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464
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
 J. COMP. PHYS
, 1981
"... Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution ..."
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Cited by 1010 (2 self)
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Several numerical schemes for the solution of hyperbolic conservation laws are based on exploiting the information obtained by considering a sequence of Riemann problems. It is argued that in existing schemes much of this information is degraded, and that only certain features of the exact solution
Deciding the nature of the coarse equation through microscopic simulations: the BabyBathwater scheme
 SIAM MMS
"... Abstract. Recent developments in multiscale computation allow the solution of coarse equations for the expected macroscopic behavior of microscopically evolving particles without ever obtaining these coarse equations in closed form. The closure is obtained on demand through appropriately initialized ..."
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Cited by 23 (10 self)
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the equation satisfies certain conservation laws, and (c) whether the coarse dynamics is Hamiltonian. These decisions affect the number and type of boundary conditions as well as the algorithms employed in good solution practice. In the absence of an explicit formula for the temporal derivative, we propose
The Conservation Law
, 2001
"... Introduction For more than 150 years, starting with mechanical systems, the fact that certain quantities such as energy, momentum, etc. are constant in physical processes has led to an increasing number of conservation laws. With the advent of quantum physics, new conserved quantities, such as bary ..."
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Introduction For more than 150 years, starting with mechanical systems, the fact that certain quantities such as energy, momentum, etc. are constant in physical processes has led to an increasing number of conservation laws. With the advent of quantum physics, new conserved quantities
On Hamiltonian perturbations of hyperbolic systems of conservation laws
, 2004
"... We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially onedimensional systems of hyperbolic PDEs vt + [φ(v)]x = 0. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders of the pert ..."
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Cited by 74 (12 self)
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We study the general structure of formal perturbative solutions to the Hamiltonian perturbations of spatially onedimensional systems of hyperbolic PDEs vt + [φ(v)]x = 0. Under certain genericity assumptions it is proved that any bihamiltonian perturbation can be eliminated in all orders
Transitional waves for conservation laws
 SIAM J. Math. Anal
, 1990
"... Abstract. A new class of fundamental waves arises in conservation laws that are not strictly hyperbolic. These waves serve as transitions between wave groups associated with particular characteristic families. Transitional shock waves are discontinuous solutions that possess viscous profiles but do ..."
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Cited by 37 (11 self)
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for conservation laws with quadratic fluxes and arbitrary viscosity matrices; this family comprises all transitional shock waves for a certain class of such quadratic models. The paper also establishes, for general systems of two conservation laws, the generic nature of rarefaction curves near an elliptic region
Numerical Schemes For Hyperbolic Conservation Laws With Stiff Relaxation Terms
 J. Comput. Phys
, 1996
"... Hyperbolic systems often have relaxation terms that give them a partially conservative form and that lead to a longtime behavior governed by reduced systems that are parabolic in nature. In this article it is shown by asymptotic analysis and numerical examples that semidiscrete high resolution meth ..."
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Cited by 77 (11 self)
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methods for hyperbolic conservation laws fail to capture this asymptotic behavior unless the small relaxation rate is resolved by a fine spatial grid. We introduce a modification of higher order Godunov methods that possesses the correct asymptotic behavior, allowing the use of coarse grids (large cell
Numerical Methods For Hyperbolic Conservation Laws With Stiff Relaxation I. Spurious Solutions
 SIAM J. Sci. Comput
, 1992
"... . We consider the numerical solution of hyperbolic systems of conservation laws with relaxation using a shock capturing finite difference scheme on a fixed, uniform spatial grid. We conjecture that certain a priori criteria insure that the numerical method does not produce spurious solutions as the ..."
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Cited by 73 (2 self)
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. We consider the numerical solution of hyperbolic systems of conservation laws with relaxation using a shock capturing finite difference scheme on a fixed, uniform spatial grid. We conjecture that certain a priori criteria insure that the numerical method does not produce spurious solutions
Legendre Pseudospectral Viscosity Method For Nonlinear Conservation Laws
 SIAM J. Numer. Anal
, 1993
"... . In this paper we study the Legendre Spectral Viscosity (SV) method for the approximate solution of initialboundary value problems associated with nonlinear conservation laws. We prove that by adding a small amount of spectral viscosity, bounded solutions of the Legendre SV method converge to the e ..."
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Cited by 59 (8 self)
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. In this paper we study the Legendre Spectral Viscosity (SV) method for the approximate solution of initialboundary value problems associated with nonlinear conservation laws. We prove that by adding a small amount of spectral viscosity, bounded solutions of the Legendre SV method converge
StationarityConservation Laws for Certain Linear Fractional Differential Equations
, 2001
"... The Leibniz’s rule for fractional RiemannLiouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz’s rule is used in construction of explicit form of stationaryconserved currents for linear fractional differential equations. The ex ..."
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The Leibniz’s rule for fractional RiemannLiouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz’s rule is used in construction of explicit form of stationaryconserved currents for linear fractional differential equations
Results 1  10
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464