pinecone/core-2020-05-10-deduplication huggingface dataset:
Implementation of semi-discrete, non-staggered central schemes in a collated, polyhedral, finite volume framework, for high-speed viscous flows

We describe the implementation of a computational fluid dynamics solver for the simulation of high-speed flows. It comprises a finite volume (FV) discretization using semi-discrete, non-staggered central schemes for colocated variables prescribed on a mesh of polyhedral cells that have an arbitrary number of faces. We describe the solver in detail, explaining the choice of variables whose face interpolation is limited, the choice of limiter, and a method for limiting the interpolation of a vector field that is independent of the coordinate system. The solution of momentum and energy transport in the Navier-Stokes equations uses an operator-splitting approach: first, we solve an explicit predictor equation for the convection of conserved variables, then an implicit corrector equation for the diffusion of primitive variables. Our solver is validated against four sets of data: (1) an analytical solution of the one-dimensional shock tube case; (2) a numerical solution of two dimensional, transient, supersonic flow over a forward-facing step; (3) interferogram density measurements of a supersonic jet from a circular nozzle; and (4) pressure and heat transfer measurements in hypersonic flow over a 25-55 biconic. Our results indicate that the central-upwind scheme of Kurganov, Noelle and Petrova (SIAM J. Sci. Comput. 2001; 23:707-740) is competitive with the best methods previously published (e.g. piecewise parabolic method, Roe solver with van Leer limiting) and that it is inherently simple and well suited to a colocated, polyhedral FV framework. Copyright © 2009 John Wiley & Sons, Ltd
Calibration of POD reduced-order models using Tikhonov regularization

International audienceIn this paper we compare various methods of calibration that can be used in practice to improve the accuracy of reduced-order models based on Proper Orthogonal Decomposition. The bench mark configuration retained corresponds to a case of relatively simple dynamics: a two-dimensional flow around a cylinder for a Reynolds number of 200. We generalize to the first and second-order the method of calibration based on Tikhonov regularization recently used in [1]. Finally, we show that for this flow configuration this procedure is the most effective in terms of reduction of errors
An efficient scaled boundary FEM model for wave interaction with a nonuniform porous cylinder

The scaled boundary finite-element method (SBFEM) by Tao et al. (Comput. Methods Appl. Mech. Engrg 2007; 197:232-242) is only applicable for wave scattering problems by a structure of homogenous material. In this paper, the SBFEM is extended to deal with the interaction of water waves and porous offshore structure with a partially solid wall or opening. The cylindrical structure is considered as a circular cylinder of anisotropic material in the form of variable porosity. A central feature of the newly extended method is that the non-homogenous term caused by the complex configuration of the structure is processed by introducing a variable porous-effect parameter G. This leads to the final scaled boundary finite-element equation is still homogenous and can be solved in a similar manner. The modified SBFEM thus remains a semi-analytical fundamental-solution-less method. Numerical experiments in water wave interaction with a typical coastal/offshore structure-a cylinder with a partially solid wall or opening attest to the efficacy and accuracy of the proposed approach.Griffith Sciences, Griffith School of EngineeringFull Tex
Discontinuous Galerkin solution of preconditioned Euler equations for very low Mach number flows

In this work  we present a Discontinuous Galerkin (DG) method designed to improve the accuracy and efficiency of the solution at very low Mach number flows using an explicit scheme for the temporal discretization of the compressible Euler equations. The algorithm is based on a perturbed formulation of the governing equ\ud
ations and employs the preconditioning of both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). The performance of the method is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different very low Mach numbers using various degrees of polynomial approximations. We present numerical results computed with and without perturbed variables which illustrate the influence of the cancellation errors on both the convergence and the accuracy of the DG solutions at low Mach numbers
An EBE finite element method for simulating nonlinear flows in rotating spheroidal cavities

Many planetary and astrophysical bodies are rotating rapidly, fluidic and, as a consequence of rapid rotation, in the shape of an ablate spheroid. We present an efficient element-by-element (EBE) finite element method for the numerical simulation of nonlinear flows in rotating incompressible fluids that are confined in an ablate spheroidal cavity with arbitrary eccentricity. Our focus is placed on temporal and spatial tetrahedral discretization of the EBE finite element method in spheroidal geometry, the EBE parallelization scheme and the validation of the nonlinear spheroidal code via both the constructed exact nonlinear solution and the special resonant forcing in the inviscid limit. Copyright © 2009 John Wiley & Sons, Ltd.postprin
High-order semi-implicit time-integrators for a triangular discontinuous Galerkin oceanic shallow water model

The Discontinuous Galerkin Coastal Ocean Model (DGCOM) is a two-dimensional shallow water model for simulating coastal ocean processes.The article of record may be found at http://www.doi.org/10.1002/fld.2118We extend the explicit in time high-order triangular discontinuous Galerkin (DG) method to semi-implicit (SI) and then apply the algorithm to the two-dimensional oceanic shallow water equations; we implement high-order SI time-integrators using the backward difference formulas from orders one to six. The reason for changing the time-integration method from explicit to SI is that explicit methods require a very small time step in order to maintain stability, especially for high-order DG methods. Changing the time- integration method to SI allows one to circumvent the stability criterion due to the gravity waves, which for most shallow water applications are the fastest waves in the system (the exception being supercritical flow where the Froude number is greater than one). The challenge of constructing a SI method for a DG model is that the DG machinery requires not only the standard finite element-type area integrals, but also the finite volume-type boundary integrals as well. These boundary integrals pose the biggest challenge in a SI discretization because they require the construction of a Riemann solver that is the true linear representation of the nonlinear Riemann problem; if this condition is not satisfied then the resulting numerical method will not be consistent with the continuous equations. In this paper we couple the SI time-integrators with the DG method while maintaining most of the usual attributes associated with DG methods such as: high-order accuracy (in both space and time), parallel efficiency, excellent stability, and conservation. The only property lost is that of a compact communication stencil typical of time-explicit DG methods; implicit methods will always require a much larger communication stencil. We apply the new high-order SI DG method to the shallow water equations and show results for many standard test cases of oceanic interest such as: standing, Kelvin and Rossby soliton waves, and the Stommel problem. The results show that the new high-order SI DG model, that has already been shown to yield exponentially convergent solutions in space for smooth problems, results in a more efficient model than its explicit counterpart. Furthermore, for those problems where the spatial resolution is sufficiently high compared with the length scales of the flow, the capacity to use high-order (HO) time-integrators is a necessary complement to the employment of HO space discretizations, since the total numerical error would be otherwise dominated by the time discretization error. In fact, in the limit of increasing spatial resolution, it makes little sense to use HO spatial discretizations coupled with low-order time discretizations
Numerical simulations of massively separated turbulent flows

<p>It is well known that most fluid flows observed in nature or encountered in engineering applications are turbulent and involve separation. Fluid flows in turbines, diffusers and channels with sudden expansions are among the widely observed areas where separation substantially alters the flow field and gives rise to complex flow dynamics. Such types of flows are referred to as internal flows since they are confined within solid surfaces and predominantly involve the generation or utilization of mechanical power. However, there is also a vast variety of engineering applications where the fluid flows past solid structures, such as the flow of air around an airplane or that of water around a submarine. These are called external flows and as in the former case the downstream evolution of the flow field is crucially influenced by separation.</p><p>The present doctoral thesis addresses both internal and external separated flows by means of direct numerical simulations of the incompressible Navier-Stokes equations. For internal flows, the wall-driven flow in a onesided expansion channel and the pressure-driven flow in a plane channel with a single thin-plate obstruction have been studied in the fully developed turbulent state. Since such geometrical configurations involve spatially developing turbulent flows, proper inflow conditions are to be employed in order to provide a realistic fully turbulent flow at the input. For this purpose, a newly developed technique has been used in order to mimic an infinitely long channel section upstream of the expansion and the obstruction, respectively. With this approach, we are able to gather accurate mean flow and turbulence statistics throughout each flow domain and to explore in detail the instantaneous flow topology in the separated shear layers, recirculation regions as well as the recovery zones.</p><p>For external flows, on the other hand, the flow past a prolate spheroid has been studied. Here, a wide range of Reynolds numbers is taken into consideration. Based on the characteristics of the vortical structures in the wake, the flow past a prolate spheroid is classified as laminar (steady or unsteady), transitional or turbulent. In each flow regime, the characteristic features of the flow are investigated by means of detailed frequency analysis, instantaneous vortex topology and three-dimensional flow visualizations.</p>PhD i marin teknikkPhD in Marine Technolog
Finite Element Framework for Describing Dynamic Wetting Phenomena

The finite element simulation of dynamic wetting phenomena, requiring the
computation of flow in a domain confined by intersecting a liquid-fluid free
surface and a liquid-solid interface, with the three-phase contact line moving
across the solid, is considered. For this class of flows, different finite
element method (FEM) implementations have been proposed in the literature and
these are seen to produce apparently contradictory results. The purpose of this
paper is to develop a robust framework for the FEM simulation of these flows
and then, by performing numerical experiments, provide guidelines for future
investigations. In the new framework, the boundary conditions on the
liquid-solid interface are implemented in a methodologically similar way to
those on the free surface so that the equations at the contact line, where the
interfaces meet, are applied without any ad-hoc alterations. The new
implementation removes the need for complex rotations of the momentum
equations, usually required to apply boundary conditions normal and tangent to
the solid surface. The developed code allows the convergence of the solution to
be studied as the spatial resolution of the computational mesh is varied over
many orders of magnitude. This makes it possible to provide practical
recommendations on the spatial resolution required by a numerical scheme for a
given set of non-dimensional similarity parameters. Furthermore, one can
examine various implementations used in the literature and evaluate their
performance. Finally, it is shown how the framework may be generalized to
account for additional physical effects, such as gradients in surface tensions.
A user-friendly step-by-step guide specifying the entire implementation and
allowing the reader to easily reproduce all presented results is provided in
the Appendix
Cell face velocity alternatives in a structured colocated grid for the unsteady Navier-Stokes equations

PACS: 47.11.+jThe use of a colocated variable arrangement for the numerical solution of ﬂuid ﬂow is becoming more\ud
and more popular due to its coding simplicity. The inherent decoupling of the pressure and velocity ﬁelds\ud
in this arrangement can be handled via a special interpolation procedure for the calculation of the cell\ud
face velocity named pressure-weighted interpolation method (PWIM) (AIAA J. 1983; 21(11):1525–1532).\ud
In this paper a discussion on the alternatives to extend PWIM to unsteady ﬂows is presented along with\ud
a very simple criterion to ascertain if a given interpolation practice will produce steady results that are\ud
relaxation dependent or time step dependent. Following this criterion it will be shown that some prior\ud
schemes presented as time step independent are actually not, although by using special interpolations can\ud
be readily adapted to be. A systematic way of deriving different cell face velocity expressions will be\ud
presented and new formulae free of  t dependence will be derived. Several computational exercises will\ud
accompany the theoretical discussion to support our claimsContract/grant sponsor: Spanish Ministry of Education; contract/grant numbers: CIT-370200-2005-6, ENE-2005-\ud
09214-204-03/ALTPeer reviewe
A conservative momentum exchange algorithm for interaction problem between fluid and deformable particles

This is the peer reviewed version of the following article:Shintaro Takeuchi, Yoshihiko Yuki, Atsushi Ueyama, Takeo Kajishima, "A conservative momentum exchange algorithm for interaction problem between fluid and deformable particles," International Journal for Numerical Methods in Fluids, Vol.64, Issue 10-12, pp.1084-1101, John Wiley & Sons, 2010, which has been published in final form at http://dx.doi.org/10.1002/fld.2272. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving
Central finite volume methods for ideal and shallow water magnetohydrodynamics

We propose two-dimensional central finite volume methods based on our multidimensional extensions of Nessyahu and Tadmor's one-dimensional non-oscillatory central scheme and a constrained transport-type method to solve ideal magnetohydrodynamic problems (MHD) and shallow water magnetohydrodynamic problems (SMHD). The main numerical scheme is second-order accurate both in space and time and uses an original Cartesian grid coupled to a Cartesian- or diamond-staggered dual grid to by-pass the resolution of the Riemann problems at the cell interfaces. To treat the non-vanishing magnetic field/flux divergence we have constructed an adaptation of Evans and Hawley's constrained transport method specifically designed for central schemes. Our numerical results show the efficiency and the potential of the schemePublishedN/
The Moment Guided Monte Carlo Method

In this work we propose a new approach for the numerical simulation of
kinetic equations through Monte Carlo schemes. We introduce a new technique
which permits to reduce the variance of particle methods through a matching
with a set of suitable macroscopic moment equations. In order to guarantee that
the moment equations provide the correct solutions, they are coupled to the
kinetic equation through a non equilibrium term. The basic idea, on which the
method relies, consists in guiding the particle positions and velocities
through moment equations so that the concurrent solution of the moment and
kinetic models furnishes the same macroscopic quantities.Comment: 24 page
Determination of the anisotropic permeability of a carbon cloth gas diffusion layer through X-ray computer micro-tomography and single-phase lattice Boltzmann simulation

This is the peer reviewed version of the following article: RAMA, P. ... et al, 2011. Determination of the anisotropic permeability of a carbon cloth gas diffusion layer through X-ray computer micro-tomography and single-phase lattice Boltzmann simulation. International Journal for Numerical Methods in Fluids, 67 (4), pp. 518 - 530, which has been published in final form at: http://dx.doi.org/10.1002/fld.2378. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.An investigation of the anisotropic permeability of a carbon cloth gas diffusion layer (GDL) based on the integration of X-ray micro-tomography and lattice Boltzmann (LB) simulation is presented. The method involves the generation of a 3D digital model of a carbon cloth GDL as manufactured using X-ray shadow images acquired through X-ray micro-tomography at a resolution of 1.74 µm. The resulting 3D model is then split into 21 volumes and integrated with a LB single-phase numerical solver in order to predict three orthogonal permeability tensors when a pressure difference is prescribed in the through-plane direction. The 21 regions exhibit porosity values in the range of 0.910–0.955, while the average fibre diameter is 4 µm. The results demonstrate that the simulated through-plane permeability is about four times higher than the in-plane permeability for the sample imaged and that the corresponding degrees of anisotropy for the two orthogonal off-principal directions are 0.22 and 0.27. The results reveal that flow channelling can play an important role in gas transport through the GDL structure due to the non-homogeneous porosity distribution through the material. The simulated results are also applied to generate a parametric coefficient for the Kozeny–Carman (KC) method of determining permeability. The current research reveals that by applying the X-ray tomography and LB techniques in a complementary manner, there is a strong potential to gain a deeper understanding of the microscopic fluidic phenomenon in representative models of porous fuel cell structures and how this can influence macroscopic transport characteristics which govern fuel cell performance
Enforcing the non-negativity constraint and maximum principles for
  diffusion with decay on general computational grids

In this paper, we consider anisotropic diffusion with decay, and the
diffusivity coefficient to be a second-order symmetric and positive definite
tensor. It is well-known that this particular equation is a second-order
elliptic equation, and satisfies a maximum principle under certain regularity
assumptions. However, the finite element implementation of the classical
Galerkin formulation for both anisotropic and isotropic diffusion with decay
does not respect the maximum principle.
  We first show that the numerical accuracy of the classical Galerkin
formulation deteriorates dramatically with increase in the decay coefficient
for isotropic medium and violates the discrete maximum principle. However, in
the case of isotropic medium, the extent of violation decreases with mesh
refinement. We then show that, in the case of anisotropic medium, the classical
Galerkin formulation for anisotropic diffusion with decay violates the discrete
maximum principle even at lower values of decay coefficient and does not vanish
with mesh refinement. We then present a methodology for enforcing maximum
principles under the classical Galerkin formulation for anisotropic diffusion
with decay on general computational grids using optimization techniques.
Representative numerical results (which take into account anisotropy and
heterogeneity) are presented to illustrate the performance of the proposed
formulation
Compressible air flow through a collapsing liquid cavity

We present a multiscale approach to simulate the impact of a solid object on
a liquid surface: upon impact a thin liquid sheet is thrown upwards all around
the rim of the impactor while in its wake a large surface cavity forms. Under
the influence of hydrostatic pressure the cavity immediately starts to collapse
and eventually closes in a single point from which a thin, needle-like jet is
ejected. Existing numerical treatments of liquid impact either consider the
surrounding air as an incompressible fluid or neglect air effects altogether.
In contrast, our approach couples a boundary-integral method for the liquid
with a Roe scheme for the gas domain and is thus able to handle the fully
\emph{compressible} gas stream that is pushed out of the collapsing impact
cavity. Taking into account air compressibility is crucial, since, as we show
in this work, the impact crater collapses so violently that the air flow
through the cavity neck attains supersonic velocities already at cavity
diameters larger than 1 mm. Our computational results are validated through
corresponding experimental data.Comment: Submitted to Comput Mec
A high-order upwind control-volume method based on integrated RBFs for fluid-flow problems

This paper is concerned with the development of a high-order upwind conservative discretization method for the simulation of flows of a Newtonian fluid in two dimensions. The fluid-flow domain is discretized using a Cartesian grid from which non-overlapping rectangular control volumes are formed. Line integrals arising from the integration of the diffusion and convection terms over control volumes are evaluated using the middle-point rule. One-dimensional integrated radial basis function schemes using the multiquadric basis function are employed to represent the variations of the field variables along the grid lines. The convection term is effectively treated using an upwind scheme with the deferred-correction strategy. Several highly non-linear test problems governed by the Burgers and the Navier–Stokes equations are simulated, which show that the proposed technique is stable, accurate and converges well.
Comparison of outflow boundary conditions for subsonic aeroacoustic simulations

Aeroacoustics simulations require much more precise boundary conditions than classical aerodynamics. Two classes of non-reflecting boundary conditions for aeroacoustics are compared in the present work: characteristic analysis based methods and Tam and Dong approach. In characteristic methods, waves are identified and manipulated at the boundaries while Tam and Dong use modified linearized Euler equations in a buffer zone near outlets to mimic a non-reflecting boundary. The principles of both approaches are recalled and recent characteristic methods incorporating the treatment of transverse terms are discussed. Three characteristic techniques (the original NSCBC formulation of Poinsot and Lele and two versions of the modified method of Yoo and Im) are compared to the Tam and Dong method for four typical aeroacoustics problems: vortex convection on a uniform flow, vortex convection on a shear flow, acoustic propagation from a monopole and from a dipole. Results demonstrate that the Tam and Dong method generally provides the best results and is a serious alternative solution to characteristic methods even though its implementation might require more care than usual NSCBC approaches