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State estimation for polyhedral hybrid systems and applications to the Godunov scheme

Jerome Thai, Alexandre Bayen
2013 Proceedings of the 16th international conference on Hybrid systems: computation and control - HSCC '13  
The discretization of the Lighthill-Whitham-Richards equation with a triangular flux function using the Godunov scheme is shown to lead to a hybrid linear system or Switched Linear Systems (SLS) with a  ...  This motivates a new approach inspired from a well established technique for hybrid system estimation, namely the interactive multiple model (IMM). qThe performance of this new variant of the IMM is compared  ...  For a triangular flux function, the Godunov scheme applied to the LWR model can be proven to lead to a piecewise affine (PWA) hybrid system.  ... 
doi:10.1145/2461328.2461354 dblp:conf/hybrid/ThaiB13 fatcat:hgw2syuijbhsdnrx7isqbw6ihu

State Estimation for Polyhedral Hybrid Systems and Applications to the Godunov Scheme for Highway Traffic Estimation

Jerome Thai, Alexandre M. Bayen
2015 IEEE Transactions on Automatic Control  
It uses a Godunov scheme to discretize the so-called Lighthill-Whitham-Richards equation with a triangular flux function, and proves that the resulting nonlinear dynamical system can be decomposed in a  ...  We propose a feasible approach based on the interactive multiple model (IMM) which is a widely used algorithm for estimation of hybrid systems in the scientific community.  ...  The authors would like to thank Professor Claire Tomlin from University of California, Berkeley for insightful discussions on hybrid systems and the members of the staff of the California Institute for  ... 
doi:10.1109/tac.2014.2342151 fatcat:pnp6fzrv4nax3prnqkzie4vnim

State Estimation for the discretized LWR PDE using explicit polyhedral representations of the Godunov scheme

Jerome Thai, Boris Prodhomme, Alexandre M. Bayen
2013 2013 American Control Conference  
It uses a Godunov scheme to discretize the socalled Lighthill-Whitham-Richards equation with a triangular flux function, and proves that the resulting nonlinear dynamical system can be decomposed in a  ...  Numerical results are presented using the Mobile Millennium data set, and compared to results obtained using ensemble Kalman filtering, which is used for estimation in traffic monitoring.  ...  ACKNOWLEDGEMENTS The authors would like to thank the members of the staff of the California Institute for Innovative Transportation for its contributions to develop, build, and deploy the system infrastructure  ... 
doi:10.1109/acc.2013.6580198 fatcat:4hkve7p7oveyhgjvuh3p6aokye

2015 Index IEEE Transactions on Automatic Control Vol. 60

2015 IEEE Transactions on Automatic Control  
., TAC Feb. 2015 383-392 State Estimation for Polyhedral Hybrid Systems and Applications to the Godunov Scheme for Highway Traffic Estimation.  ...  ., +, TAC Jan. 2015 265-270 State Estimation for Polyhedral Hybrid Systems and Applications to the Godunov Scheme for Highway Traffic Estimation.  ... 
doi:10.1109/tac.2015.2512305 fatcat:5gut6qeomfh73fwfvehzujbr5q

Perspective on unstructured grid flow solvers

V. Venkatakrishnan
1996 AIAA Journal  
The integration of these components into an overall framework to solve practical problems is addressed.  ...  Different spatial and temporal discretization options for steady and unsteady flows are discussed.  ...  M -= I, the simplest way to solve the system of ODE's is to use an explicit scheme.  ... 
doi:10.2514/3.13101 fatcat:ihw66pcsxfa65k4okgt3ssmxkm

Multidimensional, compressible viscous flow on a moving Voronoi mesh

D. J. Muñoz, V. Springel, R. Marcus, M. Vogelsberger, L. Hernquist
2012 Monthly notices of the Royal Astronomical Society  
Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes.  ...  We propose a new approach to compute accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a finite volume solver of the Navier-Stokes equations.  ...  We are thankful to Joseph Barranco, Paul Duffel, Patrik Jonsson, Andrew MacFadyen and Debora Sijacki for helpful discussions.  ... 
doi:10.1093/mnras/sts015 fatcat:blztiktmdrgpboaaatm4e5fxau

Arbitrary-Lagrangian–Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

Walter Boscheri, Michael Dumbser
2017 Journal of Computational Physics  
Our numerical method belongs to the category of direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already  ...  The numerical convergence rates of the new ALE ADER-DG schemes are studied up to fourth order in space and time and several test problems are simulated.  ...  A widespread technique for the solution of nonlinear hyperbolic systems of PDE is given by Godunov-type finite volume schemes [74,126].  ... 
doi:10.1016/j.jcp.2017.06.022 fatcat:wzwrxo5ufjhavamb3txl23i4we

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
Transport processes are common in geoscience applications, and find their way into models of, e.g., the atmosphere, oceans, shallow water, subsurface, seismic inversion, and deep earth.  ...  Our approach is to develop locally conservative Eulerian-Lagrangian (or semi-Lagrangian) methods combined with ideas from Eulerian WENO schemes, since they have the potential to attain the desired properties  ...  We show how to solve the equations using a global implicit approach in an efficient way, and we present the derived computational results.  ... 
doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi

Author Index Volume 235 (2011)

2011 Journal of Computational and Applied Mathematics  
Prozorov and G. Vainikko, Application of the discrete Fourier transform to solving the Cauchy integral equation 1317-1325 Komori, Y. and K.  ...  estimates for an operator-splitting method for Navier-Stokes equa- tions: Second-order schemes" [J.  ... 
doi:10.1016/s0377-0427(11)00383-9 fatcat:iydszqpkezgivirtbnwhpwere4

Splitting-based domain decomposition methods for two-phase flow with different rock types [article]

Elyes Ahmed
2019 arXiv   pre-print
To adapt to different time scales of problem components and different rock types, the novel scheme uses a multirate time stepping strategy, by taking multiple finer time steps for saturation-advection  ...  For the discretization, the saturation-advection problem is approximated with the explicit Euler method in time, and in space with the cell-centered finite volume method of first order of Godunov type.  ...  The author thanks Jérôme Jaffré and Jean E. Roberts for helpful discussions.  ... 
arXiv:1906.03470v2 fatcat:nztb2xrky5gcldtw3rffbjk4ci

On the Convergence of SPH Method for Scalar Conservation Laws with Boundary Conditions

Bachir Ben Moussa
2006 Methods and Applications of Analysis  
To take into account nonlinear effects in agreement with Bardos, LeRoux and Nedelec boundary conditions ([1], [14] ), the state at the boundary is computed by solving appropriate Riemann problems.  ...  The convergence analysis in L p loc (p < ∞) is achieved thanks to the uniqueness result of measure-valued solutions recently established in [3] for L ∞ initial and boundary data.  ...  The author is grateful to two referees for valuable comments and suggestions. This work has been partly supported by the European network HYKE, funded by the EC contract HPRN-CT-2002-00282.  ... 
doi:10.4310/maa.2006.v13.n1.a3 fatcat:zjdjwxf3mjgarasgszunpb2ahm

The mathematics of finite elements and applications

1989 International Journal of Engineering Science  
That theory has been shown to produce good -"--" results for general elliptic systems and general hp-finite element methods.  ...  For an error estimation, use is made of a new approach which is based on the work of Ainsworth, Wu and the author.  ...  M AINSWORTH A posteriori error estimation for finite element approximation of Stokes' problem A new approach to a posteriori error estimation for linear elasticity and Stokes problems, and which is applicable  ... 
doi:10.1016/0020-7225(89)90012-8 fatcat:z6hknn325re4tbssbqqzmcketa

Stability analysis of the cell centered finite-volume Muscl method on unstructured grids

F. Haider, J.-P. Croisille, B. Courbet
2009 Numerische Mathematik  
In contrast, a general theoretical result is very difficult to obtain for the MUSCL scheme.  ...  The goal of this study is to apply the MUSCL scheme to the linear advection equation on general unstructured grids and to examine the eigenvalue stability of the resulting linear semi-discrete equation  ...  The application of the MUSCL scheme and the method of lines to a hyperbolic conservation law produces a dynamical system whose stability can be examined by the theory of dynamical systems.  ... 
doi:10.1007/s00211-009-0242-6 fatcat:vfspcde3cbe7xmyzelqpmuzrfu

A perspective on computational algorithms for aerodynamic analysis and design

Antony Jameson
2001 Progress in Aerospace Sciences  
In the future multidisciplinary analysis and optimization should be combined to take account of the trade-offs in the overall performance of the complete system.  ...  It addresses the requirements for effective industrial use, and trade-offs between modeling accuracy and computational costs.  ...  I am grateful to Juan J. Alonso and Luigi Martinelli for their assistance in assembling the text of this document.  ... 
doi:10.1016/s0376-0421(01)00004-5 fatcat:cptm6xoegbehfg7b2lt3bttbde

Domain Decomposition Approach for Automatic Parallel Generation of Tetrahedral Grids

E.G. Ivanov, H. Andrä, A.N. Kudryavtsev
2006 Computational Methods in Applied Mathematics  
The geometrical domain decomposition approach has been applied. It allows us to use classic 2D and 3D high-quality Delaunay mesh generators for independent and simultaneous volume meshing.  ...  The desire to simulate more and more geometrical and physical features of technical structures and the availability of parallel computers and parallel numerical solvers which can exploit the power of these  ...  Godunov for his interest to this work and many comments on subject.  ... 
doi:10.2478/cmam-2006-0009 fatcat:kfrmskwu4bgdpi3p4eyqyjvjb4
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