Journal ArticleDOI
Regular Article: Finite Difference Schemes for ∂u/∂t=(∂/∂x) α δG/δu That Inherit Energy Conservation or Dissipation Property
TLDR
In this article, the authors propose a new procedure for designing by rote finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations, such as the Korteweg-de Vries (KdV) equation and the Cahn-Hilliard equation.About:
This article is published in Journal of Computational Physics.The article was published on 1999-11-20. It has received 147 citations till now. The article focuses on the topics: Partial differential equation & Korteweg–de Vries equation.read more
Citations
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Journal ArticleDOI
Symmetry-preserving discretization of turbulent flow
Roel Verstappen,Arthur Veldman +1 more
TL;DR: In this article, a symmetry-preserving discretization of the Navier-Stokes equations is shown to be stable on any grid, and conserves the total mass, momentum and kinetic energy.
Journal ArticleDOI
Conservative multigrid methods for Cahn-Hilliard fluids
TL;DR: A conservative, second-order accurate fully implicit discretization of the Navier-Stokes and Cahn-Hilliard system that has an associated discrete energy functional is developed and convergence of the scheme numerically in both the presence and absence of flow is demonstrated.
Journal ArticleDOI
Preserving energy resp. dissipation in numerical PDEs using the Average Vector Field method
Elena Celledoni,Volker Grimm,Robert I. McLachlan,David I. McLaren,Dion R. J. O’Neale,Brynjulf Owren,G. R. W. Quispel +6 more
TL;DR: This work gives a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly.
Journal ArticleDOI
A stable and conservative finite difference scheme for the Cahn-Hilliard equation
TL;DR: A stable and conservative finite difference scheme to solve numerically the Cahn-Hilliard equation which describes a phase separation phenomenon and inherits characteristic properties, the conservation of mass and the decrease of the total energy, from the equation.
Journal ArticleDOI
Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
Takayasu Matsuo,Daisuke Furihata +1 more
TL;DR: In this paper, a new procedure for designing finite-difference schemes that inherit energy conservation or dissipation property from complex-valued nonlinear partial differential equations (PDEs), such as the nonlinear Schrodinger equation, the Ginzburg-Landau equation, and the Newell-Whitehead equation, was proposed.
References
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Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
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Über die partiellen Differenzengleichungen der mathematischen Physik
TL;DR: In this paper, the authors present a Gebrauch bestimmt ausschließlich für den persönlichen, nicht kommerziellen Gebrauchs, which is a rechtschutzbestimmter gebrauch, and gilt vorbehaltlich der folgenden Einschränkungen.
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Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
Difference methods for initial-value problems
Robert D. Richtmyer,K. W. Morton +1 more
TL;DR: In this article, differentielles and stabilite were used for differentiable transport in the context of transfert de chaleur and ondes Reference Record created on 2005-11-18, modified on 2016-08-08
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Symplectic integrators for Hamiltonian problems: an overview
TL;DR: Symplectic integrators as mentioned in this paper are numerical methods specifically aimed at advancing in time the solution of Hamiltonian systems, which is a characteristic property possessed by the solutions of the Hamiltonian problems.