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275
An Instability of the Godunov Scheme
, 2005
"... We construct a solution to a 2 × 2 strictly hyperbolic system of conservation laws, showing that the Godunov scheme [12] can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glim ..."
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Cited by 3 (3 self)
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We construct a solution to a 2 × 2 strictly hyperbolic system of conservation laws, showing that the Godunov scheme [12] can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from
On a rough Godunov scheme
, 1996
"... We are interested in the numerical resolution of hyperbolic systems of conservation laws which don't allow any analytical calculation and for which it is difficult to use classical schemes such as Roe's scheme. We introduce a new finite volume scheme called VFRoe. As the Roe scheme, it is ..."
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Cited by 14 (1 self)
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, it is based on the local resolution of a linearized Riemann problem. The numerical flux is defined following the Godunov scheme, as the physical flux evaluated at the interface value of the linearized solver. The VFRoe scheme is conservative and consistent without fulfilling any Roe's type condition
GODUNOV SCHEME FOR MAXWELL’S EQUATIONS WITH
"... Abstract. We study the Godunov scheme for a nonlinear Maxwell model arising in nonlinear optics, the Kerr model. This is a hyperbolic system of conservation laws with some eigenvalues of variable multiplicity, neither genuinely nonlinear nor linearly degenerate. The solution of the Riemann problem ..."
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Abstract. We study the Godunov scheme for a nonlinear Maxwell model arising in nonlinear optics, the Kerr model. This is a hyperbolic system of conservation laws with some eigenvalues of variable multiplicity, neither genuinely nonlinear nor linearly degenerate. The solution of the Riemann problem
GODUNOV SCHEMES FOR COMPRESSIBLE MULTIPHASE FLOWS
"... Abstract. Compressible multiphase models have been studied for a long time inspired on different applications in diverse engineering areas. Solutions for these equations are not simple and researcher have spent much time trying to bring answers. The possibility to properly solve these equations and ..."
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and perform real simulations represent a very ambitious goal. Today new numerical techniques show a promising path to reach the goal. We are concerned with the construction of Godunovtype schemes for compressible multiphase flows. In particular we study finite volume methods for the BaerNunziato equa
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
An ImplicitExplicit Eulerian Godunov Scheme for Compressible
, 1995
"... A hybrid implicitexplicit scheme is developed for Eulerian hydrodynamics. The hybridi~atlon is a continuous switch and operates on each characteristic field separately. The explicit scheme is a version of the secondorder Godunov scheme; the implicit method is only firstorder accurate in time but l ..."
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Cited by 7 (1 self)
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A hybrid implicitexplicit scheme is developed for Eulerian hydrodynamics. The hybridi~atlon is a continuous switch and operates on each characteristic field separately. The explicit scheme is a version of the secondorder Godunov scheme; the implicit method is only firstorder accurate in time
Adaptive mesh redistribution method based on Godunovs scheme
 Commun. Math. Sci
, 2003
"... Abstract. In this work, a detailed description for an efficient adaptive mesh redistribution algorithm based on the Godunov’s scheme is presented. After each mesh iteration a secondorder finitevolume flow solver is used to update the flow parameters at the new time level directly without using in ..."
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Cited by 7 (3 self)
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Abstract. In this work, a detailed description for an efficient adaptive mesh redistribution algorithm based on the Godunov’s scheme is presented. After each mesh iteration a secondorder finitevolume flow solver is used to update the flow parameters at the new time level directly without using
SEMIGODUNOV SCHEMES FOR MULTIPHASE FLOWS IN POROUS MEDIA
"... Abstract. We describe a class of finite volume schemes for 2 × 2 systems of conservations laws based on a”local ” decomposition of the system into a series of single conservaton laws but with discontinuous coefficients. The resulting schemes are based on Godunov type solvers of the reduced equations ..."
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Cited by 2 (0 self)
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Abstract. We describe a class of finite volume schemes for 2 × 2 systems of conservations laws based on a”local ” decomposition of the system into a series of single conservaton laws but with discontinuous coefficients. The resulting schemes are based on Godunov type solvers of the reduced
Convergence of Godunov scheme for straight line systems
 Chinese Ann. Math
, 2000
"... Consider the Cauchy problem for an n × n system of the form ut +A(u)ux = 0, u(x, 0) = ū(x). (1) Here A(u) is a map from a domain U ⊂ Rn into Rn×n, and (x, t) ∈ R×R+. We assume strict hyperbolicity, i. e. the the matrix A(u) has n real and strictly dif ..."
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Cited by 2 (0 self)
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Consider the Cauchy problem for an n × n system of the form ut +A(u)ux = 0, u(x, 0) = ū(x). (1) Here A(u) is a map from a domain U ⊂ Rn into Rn×n, and (x, t) ∈ R×R+. We assume strict hyperbolicity, i. e. the the matrix A(u) has n real and strictly dif
Results 1  10
of
275