pinecone/core-2020-05-10-deduplication huggingface dataset:
An adaptive finite element method for the modeling of the equilibrium of red blood cells

International audienceThis contribution is concerned with a the numerical modeling of an isolated red blood cell (RBC), and more generally of phospholipid membranes. We propose an adaptive Eulerian finite element approximation, based on the level set method, of a shape optimization problem arising in the study of RBC's equilibrium. We simulate the equilibrium shapes that minimize the elastic bending energy under prescribed constraints of fixed volume and surface area. An anisotropic mesh adaptation technique is used in the vicinity of the cell's membrane to enhance the robustness of the method. Efficient time and spatial discretizations are considered and implemented. We address in detail the main features of the proposed method and finally we report several numerical experiments in the two-dimensional and the three-dimensional axisymmetric cases. The effectiveness of the numerical method is further demonstrated through numerical comparisons with semi-analytical solutions provided by a reduced order model
An embedded approach for immiscible multi-fluid problems

An embedded formulation for the simulation of immiscible multi-fluid problems is proposed. The method is particularly designed for handling gas-liquid systems. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is exactly defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated, and its potential applications are shown. Copyright (C) 2015 John Wiley & Sons, Ltd.Peer ReviewedPostprint (author's final draft
Fujiwhara interaction of tropical cyclone scale vortices using a
  weighted residual collocation method

The fundamental interaction between tropical cyclones was investigated
through a series of water tank experiements by Fujiwhara [20, 21, 22]. However,
a complete understanding of tropical cyclones remains an open research
challenge although there have been numerous investigations through measurments
with aircrafts/satellites, as well as with numerical simulations. This article
presents a computational model for simulating the interaction between cyclones.
The proposed numerical method is presented briefly, where the time integration
is performed by projecting the discrete system onto a Krylov subspace. The
method filters the large scale fluid dynamics using a multiresolution
approximation, and the unresolved dynamics is modeled with a Smagorinsky type
subgrid scale parameterization scheme. Numerical experiments with Fujiwhara
interactions are considered to verify modeling accuracy. An excellent agreement
between the present simulation and a reference simulation at Re = 5000 has been
demonstrated. At Re = 37440, the kinetic energy of cyclones is seen
consolidated into larger scales with concurrent enstrophy cascade, suggesting a
steady increase of energy containing scales, a phenomena that is typical in
two-dimensional turbulence theory. The primary results of this article suggest
a novel avenue for addressing some of the computational challenges of mesoscale
atmospheric circulations.Comment: 24 pages, 11 figures, submitte
A local mesh refinement approach for large-eddy simulations of turbulent flows

In this paper, a local mesh refinement (LMR) scheme on Cartesian grids for large-eddy simulations is presented. The approach improves the calculation of ghost cell pressures and velocities and combines LMR with high-order interpolation schemes at the LMR interface and throughout the rest of the computational domain to ensure smooth and accurate transition of variables between grids of different resolution. The approach is validated for turbulent channel flow and flow over a matrix of wall-mounted cubes for which reliable numerical and experimental data are available. Comparisons of predicted first-order and second-order turbulence statistics with the validation data demonstrated a convincing agreement. Importantly, it is shown that mean streamwise velocities and fluctuating turbulence quantities transition smoothly across coarse-to-fine and fine-to-coarse interfaces
Bubble-based stabilized finite element methods for time-dependent convection–diffusion–reaction problems

In this paper, we propose a numerical algorithm for time-dependent convection–diffusion–reaction problems and compare its performance with the well-known numerical methods in the literature. Time discretization is performed by using fractional-step θ-scheme, while an economical form of the residual-free bubble method is used for the space discretization. We compare the proposed algorithm with the classical stabilized finite element methods over several benchmark problems for a wide range of problem configurations. The effect of the order in the sequence of discretization (in time and in space) to the quality of the approximation is also investigated. Numerical experiments show the improvement through the proposed algorithm over the classical methods in either cases
A variable-fidelity aerodynamic model using proper orthogonal decomposition

A variable-fidelity aerodynamic model based on proper orthogonal decomposition (POD) of an ensemble of computational fluid dynamics (CFD) solutions at different parameters is presented in this article. The ensemble of CFD solutions consists of two subsets of numerical solutions or snapshots computed at two different nominal orders of accuracy or discretization. These two subsets are referred to as the low-fidelity and high-fidelity solutions or data, whereby the low fidelity corresponds with computations made at the lower nominal order of accuracy or coarser discretization. In this model, the relatively inexpensive low-fidelity data and the more accurate but expensive high-fidelity data are considered altogether to devise an efficient prediction methodology involving as few high-fidelity analyses as possible, while obtaining the desired level of detail and accuracy. The POD of this set of variable-fidelity data produces an optimal linear set of orthogonal basis vectors that best describe the ensemble of numerical solutions altogether. These solutions are projected onto this set of basis vectors to provide a finite set of scalar coefficients that represent either the low-fidelity or high-fidelity solutions. Subsequently, a global response surface is constructed through this set of projection coefficients for each basis vector, which allows predictions to be made at parameter combinations not in the original set of observations. This approach is used to predict supersonic flow over a slender configuration using Navier–Stokes solutions that are computed at two different levels of nominal accuracy as the low-fidelity and high-fidelity solutions. The numerical examples show that the proposed model is efficient and sufficiently accurate.This work was conducted with support from the Engineering and Physical Sciences Research Council (EPSRC) Centre of Excellence for Industrial Sustainability grant number EP/I033351/1 (a research collaboration of Cambridge, Cranfield, Imperial and Loughborough Universities). No new data were created in the course of this work. The authors are grateful to Greg Boulton, Technology Enhanced Learning Designer at Cranfield University, for his help in creating Figure 1. The authors also acknowledge the pioneering work of Emeritus Professor David Tranfield who laid the foundations for systematic review in Management and Organizational Studies which continues to inspire
The Reduced-Order Hybrid Monte Carlo Sampling Smoother

Hybrid Monte-Carlo (HMC) sampling smoother is a fully non-Gaussian
four-dimensional data assimilation algorithm that works by directly sampling
the posterior distribution formulated in the Bayesian framework. The smoother
in its original formulation is computationally expensive due to the intrinsic
requirement of running the forward and adjoint models repeatedly. Here we
present computationally efficient versions of the HMC sampling smoother based
on reduced-order approximations of the underlying model dynamics. The schemes
developed herein are tested numerically using the shallow-water equations model
on Cartesian coordinates. The results reveal that the reduced-order versions of
the smoother are capable of accurately capturing the posterior probability
density, while being significantly faster than the original full order
formulation.Comment: 32 pages, 2 figure
A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK ‘Octopus’, EPSRC ‘Reactor Core-Structure Re-location Modelling for Severe Nuclear Accidents’) and Horizon 2020 ‘In-Vessel Melt Retention’. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC ‘Multi-Scale Exploration of Multi-phase Physics in Flows’. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.Peer reviewedPublisher PD
A simple phase transition relaxation solver for liquid-vapor flows

International audienceDetermining liquid-vapor phase equilibrium is often required in multiphase flow computations. Existing equilibrium solvers are either accurate but computationally expensive, or cheap but inaccurate. The present paper aims at building a fast and accurate specific phase equilibrium solver, specifically devoted to unsteady multiphase flow computations. Moreover, the solver is efficient at phase diagram bounds, where non-equilibrium pure liquid and pure gas are present. It is systematically validated against solutions based on an accurate (but expensive) solver. Its capability to deal with cavitating, evaporating and condensing two-phase flows is highlighted on severe test problems both 1D and 2D
A modified Galerkin/finite element method for the numerical solution of
  the Serre-Green-Naghdi system

A new modified Galerkin / Finite Element Method is proposed for the numerical
solution of the fully nonlinear shallow water wave equations. The new numerical
method allows the use of low-order Lagrange finite element spaces, despite the
fact that the system contains third order spatial partial derivatives for the
depth averaged velocity of the fluid. After studying the efficacy and the
conservation properties of the new numerical method, we proceed with the
validation of the new numerical model and boundary conditions by comparing the
numerical solutions with laboratory experiments and with available theoretical
asymptotic results
Turbulence modelling and role of compressibility on oil spilling from a damaged double hull tank

The viscosity plays an important role, and a multiphase solver is necessary to numerically simulate the oil spilling from a damaged double hull tank (DHT). However, it is uncertain whether turbulence modelling is necessary, which turbulence model is suitable; and what the role of compressibility of the fluids is. This paper presents experimental and numerical investigations to address these issues for various cases representing different scenarios of the oil spilling, including grounding and collision. In the numerical investigations, various approaches to model the turbulence, including the large eddy simulation (LES), direct numerical simulation and the Reynolds average Navier-Stokes equation (RANS) with different turbulence models, are employed. Based on the investigations, it is suggested that the effective Reynolds numbers corresponding to both oil outflow and water inflow shall be considered when classifying the significance of the turbulence and selecting the appropriate turbulence models. This is confirmed by new lab tests considering the axial offset between the internal and the external holes on two hulls of the DHT. The investigations conclude for numerically simulating oil spilling from a damaged DHT that when the effective Re is smaller the RANS approaches should not be used and LES modelling should be employed; while when the effective Reynolds numbers is large, the RANS models may be used as they can give similar results to LES in terms of the height of the mixture in the ballast tank and discharge but costing much less CPU time. The investigation on the role of the compressibility of the fluid reveals that the compressibility of the fluid may be considerable in a small temporal-spatial scale but plays an insignificant role on macroscopic process of the oil spilling
Numerical analysis of conservative unstructured discretisations for low Mach flows

This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. https://authorservices.wiley.com/author-resources/Journal-Authors/licensing-and-open-access/open-access/self-archiving.htmlUnstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions.\ud
However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors.\ud
An assessment of a low-Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell centred velocity reconstructions the standard first-order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm.\ud
Regarding collocated discretisations, the odd-even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable-density flows.\ud
Besides, different face interpolations schemes for unstructured meshes are analysed.\ud
A kinetic energy preserving scheme is applied to the momentum equations, namely the Symmetry-Preserving (SP) scheme. Furthermore, a new approach to define the far-neighbouring nodes of the QUICK scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not.\ud
The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self-igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable-density flows. Furthermore, the QUICK schemes shows close to second order behaviour on unstructured meshes and the SP is reliably used in all computations.Peer ReviewedPostprint (author's final draft
Computing the force distribution on the surface of complex, deforming
  geometries using vortex methods and Brinkman penalization

The distribution of forces on the surface of complex, deforming geometries is
an invaluable output of flow simulations. One particular example of such
geometries involves self-propelled swimmers. Surface forces can provide
significant information about the flow field sensed by the swimmers, and are
difficult to obtain experimentally. At the same time, simulations of flow
around complex, deforming shapes can be computationally prohibitive when
body-fitted grids are used. Alternatively, such simulations may employ
penalization techniques. Penalization methods rely on simple Cartesian grids to
discretize the governing equations, which are enhanced by a penalty term to
account for the boundary conditions. They have been shown to provide a robust
estimation of mean quantities, such as drag and propulsion velocity, but the
computation of surface force distribution remains a challenge. We present a
method for determining flow- induced forces on the surface of both rigid and
deforming bodies, in simulations using re-meshed vortex methods and Brinkman
penalization. The pressure field is recovered from the velocity by solving a
Poisson's equation using the Green's function approach, augmented with a fast
multipole expansion and a tree- code algorithm. The viscous forces are
determined by evaluating the strain-rate tensor on the surface of deforming
bodies, and on a 'lifted' surface in simulations involving rigid objects. We
present results for benchmark flows demonstrating that we can obtain an
accurate distribution of flow-induced surface-forces. The capabilities of our
method are demonstrated using simulations of self-propelled swimmers, where we
obtain the pressure and shear distribution on their deforming surfaces
Surface-sampled simulations of turbulent flow at high Reynolds number

A new approach to turbulence simulation, based on a combination of large-eddy
simulation (LES) for the whole flow and an array of non-space-filling
quasi-direct numerical simulations (QDNS), which sample the response of
near-wall turbulence to large-scale forcing, is proposed and evaluated. The
technique overcomes some of the cost limitations of turbulence simulation,
since the main flow is treated with a coarse-grid LES, with the equivalent of
wall functions supplied by the near-wall sampled QDNS. Two cases are tested, at
friction Reynolds number Re$_\tau$=4200 and 20,000. The total grid node count
for the first case is less than half a million and less than two million for
the second case, with the calculations only requiring a desktop computer. A
good agreement with published DNS is found at Re$_\tau$=4200, both in terms of
the mean velocity profile and the streamwise velocity fluctuation statistics,
which correctly show a substantial increase in near-wall turbulence levels due
to a modulation of near-wall streaks by large-scale structures. The trend
continues at Re$_\tau$=20,000, in agreement with experiment, which represents
one of the major achievements of the new approach. A number of detailed aspects
of the model, including numerical resolution, LES-QDNS coupling strategy and
sub-grid model are explored. A low level of grid sensitivity is demonstrated
for both the QDNS and LES aspects. Since the method does not assume a law of
the wall, it can in principle be applied to flows that are out of equilibrium.Comment: Author accepted version. Accepted for publication in the
  International Journal for Numerical Methods in Fluids on 26 April 201
Wall modeling via function enrichment within a high-order DG method for
  RANS simulations of incompressible flow

We present a novel approach to wall modeling for RANS within the
discontinuous Galerkin method. Wall functions are not used to prescribe
boundary conditions as usual but they are built into the function space of the
numerical method as a local enrichment, in addition to the standard polynomial
component. The Galerkin method then automatically finds the optimal solution
among all shape functions available. This idea is fully consistent and gives
the wall model vast flexibility in separated boundary layers or high adverse
pressure gradients. The wall model is implemented in a high-order discontinuous
Galerkin solver for incompressible flow complemented by the Spalart-Allmaras
closure model. As benchmark examples we present turbulent channel flow starting
from $Re_{\tau}=180$ and up to $Re_{\tau}=100{,}000$ as well as flow past
periodic hills at Reynolds numbers based on the hill height of $Re_H=10{,}595$
and $Re_{H}=19{,}000$
A numerical stabilization framework for viscoelastic fluid flow using
  the finite volume method on general unstructured meshes

A robust finite volume method for viscoelastic flow analysis on general
unstructured meshes is developed. It is built upon a general-purpose
stabilization framework for high Weissenberg number flows. The numerical
framework provides full combinatorial flexibility between different kinds of
rheological models on the one hand, and effective stabilization methods on the
other hand. A special emphasis is put on the velocity-stress-coupling on
co-located computational grids. Using special face interpolation techniques, a
semi-implicit stress interpolation correction is proposed to correct the
cell-face interpolation of the stress in the divergence operator of the
momentum balance. Investigating the entry-flow problem of the 4:1 contraction
benchmark, we demonstrate that the numerical methods are robust over a wide
range of Weissenberg numbers and significantly alleviate the high Weissenberg
number problem. The accuracy of the results is evaluated in a detailed mesh
convergence study
Efficient computation of two-dimensional steady free-surface flows

We consider a family of steady free-surface flow problems in two dimensions,
concentrating on the effect of nonlinearity on the train of gravity waves that
appear downstream of a disturbance. By exploiting standard complex variable
techniques, these problems are formulated in terms of a coupled system of
Bernoulli's equation and an integral equation. When applying a numerical
collocation scheme, the Jacobian for the system is dense, as the integral
equation forces each of the algebraic equations to depend on each of the
unknowns. We present here a strategy for overcoming this challenge, which leads
to a numerical scheme that is much more efficient than what is normally
employed for these types of problems, allowing for many more grid points over
the free surface. In particular, we provide a simple recipe for constructing a
sparse approximation to the Jacobian that is used as a preconditioner in a
Jacobian-free Newton-Krylov method for solving the nonlinear system. We use
this approach to compute numerical results for a variety of prototype problems
including flows past pressure distributions, a surface-piercing object and
bottom topographies.Comment: 20 pages, 13 figures, under revie
Improved multislope MUSCL reconstruction on unstructured grids for shallow water equations

In shallow water flow and transport modeling, the monotonic upstream‐centered scheme for conservation laws (MUSCL) is widely used to extend the original Godunov scheme to second‐order accuracy. The most important step in MUSCL‐type schemes is MUSCL reconstruction, which calculate‐extrapolates the values of independent variables from the cell center to the edge. The monotonicity of the scheme is preserved with the help of slope limiters that prevent the occurrence of new extrema during reconstruction. On structured grids, the calculation of the slope is straightforward and usually based on a 2‐point stencil that uses the cell centers of the neighbor cell and the so‐called far‐neighbor cell of the edge under consideration. On unstructured grids, the correct choice for the upwind slope becomes nontrivial. In this work, 2 novel total variation diminishing schemes are developed based on different techniques for calculating the upwind slope and the downwind slope. An additional treatment that stabilizes the scheme is discussed. The proposed techniques are compared to 2 existing MUSCL reconstruction techniques, and a detailed discussion of the results is given. It is shown that the proposed MUSCL reconstruction schemes obtain more accurate results with less numerical diffusion and higher efficiency