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On Large Time Step Godunov Scheme for Hyperbolic Conservation
"... In this paper we study the large time step (LTS) Godunov scheme proposed by LeVeque for nonlinear hyperbolic conservation laws. As we known, when the Courant number is larger than 1, the linear interactions of the elementary waves in this scheme will be much more complicated than those for Courant n ..."
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In this paper we study the large time step (LTS) Godunov scheme proposed by LeVeque for nonlinear hyperbolic conservation laws. As we known, when the Courant number is larger than 1, the linear interactions of the elementary waves in this scheme will be much more complicated than those for Courant
Large timestep positivitypreserving method for multiphase flows
"... Summary. Using a relaxation strategy in a LagrangianEulerian formulation, we propose a scheme in local conservation form for approximating weak solutions of complex compressible flows involving wave speeds of different orders of magnitude. Explicit time integration is performed on slow transport wa ..."
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Cited by 1 (1 self)
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waves for the sake of accuracy while fast acoustic waves are dealt with implicitly to enable large time stepping. A CFL condition based on the slow waves is derived ensuring positivity properties on the density and the mass fraction. Numerical benchmarks validate the method. 1 Statement of the problem
Entropysatisfying relaxation method with large timesteps for Euler IBVPs
, 2007
"... This paper could have been given the title: “How to positively and implicitly solve Euler equations using only linear scalar advections. ” The new relaxation method we propose is able to solve Eulerlike systems —as well as initial and boundary value problems — with real state laws at very low cost, ..."
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Cited by 7 (4 self)
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of entropy inequality, under an expressible bound on the CFL ratio. The design of this optimal timestep, which takes into account data not only from the inner domain but also from the boundary conditions, is the main novel feature we emphasize on.
www.elsevier.com/locate/apnum On large timestepping methods for the Cahn–Hilliard equation
, 2006
"... In this work, we will analyze a class of large timestepping methods for the Cahn–Hilliard equation. The equation is discretized by Fourier spectral method in space and semiimplicit schemes in time. For firstorder semiimplicit scheme, the stability and convergence properties are investigated base ..."
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In this work, we will analyze a class of large timestepping methods for the Cahn–Hilliard equation. The equation is discretized by Fourier spectral method in space and semiimplicit schemes in time. For firstorder semiimplicit scheme, the stability and convergence properties are investigated
Large timestep numerical modelling of the flow of Maxwell materials
, 2003
"... Maxwell viscoelastic materials are commonly simulated numerically in order to model the stresses and deformations associated with largescale earth processes, such as mantle convection or crustal deformation. Both implicit and explicit timemarching methods require that the timesteps used be small ..."
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Maxwell viscoelastic materials are commonly simulated numerically in order to model the stresses and deformations associated with largescale earth processes, such as mantle convection or crustal deformation. Both implicit and explicit timemarching methods require that the timesteps used
Equicontinuity Of Some Large TimeStep Approximations To Convex HamiltonJacobi Equations
"... . We consider a class of semilagrangian highorder approximation schemes for convex HamiltonJacobi equations. In this framework, we prove that under certain restrictions on the relationship between \Deltax and \Deltat, the sequence of approximate solutions is uniformly Lipschitz continuous (and ..."
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. We consider a class of semilagrangian highorder approximation schemes for convex HamiltonJacobi equations. In this framework, we prove that under certain restrictions on the relationship between \Deltax and \Deltat, the sequence of approximate solutions is uniformly Lipschitz continuous (and hence, by standard arguments, that it admits a subsequence converging to the exact solution). The argument is suitable for most reconstructions of interest, including highorder polinomials and Essentially NonOscillatory (ENO) reconstructions. Key words. Convex HamiltonJacobi equations, highorder schemes, semilagrangian schemes, convergence. AMS(MOS) subject classification. 65M25, 65M12, 65M06. 1. Introduction. Although the numerical solution of first order HamiltonJacobi equations is a widely studied topic in many applications, it is well known that, when highorder schemes are considered (see [OS], [JP], [LT1]), very few convergence results are available (one such result is g...
Convergence of Godunovtype schemes for scalar conservation laws under large time steps
 SIAM J. Numer. Anal
"... In this paper, we consider convergence of classical high order Godunovtype schemes towards entropy solutions for scalar conservation laws. It is well known that sufficient conditions for such convergence include total variation boundedness of the reconstruction and cell or wavewise entropy inequal ..."
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Cited by 3 (0 self)
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inequalities. We prove that under large time steps, we only need total variation boundedness of the reconstruction to guarantee such convergence. We discuss high order total variation bounded reconstructions to fulfill this sufficient condition and provide numerical examples on one dimensional convex
Numerical Solution Of Reservoir Flow Models Based On Large Time Step Operator Splitting Algorithms
 FILTRATION IN POROUS MEDIA AND INDUSTRIAL APPLICATIONS, LECTURE NOTES IN MATHEMATICS
, 1999
"... During recent years the authors and collaborators have been involved in an activity related to the construction and analysis of large time step operator splitting algorithms for the numerical simulation of multiphase flow in heterogeneous porous media. The purpose of these lecture notes is to revie ..."
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Cited by 46 (22 self)
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During recent years the authors and collaborators have been involved in an activity related to the construction and analysis of large time step operator splitting algorithms for the numerical simulation of multiphase flow in heterogeneous porous media. The purpose of these lecture notes
Results 1  10
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