2,523 research outputs found
A finite element flux-corrected transport method for wave propagation in heterogeneous solids
When moving discontinuities in solids need to be simulated, standard finite element (FE) procedures usually attain low accuracy because of spurious oscillations appearing behind the discontinuity fronts. To assure an accurate tracking of traveling stress waves in heterogeneous media, we propose here a flux-corrected transport (FCT) technique for structured as well as unstructured space discretizations. The FCT technique consists of post-processing the FE velocity field via diffusive/antidiffusive fluxes, which rely upon an algorithmic length-scale parameter. To study the behavior of heterogeneous bodies featuring compliant interphases of any shape, a general scheme for computing diffusive/antidiffusive fluxes close to phase boundaries is proposed too. The performance of the new FE-FCT method is assessed through one-dimensional and two-dimensional simulations of dilatational stress waves propagating along homogeneous and composite rods
Depth-averaged and 3D Finite Volume numerical models for viscous fluids, with application to the simulation of lava flows
This Ph.D. project was initially born from the motivation to contribute to the depth-averaged and 3D modeling of lava flows. Still, we can frame the work done in a broader and more generalist vision. We developed two models that may be used for generic viscous fluids, and we applied efficient numerical schemes for both cases, as explained in the following.
The new solvers simulate free-surface viscous fluids whose temperature changes are due to radiative, convective, and conductive heat exchanges. A temperature-dependent viscoplastic model is used for the final application to lava flows. Both the models behind the solvers were derived from mass, momentum, and energy conservation laws. Still, one was obtained by following the depth-averaged model approach and the other by the 3D model approach. The numerical schemes adopted in both our models belong to the family of finite volume methods, based on the integral form of the conservation laws. This choice of methods family is fundamental because it allows the creation and propagation of discontinuities in the solutions and enforces the conservation properties of the equations.
We propose a depth-averaged model for a viscous fluid in an incompressible and laminar regime with an additional transport equation for a scalar quantity varying horizontally and a variable density that depends on such transported quantity. Viscosity and non-constant vertical profiles for the velocity and the transported quantity are assumed, overtaking the classic shallow-water formulation. The classic formulation bases on several assumptions, such as the fact that the vertical pressure distribution is hydrostatic, that the vertical component of the velocity can be neglected, and that the horizontal velocity field can be considered constant with depth because the classic formulation accounts for non-viscous fluids. When the vertical shear is essential, the last assumption is too restrictive, so it must relax, producing a modified momentum equation in which a coefficient, known as the Boussinesq factor, appears in the advective term. The spatial discretization method we employed is a modified version of the central-upwind scheme introduced by Kurganov and Petrova in 2007 for the classical shallow water equations. This method is based on a semi-discretization of the computational domain, is stable, and, being a high-order method, has a low numerical diffusion. For the temporal discretization, we used an implicit-explicit Runge-Kutta technique discussed by Russo in 2005 that permits an implicit treatment of the stiff terms. The whole scheme is proved to preserve the positivity of flow thickness and the stationary steady-states. Several numerical experiments validate the proposed method, show the incidence on the numerical solutions of shape coefficients introduced in the model and present the effects of the viscosity-related parameters on the final emplacement of a lava flow.
Our 3D model describes the dynamics of two incompressible, viscous, and immiscible fluids, possibly belonging to different phases. Being interested in the final application of lava flows, we also have an equation for energy that models the thermal exchanges between the fluid and the environment. We implemented this model in OpenFOAM, which employs a segregated strategy and the Finite Volume Methods to solve the equations. The Volume of Fluid (VoF) technique introduced by Hirt and Nichols in 1981 is used to deal with the multiphase dynamics (based on the Interphase Capturing strategy), and hence a new transport equation for the volume fraction of one phase is added. The challenging effort of maintaining an accurate description of the interphase between fluids is solved by using the Multidimensional Universal Limiter for Explicit Solution (MULES) method (described by Marquez Damian in 2013) that implements the Flux-Corrected Transport (FCT) technique introduced by Boris and Book in 1973, proposing a mix of high and low order schemes. The choice of the framework to use for any new numerical code is crucial.
Our contribution consists of creating a new solver called interThermalRadConvFoam in the OpenFOAM framework by modifying the already existing solver interFoam (described by Deshpande et al. in 2012). Finally, we compared the results of our simulations with some benchmarks to evaluate the performances of our model
Simulation of flows with violent free surface motion and moving objects using unstructured grids
This is the peer reviewed version of the following article: [Löhner, R. , Yang, C. and Oñate, E. (2007), Simulation of flows with violent free surface motion and moving objects using unstructured grids. Int. J. Numer. Meth. Fluids, 53: 1315-1338. doi:10.1002/fld.1244], which has been published in final form at https://doi.org/10.1002/fld.1244. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.Peer ReviewedPostprint (author's final draft
Recommended from our members
Direct Numerical Simulations of Multiphase, Stratified, Environmental Fluid Flows
Many fundamental processes in oceanic transport and limnology occur in geophysical flows that are both local in space and transient in time, and that require equally space and time-resolved methods of analysis. The importance of providing physics-based, quantitative modeling of such flows has driven the development of numerical methods for geophysical fluid dynamics for over three decades. Here, we use direct numerical simulations to investigate a range of stratified, particle-laden flows that are accurately described by the three-dimensional Navier-Stokes equations for an incompressible flow in the Boussinesq limit. We firstly investigate the propagation, transport and mixing dynamics of density-driven gravity currents moving in stratified environments. We propose new models for the intrusion of a turbidity current into a linearly stratified ambient based on three-dimensional simulations. We then describe the interaction between a gravity-current and an internal wave and characterize a phenomenological change in the long-term effect of the interaction at a critical wave height. We then quantify the role of double-diffusive processes in the Dead Sea in Summer and their role in the seasonality of salt crystallization and deposition. We also describe large-scale double-diffusive instabilities that arise in high-Prandtl sedimentary double-diffusive systems such as linearly stratified particle-laden salt water. Finally, we quantify mixing induced by a swarm of small-scale self-propelled organisms migrating in a stratified ambient fluid. We compare the relative contribution to mixing by individual swimmers within the swarm to that of the large-scale motion produced by the collective motion of the swarm
Implicit High-Order Flux Reconstruction Solver for High-Speed Compressible Flows
The present paper addresses the development and implementation of the first
high-order Flux Reconstruction (FR) solver for high-speed flows within the
open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid
Dynamics) platform. The resulting solver is fully implicit and able to simulate
compressible flow problems governed by either the Euler or the Navier-Stokes
equations in two and three dimensions. Furthermore, it can run in parallel on
multiple CPU-cores and is designed to handle unstructured grids consisting of
both straight and curved edged quadrilateral or hexahedral elements. While most
of the implementation relies on state-of-the-art FR algorithms, an improved and
more case-independent shock capturing scheme has been developed in order to
tackle the first viscous hypersonic simulations using the FR method. Extensive
verification of the FR solver has been performed through the use of
reproducible benchmark test cases with flow speeds ranging from subsonic to
hypersonic, up to Mach 17.6. The obtained results have been favorably compared
to those available in literature. Furthermore, so-called super-accuracy is
retrieved for certain cases when solving the Euler equations. The strengths of
the FR solver in terms of computational accuracy per degree of freedom are also
illustrated. Finally, the influence of the characterizing parameters of the FR
method as well as the the influence of the novel shock capturing scheme on the
accuracy of the developed solver is discussed
A "well-balanced" finite volume scheme for blood flow simulation
We are interested in simulating blood flow in arteries with a one dimensional
model. Thanks to recent developments in the analysis of hyperbolic system of
conservation laws (in the Saint-Venant/ shallow water equations context) we
will perform a simple finite volume scheme. We focus on conservation properties
of this scheme which were not previously considered. To emphasize the necessity
of this scheme, we present how a too simple numerical scheme may induce
spurious flows when the basic static shape of the radius changes. On contrary,
the proposed scheme is "well-balanced": it preserves equilibria of Q = 0. Then
examples of analytical or linearized solutions with and without viscous damping
are presented to validate the calculations. The influence of abrupt change of
basic radius is emphasized in the case of an aneurism.Comment: 36 page
A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations
A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma
system is presented. The method uses a second or third order discontinuous
Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping
scheme. The method is benchmarked against an analytic solution of a dispersive
electron acoustic square pulse as well as the two-fluid electromagnetic shock
and existing numerical solutions to the GEM challenge magnetic reconnection
problem. The algorithm can be generalized to arbitrary geometries and three
dimensions. An approach to maintaining small gauge errors based on error
propagation is suggested.Comment: 40 pages, 18 figures
A simple immersed-boundary method for solid-fluid interaction in constant- and stratified-density flows
The present work reports on the simulation of two- and three-dimensional constant- and stratifieddensity flows involving fixed or moving objects using an immersed-boundary method. The numerical approach is based on a simple immersed-boundary method in which no explicit Lagrangian marking of the immersed boundary is used. The solid object is defined by a continuous solid volume fraction which is updated thanks to the resolution of the Newton’s equations of motion for the immersed object. As shown on several test cases, this algorithm allows the flow field near the solid boundary to be correctly captured even though the numerical thickness of the transition region separating the fluid from the object is within three computational cells approximately. The full set of governing equations is then used
to investigate some fundamental aspects of solid–fluid interaction, including fixed and moving objects in constant and stratified-density flows. In particular, the method is shown to accurately reproduce the steady-streaming patterns observed in the near-region of an oscillating sphere, as well as the so-called Saint Adrew’s cross in the far-field when the sphere oscillates in a rotating stratified fluid. The sedimentation of a particle in a stratified ambient is investigated for particle Reynolds numbers up to Oð103Þ and the effect of stratification and density ratio is addressed. While the present paper only consider
fluid–solid interaction for a single object, the present approach can be straightforwardly extended to the case of multiple objects of arbitrary shape moving in a stratified-density flow
- …