511 research outputs found
An ALE formulation for explicit Runge-Kutta Residual Distribution
No full textIn this paper we consider the solution of hyperbolic conservation laws on moving meshes by means of an Arbitrary Lagrangian Eulerian (ALE) formulation. In particular we propose an ALE framework for the genuinely explicit residual distribution schemes of (Ricchiuto and Abgrall {\it J.Comput.Phys} 229, 2010). The discretizations obtained are thoroughly tested on a large number of benchmarks.Dans ce travail on considére la resolution de lois de conservation sur maillages mobiles par une formulation Arbitrary Lagrangian Eulerian (ALE). On propose en particulier un formalisme ALE pour les schémas RD explicites de (Ricchiuto and Abgrall {\it J.Comput.Phys} 229, 2010). Les schémas ainsi obtenus sont testés sur des nombreux benchmarks
An ALE formulation for explicit Runge-Kutta Residual Distribution
No full textIn this paper we consider the solution of hyperbolic conservation laws on moving meshes by means of an Arbitrary Lagrangian Eulerian (ALE) formulation. In particular we propose an ALE framework for the genuinely explicit residual distribution schemes of (Ricchiuto and Abgrall {\it J.Comput.Phys} 229, 2010). The discretizations obtained are thoroughly tested on a large number of benchmarks.Dans ce travail on considére la resolution de lois de conservation sur maillages mobiles par une formulation Arbitrary Lagrangian Eulerian (ALE). On propose en particulier un formalisme ALE pour les schémas RD explicites de (Ricchiuto and Abgrall {\it J.Comput.Phys} 229, 2010). Les schémas ainsi obtenus sont testés sur des nombreux benchmarks
Economic Impact of Rural Development Plan 2007 2013 in Tuscany
Full text linkIn 2007 in every European Union region, involved in the planning of Rural Development Plan (RDP), an independent evaluator should asses the impact of the plan in term of value added and productivity. Each region has adopted different methodologies but few of them have followed the indications of Common and Monitoring Evaluation Framework (CMEF) to evaluate the net value deriving by direct and indirect effect. IRPET, the Independent evaluator of Tuscany, utilising REMI-IRPET model has assed the impact of RDP on the main economic variables until 2020. Among 30 different measures it has been chosen only 5 of them that cover more than 54% of total amount of public and private investments. The economic impacts are also evaluated at provincial level.evaluation, regional model, rural development, Community/Rural/Urban Development,
Reforming tradition : a conversation with Remi De Roo
No full textOne of Canada’s longest serving Catholic bishops, participant in Vatican II, scholar,
author, advocate on behalf of the poor and critic of capitalism--Remi De Roo has led a
remarkable 94 year life of faith in action. Join him for an intimate encounter that includes
a public interview with former CBC host Ian Alexander, and questions from the audience.John Albert Hall lectures (University of Victoria, B.C.)FacultyUnreviewe
A simple construction of very high order non oscillatory compact schemes on unstructured meshes.
Full text linkInternational audienceIn \cite{abgrall-roe} have been constructed very high order residual distribution schemes for scalar problems. They were using triangle unstructured meshes. However, the construction was quite involved and was not very flexible. Here, following \cite{abgrall}, we develop a systematic way of constructing very high order non oscillatory schemes for such meshes. Applications to scalar and systems problems are given
Staggered Schemes for Compressible Flow: A General Construction
No full textThis paper is focused on the approximation of the Euler equations of compressible fluid dynamics on a staggered mesh. With this aim, the flow parameters are described by the velocity, the density, and the internal energy. The thermodynamic quantities are described on the elements of the mesh, and thus the approximation is only in L2, while the kinematic quantities are globally continuous. The method is general in the sense that the thermodynamic and kinetic parameters are described by an arbitrary degree of polynomials. In practice, the difference between the degrees of the kinematic parameters and the thermodynamic ones is set to 1. The integration in time is done using the forward Euler method but can be extended straightforwardly to higher-order methods. In order to guarantee that the limit solution will be a weak solution of the problem, we introduce a general correction method in the spirit of the Lagrangian staggered method described in [R. Abgrall and S. Tokareva, SIAM J. Sci. Comput., 39 (2017), pp. A2345--A2364; R. Abgrall, K. Lipnikov, N. Morgan, and S. Tokareva, SIAM J. Sci. Comput., 2 (2020), pp. A343--A370; V. A. Dobrev, T. V. Kolev, and R. N. Rieben, SIAM J. Sci. Comput., 34 (2012), pp. B606--B641], and we prove a Lax--Wendroff theorem. The proof is valid for multidimensional versions of the scheme, even though most of the numerical illustrations in this work, on classical benchmark problems, are one-dimensional because we have easy access to the exact solution for comparison. We conclude by explaining that the method is general and can be used in different settings, for example, finite volume or discontinuous Galerkin method, not just the specific one presented in this paper
A simple semi-intrusive method for Uncertainty Quantification of shocked flows, comparison with a non-intrusive Polynomial Chaos method
No full textInternational audienceThe purpose of this paper is to provide a description and a comparison of a method already described in \cite{abgrall} with more standard UQ tools
Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes
Full text linkInternational audienceIn this paper we consider the very high order approximation of solutions of the Euler equations. We present a systematic generalization of the residual distribution method of (Abgrall, J.ComputPhys 2006) to very high order of accuracy, by extending the preliminary work discussed in (Abgrall, Larat, Ricchiuto, Tave, Computers and Fluids 2009) to systems and hybrid meshes. We present extensive numerical validation for the third and fourth order cases with Lagrange finite elements. In particular, we demonstrate that we both have a non-oscillatory behavior, even for very strong shocks and complex flow patterns, and the expected accuracy on smooth problems
Essentially non-oscillatory residual distribution schemes for hyperbolic problems
Full text linkInternational audienceThe residual distribution (RD) schemes are an alternative to standard high order accurate finite volume schemes. They have several advantages: a better accuracy, a much more compact stencil, easy parallelization. However, they face several problems, at least for steady problems which are the only cases considered here. The solution is obtained via an iterative method. The iterative convergence must be good in order to get spatially accurate solutions, as suggested by the few theoretical results available for the RD schemes. In many cases, especially for systems, the iterative convergence is not sufficient to guaranty the theoretical accuracy. In fact, up to our knowledge, the iterative convergence is correct in only two cases: for first order monotone schemes and the (scalar) Struij's PSI scheme which is a multidimensional upwind scheme. Up to our knowledge, the iterative convergence is poor for systems, except for the blended scheme of Deconinck et al. [{\it Á. Cs\'{\i}k, M. Ricchiuto}, and {\it H. Deconinck}, J. Comput. Phys. 179, No.~1, 286--312 (2002; Zbl 1005.65111)] and [{\it R. Abgrall}, ibid. 167, No.~2, 277--315 (2001; Zbl 0988.76055)] which are also a genuinely multidimensional upwind scheme. A second drawback is that their construction relies, up to now, on a single first order scheme: the scheme. However, it is known that standard first order finite volume schemes can be rephrased into a residual distribution framework. Unfortunately, the standard way of upgrading the order of accuracy to second order leads to very unsatisfactory results but clearly the construction of good schemes based on a wider class of first order schemes would be interesting. In this paper, we analyze these two problems, and show they are linked. We propose a fix and demonstrate its efficiency on several test cases that cover a wide range of applications. Our solution extends considerably the number of working RD schemes.}", keywords="{essentially non-oscillatory; ENO schemes; Euler equation; residual distribution schemes; finite volume schemes; iterative method; convergence; monotone schemes; PSI scheme; upwind schem
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