pinecone/core-2020-05-10-deduplication huggingface dataset:
A Radial Basis Function (RBF)-Finite Difference Method for the
  Simulation of Reaction-Diffusion Equations on Stationary Platelets within the
  Augmented Forcing Method

We present a computational method for solving the coupled problem of chemical
transport in a fluid (blood) with binding/unbinding of the chemical to/from
cellular (platelet) surfaces in contact with the fluid, and with transport of
the chemical on the cellular surfaces. The overall framework is the Augmented
Forcing Point Method (AFM) (\emph{L. Yao and A.L. Fogelson, Simulations of
chemical transport and reaction in a suspension of cells I: An augmented
forcing point method for the stationary case, IJNMF (2012) 69, 1736-52.}) for
solving fluid-phase transport in a region outside of a collection of cells
suspended in the fluid. We introduce a novel Radial Basis Function-Finite
Difference (RBF-FD) method to solve reaction-diffusion equations on the surface
of each of a collection of 2D stationary platelets suspended in blood.
Parametric RBFs are used to represent the geometry of the platelets and give
accurate geometric information needed for the RBF-FD method. Symmetric
Hermite-RBF interpolants are used for enforcing the boundary conditions on the
fluid-phase chemical concentration, and their use removes a significant
limitation of the original AFM. The efficacy of the new methods are shown
through a series of numerical experiments; in particular, second order
convergence for the coupled problem is demonstrated.Comment: 27 pages, 7 figures, 9 table
A finite element/volume method model of the depth-averaged horizontally 2D shallow water equations

Analysis of surface water flows is of central importance in understanding and predicting a wide range of water engineering issues. Dynamics of surface water is reasonably well described using the shallow water equations (SWEs) with the hydrostatic pressure assumption. The SWEs are nonlinear hyperbolic partial differential equations that are in general required to be solved numerically. Application of a simple and efficient numerical model is desirable for solving the SWEs in practical problems. This study develops a new numerical model of the depth-averaged horizontally 2D SWEs referred to as 2D finite element/volume method (2D FEVM) model. The continuity equation is solved with the conforming, standard Galerkin FEM scheme and momentum equations with an upwind, cell-centered finite volume method scheme, utilizing the water surface elevation and the line discharges as unknowns aligned in a staggered manner. The 2D FEVM model relies on neither Riemann solvers nor high-resolution algorithms in order to serve as a simple numerical model. Water at a rest state is exactly preserved in the model. A fully explicit temporal integration is achieved in the model using an efficient approximate matrix inversion method. A series of test problems, containing three benchmark problems and three experiments of transcritical flows, are carried out to assess accuracy and versatility of the model
A Chimera method for the incompressible Navier-Stokes equations

The Chimera method was developed three decades ago as a meshing simplification tool. Different components are meshed independently and then glued together using a domain decomposition technique to couple the equations solved on each component. This coupling is achieved via transmission conditions (in the finite element context) or by imposing the continuity of fluxes (in the finite volume context). Historically, the method has then been used extensively\ud
to treat moving objects, as the independent meshes are free to move with respect to the others. At each time step, the main task consists in recomputing the interpolation of the transmission conditions or fluxes. This paper presents a Chimera method applied to the Navier-Stokes equations. After an introduction on the Chimera method, we describe in two different sections the two independent steps of the method: the hole cutting to create the interfaces of the subdomains, and the coupling of the subdomains. Then we present the Navier-Stokes solver considered in this work. Implementation aspects are then detailed in order to apply efficiently the method to this specific parallel Navier-Stokes solver. We conclude with some examples to demonstrate the reliability and the application of the proposed method.This work has been partly carried out in the framework of the FP7 European projects W2Plastics. Part of the work of Beatriz Eguzkitza was sponsored by an IBERDROLA grant.Peer ReviewedPostprint (author's final draft
Interface control domain decomposition methods for heterogeneous problems

This is the peer reviewed version of the following article: DISCACCIATI, M., GERVASIO, P. and QUARTERONI, A., 2014. Interface control domain decomposition methods for heterogeneous problems. International Journal for Numerical Methods in Fluids, 76 (8), pp. 471 - 496, which has been published in final form at http://dx.doi.org/10.1002/fld.3942 This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.This paper is concerned with the solution of heterogeneous problems by the interface control domain decomposition (ICDD) method, a strategy introduced for the solution of partial differential equations in computational domains partitioned into subdomains that overlap. After reformulating the original boundary value problem by introducing new additional control variables, the unknown traces of the solution at internal subdomain interfaces; the latter are determined by requiring that the (a priori) independent solutions in each subdomain undergo the minimization of a suitable cost functional.\ud
\ud
We provide an abstract formulation for coupled heterogeneous problems and a general theorem of well-posedness for the associated ICDD problem. Then, we illustrate and validate an efficient algorithm based on the solution of the Schur-complement system restricted solely to the interface control variables by considering two kinds of heterogeneous boundary value problems: the coupling between pure advection and advection–diffusion equations and the coupling between Stokes and Darcy equations. In the latter case, we also compare the ICDD method with a classical approach based on the Beavers–Joseph–Saffman conditions
Comparison of POD reduced order strategies for the nonlinear 2D Shallow
  Water Equations

This paper introduces tensorial calculus techniques in the framework of
Proper Orthogonal Decomposition (POD) to reduce the computational complexity of
the reduced nonlinear terms. The resulting method, named tensorial POD, can be
applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms
have an on-line complexity of $\mathcal{O}(k^{p+1})$, where $k$ is the
dimension of POD basis, and therefore is independent of full space dimension.
However it is efficient only for quadratic nonlinear terms since for higher
nonlinearities standard POD proves to be less time consuming once the POD basis
dimension $k$ is increased. Numerical experiments are carried out with a two
dimensional shallow water equation (SWE) test problem to compare the
performance of tensorial POD, standard POD, and POD/Discrete Empirical
Interpolation Method (DEIM). Numerical results show that tensorial POD
decreases by $76\times$ times the computational cost of the on-line stage of
standard POD for configurations using more than $300,000$ model variables. The
tensorial POD SWE model was only $2-8\times$ slower than the POD/DEIM SWE model
but the implementation effort is considerably increased. Tensorial calculus was
again employed to construct a new algorithm allowing POD/DEIM shallow water
equation model to compute its off-line stage faster than the standard and
tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table
High Order Lagrangian ADER-WENO Schemes on Unstructured Meshes -
  Application of Several Node Solvers to Hydrodynamics and Magnetohydrodynamics

In this paper we present a class of high order accurate cell-centered
Arbitrary-Eulerian-Lagrangian (ALE) one-step ADER-WENO finite volume schemes
for the solution of nonlinear hyperbolic conservation laws on two-dimensional
unstructured triangular meshes. High order of accuracy in space is achieved by
a WENO reconstruction algorithm, while a local space-time Galerkin predictor
allows the schemes to be high order accurate also in time by using an
element-local weak formulation of the governing PDE on moving meshes. The mesh
motion can be computed by choosing among three different node solvers, which
are for the first time compared with each other in this article: the node
velocity may be obtained i) either as an arithmetic average among the states
surrounding the node, or, ii) as a solution of multiple one-dimensional
half-Riemann problems around a vertex, or, iii) by solving approximately a
multidimensional Riemann problem around each vertex of the mesh using the
genuinely multidimensional HLL Riemann. Once the vertex velocity and thus the
new node location has been determined by the node solver, the local mesh motion
is then constructed by straight edges connecting the vertex positions at the
old time level with the new ones at the next time level. If necessary, a
rezoning step can be introduced here to overcome mesh tangling or highly
deformed elements. We apply the high order algorithm presented in this paper to
the Euler equations of compressible gas dynamics as well as to the ideal
classical and relativistic MHD equations. We show numerical convergence results
up to fifth order of accuracy in space and time together with some classical
numerical test problems for each hyperbolic system under consideration
Topology optimisation for natural convection problems

This paper demonstrates the application of the density-based topology
optimisation approach for the design of heat sinks and micropumps based on
natural convection effects. The problems are modelled under the assumptions of
steady-state laminar flow using the incompressible Navier-Stokes equations
coupled to the convection-diffusion equation through the Boussinesq
approximation. In order to facilitate topology optimisation, the Brinkman
approach is taken to penalise velocities inside the solid domain and the
effective thermal conductivity is interpolated in order to accommodate
differences in thermal conductivity of the solid and fluid phases. The
governing equations are discretised using stabilised finite elements and
topology optimisation is performed for two different problems using discrete
adjoint sensitivity analysis. The study shows that topology optimisation is a
viable approach for designing heat sink geometries cooled by natural convection
and micropumps powered by natural convection.Comment: Submitted to the 'International Journal for Numerical Methods in
  Fluids' on 28th of August 2013 - currently under revie
Flooding in urban drainage systems: Coupling hyperbolic conservation
  laws for sewer systems and surface flow

In this paper we propose a model for a sewer network coupled to surface flow
and investigate it numerically. In particular, we present a new model for the
manholes in storm sewer systems. It is derived using the balance of the total
energy in the complete network. The resulting system of equations contains,
aside from hyperbolic conservation laws for the sewer network and algebraic
relations for the coupling conditions, a system of ODEs governing the flow in
the manholes. The manholes provide natural points for the interaction of the
sewer system and the run off on the urban surface modelled by shallow water
equations. Finally, a numerical method for the coupled system is presented. In
several numerical tests we study the influence of the manhole model on the
sewer system and the coupling with 2D surface flow
Adjoint-Based Error Estimation and Mesh Adaptation for Hybridized
  Discontinuous Galerkin Methods

We present a robust and efficient target-based mesh adaptation methodology,
building on hybridized discontinuous Galerkin schemes for (nonlinear)
convection-diffusion problems, including the compressible Euler and
Navier-Stokes equations. Hybridization of finite element discretizations has
the main advantage, that the resulting set of algebraic equations has globally
coupled degrees of freedom only on the skeleton of the computational mesh.
Consequently, solving for these degrees of freedom involves the solution of a
potentially much smaller system. This not only reduces storage requirements,
but also allows for a faster solution with iterative solvers. The mesh
adaptation is driven by an error estimate obtained via a discrete adjoint
approach. Furthermore, the computed target functional can be corrected with
this error estimate to obtain an even more accurate value. The aim of this
paper is twofold: Firstly, to show the superiority of adjoint-based mesh
adaptation over uniform and residual-based mesh refinement, and secondly to
investigate the efficiency of the global error estimate
Discontinuous Galerkin methods on graphics processing units for
  nonlinear hyperbolic conservation laws

We present a novel implementation of the modal discontinuous Galerkin (DG)
method for hyperbolic conservation laws in two dimensions on graphics
processing units (GPUs) using NVIDIA's Compute Unified Device Architecture
(CUDA). Both flexible and highly accurate, DG methods accommodate parallel
architectures well as their discontinuous nature produces element-local
approximations. High performance scientific computing suits GPUs well, as these
powerful, massively parallel, cost-effective devices have recently included
support for double-precision floating point numbers. Computed examples for
Euler equations over unstructured triangle meshes demonstrate the effectiveness
of our implementation on an NVIDIA GTX 580 device. Profiling of our method
reveals performance comparable to an existing nodal DG-GPU implementation for
linear problems.Comment: 36 pages, 14 figures, 6 table
Wetting Boundary Conditions in Phase-Field-Based Simulation of Binary
  Fluids: Some Comparative Studies and New Development

We studied several wetting boundary conditions (WBCs) in the simulation of
binary fluids based on phase-field theory. Five WBCs, three belonging to the
surface energy (SE) formulation using the linear, cubic and sine functions
(denoted as LinSE, CubSE and SinSE), the fourth using a geometric formulation
(Geom), and the fifth using a characteristic interpolation (CI), were compared
with each other through the study of several problems: (1) the static contact
angle of a drop; (2) a Poiseuille flow-driven liquid column; (3) a wettability
gradient (WG)-driven liquid column; (4) drop dewetting. It was found that while
all WBCs can predict the static contact angle fairly accurately, they may
affect the simulation outcomes of dynamic problems differently, depending on
the driving mechanism. For the flow-driven problem, to use different WBCs had
almost no effect on the flow characteristics over a large scale. But for other
capillarity-driven problems, the WBC had some noticeable effects. For the
WG-driven liquid column, Geom gave the most consistent prediction between the
drop velocity and dynamic contact angles, and LinSE delivered the poorest
prediction in this aspect. Except for Geom, the dynamic contact angle differed
from the prescribed (static) one when other WBCs were used. For drop dewetting,
Geom led to the most violent drop motion whereas CubSE caused the weakest
motion; the initial contact line velocity was also found to be dependent on the
WBC. For several problems, CubSE and SinSE gave almost the same results, and
those by Geom and CI were close as well, possibly due to similar consideration
in their design. Besides various comparisons, a new implementation that may be
used for all WBCs was proposed to mimic the wall energy relaxation and control
the degree of slip. This new procedure made it possible to allow the
simulations to match experimental measurements well
Finite volume/mixed finite element analysis of pollutant transport and bioremediation in heterogeneous saturated aquifers

The adoption of a suitable pumping–injecting well network and the human enhancement of the activity of soil bacteria, whose metabolism contributes to degrade and transform many pollutants in non-toxic substances, may be crucial in the process of remediation of contaminated soils. Organic contaminant transport in a subsurface aquifer and its biological degradation kinetics is numerically addressed by using a four contaminant species model. A numerical approach is proposed, that is based on a cell-centre finite volume method for the system of advection–dispersion equations of contaminants with a mixed-hybrid finite element method for the solution of a single-phase Darcy's equation. The effectiveness of the method and its accuracy in retaining the main physical properties of the continuous mathematical model is illustrated by simulating the time evolution of contaminant concentrations in a set of realistic scenarios.1-21Pubblicat
An adaptive multiresolution semi-intrusive scheme for UQ in compressible fluid problems

This paper deals with the introduction of a multiresolution strategy into the semi-intrusive scheme, recently introduced by the authors, aiming to propagate uncertainties in unsteady compressible fluid applications. The mathematical framework of the multiresolution setting is presented for the cell-average case, and the coupling with the semi-intrusive scheme is described from both the theoretical and algorithmic point-of-view. Some reference test cases are performed to demonstrate the convergence properties and the efficiency of the overall scheme: the linear advection problem for both smooth and discontinuous initial conditions, the inviscid Burgers equation, and an uncertain shock tube problem obtained by modifying the well-known Sod shock problem. For all the cases, the convergence curves are computed with respect to semi-analytical (exact) solutions. In the case of the shock tube problem, an original technique to obtain a reference highly-accurate numerical stochastic solution has also been developed
Radial Basis Function (RBF)-based Parametric Models for Closed and Open
  Curves within the Method of Regularized Stokeslets

The method of regularized Stokeslets (MRS) is a numerical approach using
regularized fundamental solutions to compute the flow due to an object in a
viscous fluid where inertial effects can be neglected. The elastic object is
represented as a Lagrangian structure, exerting point forces on the fluid. The
forces on the structure are often determined by a bending or tension model,
previously calculated using finite difference approximations. In this paper, we
study Spherical Basis Function (SBF), Radial Basis Function (RBF) and
Lagrange-Chebyshev parametric models to represent and calculate forces on
elastic structures that can be represented by an open curve, motivated by the
study of cilia and flagella. The evaluation error for static open curves for
the different interpolants, as well as errors for calculating normals and
second derivatives using different types of clustered parametric nodes, are
given for the case of an open planar curve. We determine that SBF and RBF
interpolants built on clustered nodes are competitive with Lagrange-Chebyshev
interpolants for modeling twice-differentiable open planar curves. We propose
using SBF and RBF parametric models within the MRS for evaluating and updating
the elastic structure. Results for open and closed elastic structures immersed
in a 2D fluid are presented, showing the efficacy of the RBF-Stokeslets method.Comment: 23 pages, 11 figures, 1 tabl
Numerical Simulations of Bouncing Jets

Bouncing jets are fascinating phenomenons occurring under certain conditions
when a jet impinges on a free surface. This effect is observed when the fluid
is Newtonian and the jet falls in a bath undergoing a solid motion. It occurs
also for non-Newtonian fluids when the jets falls in a vessel at rest
containing the same fluid.
  We investigate numerically the impact of the experimental setting and the
rheological properties of the fluid on the onset of the bouncing phenomenon.
Our investigations show that the occurrence of a thin lubricating layer of air
separating the jet and the rest of the liquid is a key factor for the bouncing
of the jet to happen.
  The numerical technique that is used consists of a projection method for the
Navier-Stokes system coupled with a level set formulation for the
representation of the interface. The space approximation is done with adaptive
finite elements. Adaptive refinement is shown to be very important to capture
the thin layer of air that is responsible for the bouncing
Efficient multigrid preconditioners for atmospheric flow simulations at high aspect ratio

Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in ‘flat’ domains. For example, in numerical weather and climate prediction, an elliptic PDE for the pressure correction has to be solved at every time step in a thin spherical shell representing the global atmosphere. This elliptic solve can be one of the computationally most demanding components in semi-implicit semi-Lagrangian time stepping methods, which are very popular as they allow for larger model time steps and better overall performance. With increasing model resolution, algorithmically efficient and scalable algorithms are essential to run the code under tight operational time constraints. We discuss the theory and practical application of bespoke geometric multigrid preconditioners for equations of this type. The algorithms deal with the strong anisotropy in the vertical direction by using the tensor-product approach originally analysed by Börm and Hiptmair [Numer. Algorithms, 26/3 (2001), pp. 219–234]. We extend the analysis to three dimensions under slightly weakened assumptions and numerically demonstrate its efficiency for the solution of the elliptic PDE for the global pressure correction in atmospheric forecast models. For this, we compare the performance of different multigrid preconditioners on a tensor-product grid with a semi-structured and quasi-uniform horizontal mesh and a one-dimensional vertical grid. The code is implemented in the Distributed and Unified Numerics Environment, which provides an easy-to-use and scalable environment for algorithms operating on tensor-product grids. Parallel scalability of our solvers on up to 20 480 cores is demonstrated on the HECToR supercompute
A refined r-factor algorithm for TVD schemes on arbitrary unstructured meshes

A refined r-factor algorithm for implementing TVD schemes on arbitrary unstructured meshes, referred to henceforth as FFISAM (a Face-perpendicular Far-upwind Interpolation Scheme for Arbitrary Meshes), is proposed based on an extensive review of the existing r-factor algorithms available in the literature. The design principles, as well as the respective advantages and disadvantages, of the existing algorithms are first systematically analyzed before presenting the FFISAM. The FFISAM is designed to combine the merits of various existing r-factor algorithms. The performance of the FFISAM, implemented in ten classical TVD schemes, is evaluated against four two-dimensional pure-advection benchmark test cases where analytical solutions are available. The numerical results clearly show that the FFISAM leads to a better overall performance than the existing algorithms in terms of accuracy and convergence on arbitrary unstructured meshes for the ten classical TVD schemes.The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant No. 51279082) and the support from Australian Research Council through a Discovery Grant (Project ID: DP110105171).This is the author accepted manuscript. The final version is available from Wiley at http://onlinelibrary.wiley.com/doi/10.1002/fld.4073/abstract