1,404 research outputs found
Lattice-Boltzmann LES modelling of a full-scale, biogas-mixed anaerobic digester
An Euler–Lagrange multicomponent, non-Newtonian Lattice-Boltzmann method is applied for the first time to model a full-scale gas-mixed anaerobic digester for wastewater treatment. Rheology is modelled through a power-law model and, for the first time in gas-mixed anaerobic digestion modelling, turbulence is modelled through a Smagorinsky Large Eddy Simulation model. The hydrodynamics of the digester is studied by analysing flow and viscosity patterns, and assessing the degree of mixing through the Uniformity Index method. Results show independence from the grid size and the number of Lagrangian substeps employed for the Lagrangian sub-grid simulation model. Flow patterns are shown to depend mildly on the choice of bubble size, but not the asymptotic degree of mixing. Numerical runs of the model are compared to previous results in the literature, from a second-ordered Finite-Volume Method approach, and demonstrate an improvement, compared to literature data, of 1000-fold computational efficiency, massive parallelizability and much finer attainable spatial resolution. Whilst previous research concluded that the application of LES to full-scale anaerobic digestion mixing is unfeasible because of high computational expense, the increase in computational efficiency demonstrated here, now makes LES a feasible option to industries and consultancies
A new ghost-cell/level-set method for three-dimensional flows
This study presents the implementation of a tailored ghost cell method in Hydro3D, an open-source large eddy simulation (LES) code for computational fluid dynamics based on the finite difference method. The former model for studying the interaction between an immersed object and the fluid flow is the immersed boundary method (IBM) which has been validated for a wide range of Reynolds number flows. However, it is challenging to ensure no-slip and zero gradient boundary conditions on the surface of an immersed body. In order to deal with this, a new sharp-interface ghost-cell method (GCM) is developed for Hydro3D. The code also employs a level-set method to capture the motion of the air-water interface and solves the spatially filtered Navier-Stokes equations in a Cartesian staggered grid with the fractional step method. Both the new GCM and IBM are compared in a single numerical framework. They are applied to simulate benchmark cases in order to validate the numerical results, which mainly comprise single-phase flow over infinite circular and square cylinders for low- and high-Reynolds number flows along with two-phase dam-break flows with a vertical cylinder, in which a good agreement is obtained with other numerical studies and laboratory experiments
Suitability of immersed-boundary methods for high-fidelity computational aeroacoustics
This work presents a preliminary assessment of the suitability of the immersed boundary method (IBM) for high-fidelity direct sound computations. A ghost-cell IBM is implemented in conjunction with a recently developed non-dissipative and robust numerical framework based on kinetic-energy and pressure-equilibrium preserving discretizations. The strategy is validated using the well-known canonical benchmark of acoustic scattering of a steady cylinder, providing
accurate results and thus holding great promise for its application in complex scenarios.Postprint (published version
Finite difference method in prolate spheroidal coordinates for freely suspended spheroidal particles in linear flows of viscous and viscoelastic fluids
A finite difference scheme is used to develop a numerical method to solve the
flow of an unbounded viscoelastic fluid with zero to moderate inertia around a
prolate spheroidal particle. The equations are written in prolate spheroidal
coordinates, and the shape of the particle is exactly resolved as one of the
coordinate surfaces representing the inner boundary of the computational
domain. As the prolate spheroidal grid is naturally clustered near the particle
surface, good resolution is obtained in the regions where the gradients of
relevant flow variables are most significant. This coordinate system also
allows large domain sizes with a reasonable number of mesh points to simulate
unbounded fluid around a particle. Changing the aspect ratio of the inner
computational boundary enables simulations of different particle shapes ranging
from a sphere to a slender fiber. Numerical studies of the latter particle
shape allow testing of slender body theories. The mass and momentum equations
are solved with a Schur complement approach allowing us to solve the zero
inertia case necessary to isolate the viscoelastic effects. The singularities
associated with the coordinate system are overcome using L'Hopital's rule. A
straightforward imposition of conditions representing a time-varying
combination of linear flows on the outer boundary allows us to study various
flows with the same computational domain geometry. {For the special but
important case of zero fluid and particle inertia we obtain a novel formulation
that satisfies the force- and torque-free constraint in an iteration-free
manner.} The numerical method is demonstrated for various flows of Newtonian
and viscoelastic fluids around spheres and spheroids (including those with
large aspect ratio). Good agreement is demonstrated with existing theoretical
and numerical results.Comment: 32 pages, 12 figures. Accepted at Journal of Computational Physic
A projection hybrid high order finite volume/finite element method for incompressible turbulent flows
In this paper the projection hybrid FV/FE method presented in Busto et al.
2014 is extended to account for species transport equations. Furthermore,
turbulent regimes are also considered thanks to the model.
Regarding the transport diffusion stage new schemes of high order of accuracy
are developed. The CVC Kolgan-type scheme and ADER methodology are extended to
3D. The latter is modified in order to profit from the dual mesh employed by
the projection algorithm and the derivatives involved in the diffusion term are
discretized using a Galerkin approach. The accuracy and stability analysis of
the new method are carried out for the advection-diffusion-reaction equation.
Within the projection stage the pressure correction is computed by a piecewise
linear finite element method. Numerical results are presented, aimed at
verifying the formal order of accuracy of the scheme and to assess the
performance of the method on several realistic test problems.Comment: arXiv admin note: text overlap with arXiv:1802.1058
Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks
This work concerns the enrichment of Discontinuous Galerkin (DG) bases, so
that the resulting scheme provides a much better approximation of steady
solutions to hyperbolic systems of balance laws. The basis enrichment leverages
a prior -- an approximation of the steady solution -- which we propose to
compute using a Physics-Informed Neural Network (PINN). To that end, after
presenting the classical DG scheme, we show how to enrich its basis with a
prior. Convergence results and error estimates follow, in which we prove that
the basis with prior does not change the order of convergence, and that the
error constant is improved. To construct the prior, we elect to use parametric
PINNs, which we introduce, as well as the algorithms to construct a prior from
PINNs. We finally perform several validation experiments on four different
hyperbolic balance laws to highlight the properties of the scheme. Namely, we
show that the DG scheme with prior is much more accurate on steady solutions
than the DG scheme without prior, while retaining the same approximation
quality on unsteady solutions
A stable free-surface boundary solution method for fully nonlinear potential flow models
This paper presents a stable method for solving the kinematic boundary condition equation (KBC) in fully nonlinear potential flow (FNPF) models. The method is motivated by a total variation diminishing (TVD) approach, which makes it especially applicable to advection-dominated partial differential equations such as the KBC. It is also simple, and can be easily implemented in existing finite volume-based FNPF models for wave hydrodynamics. The method is systematically assessed through a series of test cases: the propagation of second and fifth-order Stokes waves; focused wave propagation; and wave shoaling in both 2 and 3-D. It was found that the method stabilised the computation in every instance: it successfully eliminated the sawtooth instability, which commonly arises in FNPF models, without a reduction in computational efficiency. Consequently, we avoided the use of undesirable stabilisation techniques that involve artificial dissipation such as low-order smoothing. The method is also accurate: it produced satisfactory numerical solutions that agreed well with experimental, analytical and other published numerical results. It was also found that the method is superior than classical schemes in terms of energy conservation, applicability, and efficiency—all salient features that are essential for large-scale and long-time simulations
A Simple Embedding Method for Scalar Hyperbolic Conservation Laws on Implicit Surfaces
We have developed a new embedding method for solving scalar hyperbolic
conservation laws on surfaces. The approach represents the interface implicitly
by a signed distance function following the typical level set method and some
embedding methods. Instead of solving the equation explicitly on the surface,
we introduce a modified partial differential equation in a small neighborhood
of the interface. This embedding equation is developed based on a push-forward
operator that can extend any tangential flux vectors from the surface to a
neighboring level surface. This operator is easy to compute and involves only
the level set function and the corresponding Hessian. The resulting solution is
constant in the normal direction of the interface. To demonstrate the accuracy
and effectiveness of our method, we provide some two- and three-dimensional
examples
Energy Stable and Structure-Preserving Schemes for the Stochastic Galerkin Shallow Water Equations
The shallow water flow model is widely used to describe water flows in
rivers, lakes, and coastal areas. Accounting for uncertainty in the
corresponding transport-dominated nonlinear PDE models presents theoretical and
numerical challenges that motivate the central advances of this paper. Starting
with a spatially one-dimensional hyperbolicity-preserving,
positivity-preserving stochastic Galerkin formulation of the
parametric/uncertain shallow water equations, we derive an entropy-entropy flux
pair for the system. We exploit this entropy-entropy flux pair to construct
structure-preserving second-order energy conservative, and first- and
second-order energy stable finite volume schemes for the stochastic Galerkin
shallow water system. The performance of the methods is illustrated on several
numerical experiments
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