudes of cylinder oscillation. The measurements are made on the pressure fields around the circular cylinder by using the velocity data measured by PIV in conjunction with the pressure Poisson equation. The present result indicates that the fluid forces are enhanced by the low-frequency oscillation and are reduced at high-frequency oscillation, which are due to the modification of the wake structure by the influence of rotational oscillation. This trend is further magnified by an increase in rotational amplitude.

This paper presents an improved incompressible smoothed particle hydrodynamics (ISPH) method for wave impact applications. In most conventional ISPH techniques the source term of the pressure Poisson equation (PPE) is usually treated by either a density invariant or a velocity divergence-free formulation. In this work, both the density invariant and velocity divergence free formulations are combined in a weighted average form to determine the source term. The model is then applied to two problems: (1) dam-breaking wave impact on a vertical wall and (2) solitary wave run-up and impact on a coastal structure. The computational results have indicated that the combined source term treatment can predict the wave impact pressure and force more accurately compared with using either formulation alone. It was further found that depending on the application case, the influence of the density invariant and divergence-free parts could be quite different. For the more violent wave impact case, the divergence-f...

SUMMARY Solving the incompressible Navier‐Stokes equations requires special care if the velocity field is not discretely divergence-free. Approximate projection methods and many pressure Poisson equation methods fall into this category. The approximate projection operator does not dampen high frequency modes that represent a local decoupling of the velocity field. For robust behavior, filtering is necessary. This is especially true in two instances that were studied: long-term integrations and large density jumps. Projection-based filters and velocity-based filters are derived and discussed. A cell-centered velocity filter, in conjunction with a vertex-projection filter, was found to be the most effective in the widest range of cases. © 1998 John Wiley & Sons, Ltd.

The Smoothed Particle Hydrodynamics (SPH) method is a meshless discretization method for solving, e.g., the Navier-Stokes equations. By now, it is used for hydraulic problems as well as for solid bodies. In general, there are two distinguishable approaches for incompressible fluid flows. One is called weakly compressible SPH (WCSPH) and the other is called truly incompressible SPH (ISPH). The main difference between these two approaches is the way of pressure evaluation. In WCSPH, a state equation is used, while in ISPH the pressure Poisson equation is solved. Each approach has its advantages as well as its disadvantages, for example the complexity of the numerical algorithm for WCSPH is smaller than for ISPH, but the pressure field is more accurate for ISPH. In this work, two representative examples are studied. The simulations were performed with two different codes, one developed at the Institute of Engineering and Computational Mechanics and one at the Institute of Chemical Process Engineering. It is the aim of this work to show some properties of WCSPH and ISPH as well as to compare two different implementations that, in detail, are very complex. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We consider the time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, written in terms of velocity and pressure. A parallel algorithm, based on a direction splitting approach is implemented. We are targeting the massively parallel computer as well as clusters consisting of many-core nodes. The implementation was tested on the IBM Blue Gene/P supercomputer and two Linux clusters. We compared the results from the direction splitting algorithm with the results from a state-of-the-art Finite Element software package for solving of Stokes equation.

In our work, we consider the time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, written in terms of velocity and pressure. For this problem, a parallel algorithm based on a novel direction splitting approach is developed. Here, the pressure equation is derived from a perturbed form of the continuity equation, in which the incompressibility constraint is penalized in a negative norm induced by the direction splitting. The scheme used in the algorithm is composed of two parts: (i) velocity prediction, and (ii) pressure correction. This is a Crank‐Nicolson‐type two‐stage time integration scheme for two and three dimensional parabolic problems in which the second‐order derivative, with respect to each space variable, is treated implicitly while the other variable is made explicit at each time sub‐step. In order to achieve a good parallel performance the solution of the Poison problem for the pressure correction is replaced by solving a sequence of one‐dimensional secon...

A second-order accurate numerical procedure is presented for the solution of the incompressible Navier-Stokes equations with immersed boundaries in the formulation proposed by Peller et al. [5]. In particular we derive exact constraints for the pressure at immersed solid walls and show that the resulting Poisson equation is formally identical to the elliptic problems governing flows in porous media. An efficient iterative procedure for the computation of the pressure is then obtained by adapting the iterative-multi-scale-finite-volume procedure by Hajibeygi et al. [2].

Free surface problems in fluid mechanics are of a great applied importance, and that’s why they rouse many researchers to excitement. Numerical simulations of such problems, using the so-called meshless methods, become more and more popular today. One of the subsets of these methods is the class of meshless particle methods, which don’t use any mesh during the whole numerical simulation process, and therefore allow solving the problems with large deformations and with failure of problem domain connectivity. These reasons cause great popularity of these methods in the sphere of numerical simulation of free surface problems.

We present a novel, incompressible fluid simulation method based on the Lagrangian Smoothed Particle Hydrodynamics (SPH) model. In our method, incompressibility is enforced by using a prediction-correction scheme to determine the particle pressures. For this, the information about density fluctuations is actively propagated through the fluid and pressure values are updated until the targeted density is satisfied. With this approach, we avoid the computational expenses of solving a pressure Poisson equation, while still being able to use large time steps in the simulation. The achieved results show that our predictive-corrective incompressible SPH (PCISPH) method clearly outperforms the commonly used weakly compressible SPH (WCSPH) model by more than an order of magnitude while the computations are in good agreement with the WCSPH results.

The primary d i f f i c u l t y in computing incompressible flows is associated with f inding a sat is factory way to l ink changes in the veloc i ty f i e ld to changes in the pressure f i e l d . Of the several generic choices that are avai lable, including stream func t ion -vo r t i c i t y , v e l o c i t y v o r t i c i t y and pr im i t i ve variables formulations, we here consider one of the la t te r . Pr imit ive variables techniques can broadly be divided into methods based upon a pressure Poisson equation I -4, and methods based upon a r t i f i c i a l compressibi l i ty 5-I0. In the present paper, we consider a d i rect marching procedure that is phi losophical ly related to a r t i f i c i a l compressibi l i ty methods, although i t does not introduce a f i c t i t i o u s time der ivat ive into the cont inui ty equation. The par t icu lar method chosen is completely analogous to compressible flow schemes based upon f lux difference s p l i t t i n g l l , 12. The f lux s p l i t t i n g procedures we use for d i rect time-marching solutions of the unsteady incompressible equations are developed on the basis of the Euler equations. This s impl i f ies the notation somewhat and allows us to focus attention on those ( inv isc id) terms that cause the d i f f i c u l t i e s in l ink ing pressure and ve loc i ty . The viscous terms are then added la ter by a simple, straightforward procedure. The incompressible equations are wri t ten in the general conservation law form

For an adiabatic (q i = 0) and nonviscous (inviscid) fluid (μ = 0 and λ = 0) from (13) of the Introduction, $$\frac{{dS}}{{dt}} = 0$$ (2.1)

In this chapter, we explain the fundamental methodologies for theoretical studies stated in Chaps. 3, 5, 7 and 8, which correspond to facilities utilized in experimental studies in Chaps. 1,2,4 and 6. These methodologies consist of a mathematical part and a numerical one, which have been developed by the authors to promote the studies concerned. These methodologies are combined to obtain fruitful results in the computer which can be observed in the form of the many figures included in this book. They have contributed to deeper understanding of remarkable works of nature at environmental margins.

A major assumption of previously published PIV measurements in excised larynges, is that the vortices seen directly above the glottal exit during closing are due to the flow separation vortices (FSV) that formed in the glottis. This assumption needed experimental validation. In addition, the pressures associated with the vortices above the vocal folds may be different than the pressures generated by the intraglottal FSV. Previous studies also relied on images of the glottal opening taken from above of the folds to evaluate the displacement of the folds. This method cannot separate the dynamic of the folds that occurs along their superior and inferior edges. The current study uses a major modification of the PIV techniques previously described to simultaneously measure intraglottal velocity fields and intraglottal geometry. The intraglottal pressure distribution is computed from the velocity measurements by solving the pressure Poisson equation. The results show that strong negative pressure is formed towa...

This paper focuses on the application of the Modified Finite Particle Method (MFPM) on incompressibile elasticity problems. MFPM belongs to the class of meshless methods, nowadays widely investigated due to their characteristics of being totally free of any kind of grid or mesh. This characteristic makes meshless methods potentially useful for the study of large deformations problems and fluid dynamics. In particular, the aim of the work is to compare the results obtained with a simple displacement-based formulation, in the limit of incompressibility, and some formulations proposed in the literature for full incompressibility, where the typical divergence-free constraint is replaced by a different equation, the so-called Pressure Poisson Equation. The obtained results show that the MFPM achieves the expected second-order accuracy on formulation where the equations imposed as constraint satisfies also the original incompressibility equation. Other formulations, differently, do not satisfy the incompressibility constraint, and thus, they are not successfully applicable with the Modified Finite Particle Method.

Gli aneurismi cerebrali sono dilatazioni patologiche di arterie cerebrali. Queste patologie hanno un intrinseco rischio di rottura con conseguenti emorragie intracraniche. Sebbene i meccanismi di formazione, crescita e rottura degli aneurismi cerebrali non sono ancora del tutto compresi, è comunemente riconosciuto che in questi processi i fattori emodinamici giocano un ruolo molto importante. Le simulazioni numeriche possono fornire utili informazioni sull'emodinamica e possono essere usate per applicazioni cliniche. Nei tradizionali metodi numerici basati su una griglia di calcolo il processo di discretizzazione dei vasi cerebrali sui quali insiste un aneurisma è molto complesso. D’altra parte, il metodo Lagrangiano smoothed particle hydrodynamics (SPH ) è particolarmente adatto per la rappresentazione di domini geometricamente molto complessi, contorni mobili e processi multi-fase. In questo studio di ricerca il metodo SPH viene impiegato per modellare il flusso sanguigno all’interno di aneurismi cerebrali utilizzando un codice di calcolo open-source (PANORMUS-SPH). All’interno di questo codice sono introdotti nuovi algoritmi e procedure per migliorarne l’accuratezza, la stabilità e l’efficienza computazionale al fine di effettuare simulazioni di aneurismi cerebrali. Per risolvere le equazioni guida discretizzate viene adottato l’approccio totalmente incomprimibile (ISPH ). La conservazione della massa è imposta risolvendo un sistema di equazioni di Poisson attraverso il metodo del gradiente biconiugato stabilizzato con un algoritmo di precondizionamento. Si propone una procedura innovativa per trattare confini aperti nel metodo SPH, consentendo di imporre condizioni di Dirichlet per la pressione nelle sezioni di ingresso e di uscita oppure il profilo di velocità all’ingresso. La conservazione della massa, che è un compito arduo nella modellazione Lagrangiana di domini con confini aperti, è garantita durante la procedura. Un’originale tecnica multi-risoluzione è sviluppata nel modello SPH. Questo approccio è basato sulla decomposizione del dominio in subdomini in ognuno dei quali viene utilizzato un appropriato livello di discretizzazione. La tecnica è cruciale quando si studiano domini geometricamente irregolari, come i vasi cerebrali, per cui l’uso di un’uniforme dimensione delle particelle potrebbe risultare insostenibile in termini di costi computazionali e richieste di memoria. L’efficienza computazionale del codice SPH è notevolmente migliorata attraverso la sua parallelizzazione basata sul paradigma Message Passing Interface. L’algoritmo di distribuzione del dominio permette di ottenere un carico ben bilanciato anche con domini altamente irregolari suddivisi attraverso l’approccio multi-risoluzione. Nei trattamenti endovascolari di aneurismi cerebrali la stabilità del coagulo di sangue che si forma all’interno della sacca è un fattore chiave per il processo di guarigione. Pertanto, l’analisi del processo di coagulazione è estremamente importante per valutare i risultati del trattamento. Sfruttando la natura Lagrangiana del metodo SPH, in questo studio sono implementati i modelli del trasporto di un tracciate, del tempo di residenza e dell’attivazione meccanica delle piastrine, ciò al fine di gettare le basi per il futuro sviluppo di un modello di coagulo di sangue. Una valutazione delle prestazioni dei miglioramenti numerici implementati è condotta confrontando i risultati di casi test di riferimento, che includono anche geometrie di aneurismi ideali e reali, con soluzioni analitiche e numeriche disponibili e con misure sperimentali. Cerebral aneurysms are pathological dilations of brain arteries. These diseases carry an inherent risk of rupture with consequent intracranial hemorrhages. Although the mechanisms of initiation, growth and rupture of cerebral aneurysms are not well understood yet, it is commonly recognized that hemodynamic factors play a very important role in these processes. Numerical simulations can provide useful information on the hemodynamics and can be used for clinical applications. In the traditional grid-based numerical methods the discretization process of cerebral vessels hosting an aneurysm is very challenging. On the other hand, the Lagrangian mesh-less smoothed particle hydrodynamics (SPH) is very suitable for representing geometrically complex domains, moving boundaries and multi- phase processes. In this research study the SPH method is employed to model blood flow in cerebral aneurysms using an open-source code (PANORMUS-SPH). New algorithms and procedures are introduced in the code to improve the accuracy, stability and computational efficiency of the numerical model, focusing on cerebral aneurysm simulations. The truly incompressible SPH (ISPH ) approach is used to solve the discretized governing equations. To this aim, the mass conservation is enforced by solving a system of Pressure Poisson Equations using the preconditioned BiConjugate Gradient STABilized method. A novel procedure is proposed to treat open-boundaries in SPH, allowing to set Dirichlet pressure boundary conditions at the inlet and outlet sections or to impose the velocity profile at the inflow. Mass conservation is guaranteed during the procedure, which is a challenging task in Lagrangian modeling of domains with open-boundaries. An innovative multi-resolution technique is developed in the SPH model. This approach is based on the domain decomposition into subdomains in each of which a proper refinement is used. The technique is crucial when dealing with geometrically irregular domains, such as cerebral vessels, for which the use of a uniform particle distribution may become unsustainable in terms of CPU time and memory requirements. The computational efficiency of the SPH code is largely improved through its complete parallelization based on the Message Passing Interface paradigm. The implemented domain distribution algorithm ensures a well-balanced load even with highly irregular domains subdivided through the multi-resolution approach. In endovascular treatments of cerebral aneurysms the stability of the blood clot forming inside the aneurysm sac is a key factor for the healing process. The analysis of the blood clotting process is thus extremely important to evaluate the treatment outcomes. In this study tracer transport, residence time and mechanical platelet activation models are implemented in the SPH code in order to lay the groundwork for a future SPH-based blood clot model. A performance evaluation of the implemented numerical improvements is conducted through comparison of the results with available analytical and numerical solutions and with experimental measures obtained in benchmark test cases including also ideal and real aneurysm geometries.

This paper describes an efficient monolithic method for shell-fluid interaction problems based on the fluid pressure Poisson equation (PPE). The PPE is derived so as to be consistent with the coupled equation system for the shell-fluid interaction. In the proposed method, the fluid pressure is derived implicitly so as to satisfy the incompressibility constraint and all the other unknown variables except those for the shell are derived explicitly. The coefficient matrix of the PPE is well-conditioned even if the structure is very stiff or heavy compared to the fluid, and even if the ill-conditioned submatrix is generated due to the shell elements. These characteristics are successfully utilized to combine the proposed method with the standard conjugate gradient method. To demonstrate fundamental perfermances of the proposed method, it is applied to evaluate the vibration characteristics of a thin elastic cantilever plate in a quiescent fluid.