1,721,018 research outputs found
Some preliminary results on a high order asymptotic preserving computationally explicit kinetic scheme
No full textIn this short paper, we intend to describe one way to construct arbitrarily high order kinetic schemes on regular meshes. The method can be arbitrarily high order in space and time, and run at CFL one. This is a common feature with the Lattice Boltzmann Methods. However, the type of Maxwellian we use here are different. This results in very simple and CPU efficient methods
High order asymptotic preserving deferred correction implicit-explicit schemes for kinetic models
No full textThis work introduces an extension of the residual distribution (RD) framework to stiff relaxation problems. The RD is a class of schemes which is used to solve a hyperbolic system of partial differential equations. To our knowledge, it has been used only for systems with mild source terms, such as gravitation problems or shallow water equations. What we propose is an implicit-explicit (IMEX) version of the RD schemes that can resolve stiff source terms, without refining the discretization up to the stiffness scale. This can be particularly useful in various models, where the stiffness is given by topological or physical quantities, e.g., multiphase flows, kinetic models, or viscoelasticity problems. We will focus on kinetic models that are BGK approximation of hyperbolic conservation laws. The extension to more complicated problems will be carried out in future works. The provided scheme is able to catch different relaxation scales automatically, without losing accuracy; we prove that the scheme is asymptotic preserving and this guarantees that, in the relaxation limit, we recast the expected macroscopic behavior. To get a high order accuracy, we use an IMEX time discretization combined with a deferred correction procedure, while naturally RD provides high order space discretization. Finally, we show some numerical tests in one and two dimensions for stiff systems of equations
A pressure-based method for weakly compressible two-phase flows under a Baer–Nunziato type model with generic equations of state and pressure and velocity disequilibrium
Full text linkWithin the framework of diffuse interface methods, we derive a pressure-based Baer–Nunziato type model well-suited to weakly compressible multiphase flows. The model can easily deal with different equation of states and it includes relaxation terms characterized by user-defined finite parameters, which drive the pressure and velocity of each phase toward the equilibrium. There is no clear notion of speed of sound, and thus, most of the classical low Mach approximation cannot easily be cast in this context. The proposed solution strategy consists of two operators: a semi-implicit finite-volume solver for the hyperbolic part and an ODE integrator for the relaxation processes. Being the acoustic terms in the hyperbolic part integrated implicitly, the stability condition on the time step is lessened. The discretization of nonconservative terms involving the gradient of the volume fraction fulfills by construction the nondisturbance condition on pressure and velocity to avoid oscillations across the multimaterial interfaces. The developed simulation tool is validated through one-dimensional simulations of shock-tube and Riemann-problems, involving water-aluminum and water-air mixtures, vapor-liquid mixture of water and of carbon dioxide, and almost pure flows. The numerical results match analytical and reference ones, except some expected discrepancies across shocks, which however remain acceptable (errors within some percentage points). All tests were performed with acoustic CFL numbers greater than one, and no stability issues arose, even for CFL greater than 10. The effects of different values of relaxation parameters and of different amount equations of state—stiffened gas and Peng–Robinson—were investigated
Spectral Analysis of Continuous FEM for Hyperbolic PDEs: Influence of Approximation, Stabilization, and Time-Stepping
Full text linkWe study continuous finite element dicretizations for one dimensional hyperbolic partial differential equations. The main contribution of the paper is to provide a fully discrete spectral analysis, which is used to suggest optimal values of the CFL number and of the stabilization parameters involved in different types of stabilization operators. In particular, we analyze the streamline-upwind Petrov–Galerkin stabilization technique, the continuous interior penalty (CIP) stabilization method and the orthogonal subscale stabilization (OSS). Three different choices for the continuous finite element space are compared: Bernstein polynomials, Lagrangian polynomials on equispaced nodes, and Lagrangian polynomials on Gauss-Lobatto cubature nodes. For the last choice, we only consider inexact quadrature based on the formulas corresponding to the degrees of freedom of the element, which allows to obtain a fully diagonal mass matrix. We also compare different time stepping strategies, namely Runge–Kutta (RK), strong stability preserving RK (SSPRK) and deferred correction time integration methods. The latter allows to alleviate the computational cost as the mass matrix inversion is replaced by the high order correction iterations. To understand the effects of these choices, both time-continuous and fully discrete Fourier analysis are performed. These allow to compare all the different combinations in terms of accuracy and stability, as well as to provide suggestions for optimal values discretization parameters involved. The results are thoroughly verified numerically both on linear and non-linear problems, and error-CPU time curves are provided. Our final conclusions suggest that cubature elements combined with SSPRK and CIP or OSS stabilization are the most promising combinations
Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes
Full text linkThe Deferred Correction (DeC) methods combined with the residual distribution (RD) approach allow the construction of high order continuous Galerkin (cG) schemes avoiding the inversion of the mass matrix. With the application of entropy correction functions we can even obtain entropy conservative/dissipative spatial discretizations in this context. To handle entropy production in time, a relaxation approach has been suggested by Ketcheson. The main idea is to slightly modify the time-step size such that the approximated solution fulfills the underlying entropy conservation/dissipation constraint. In this paper, we first study the relaxation technique applied to the DeC approach as an ODE solver, then we extend this combination to the residual distribution method, requiring more technical steps. The outcome is a class of cG methods that is fully entropy conservative/dissipative and where we can still avoid the inversion of a mass matrix
Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification
No full textIn this work, we present a model order reduction (MOR) technique for hyperbolic conservation laws with applications in uncertainty quantification (UQ). The problem consists of a parametrized time dependent hyperbolic system of equations, where the parameters affect the initial conditions and the fluxes in a non- linear way. The procedure utilized to reduce the order is a combination of a Greedy algorithm in the parameter space, a proper orthogonal decomposition (POD) in time and empirical interpolation method (EIM) to deal with non-linearities (Drohmann, 2012). We provide under some hypothesis an error bound for the reduced solution with respect to the high order one. The algorithm shows small errors and savings of the computational time up to 90% in the UQ simulations, which are performed to validate the algorithm
Numerical Simulation of Weakly Compressible Multiphase Flows with a Baer-Nunziato Type Model
Full text linkWe present the results of the simulation of two-phase CO2 flows at low-Mach number, obtained through a pressure-based Baer-Nunziato type model. The underlying full non-equilibrium model enables the description of each phase with its own thermodynamic model, so it circumvents the requirement of the definition of the speed of sound of the vapor-liquid mixture. The primitive formulation, combined with a special pressure scaling to correctly capture the behavior in the zero-Mach limit, is well-suited to model weakly compressible flows, and makes easier the use of arbitrary thermodynamic models. At the interfaces, the phasic velocity and pressure are driven toward the equilibrium by means of relaxation processes, whose velocities are controlled by user-defined parameters. The set of seven partial differential equations describing the flow evolution is discretized through a finite-volume scheme in space and an hybrid implicit-explicit time discretization, to avoid the stringent time step limitation imposed by the acoustics. We compare the results of a shock-tube problem, initially containing saturated CO2, obtained according to the stiffened gas model and to the Peng-Robinson equation of state
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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