Legendre integrators , post - processing and quasiequilibrium
نویسندگان
چکیده
A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical post-processing, and the thermodynamic projector. The thermodynamic projector is the tool to transform almost any anzatz to a thermodynamically consistent model. The post-processing is the cheapest way to improve the solution obtained by the Legendre integrators. Legendre integrators give the opportunity to solve linear equations instead of nonlinear ones for quasiequilibrium (“maximum entropy”, MaxEnt) approximations. The essentially new element of this toolbox, the method of thermodynamic projector, is demonstrated on application to the FENE-P model of polymer kinetic theory. The multi-peak model of polymer dynamics is developed. © 2004 Elsevier B.V. All rights reserved.
منابع مشابه
A ug 2 00 3 Legendre Integrators , Post - Processing and Quasiequilibrium
A toolbox for the development and reduction of the dynamical models of nonequilibrium systems is presented. The main components of this toolbox are: Legendre integrators, dynamical postprocessing, and thermodynamic projector. Thermodynamic projector is the tool to transform almost arbitrary anzatz to a thermodynamically consistent model, the postprocessing is the cheapest way to improve the sol...
متن کاملDiscrete Hamiltonian variational integrators
We derive a variational characterization of the exact discrete Hamiltonian, which is a Type II generating function for the exact flow of a Hamiltonian system, by considering a Legendre transformation of Jacobi’s solution of the Hamilton–Jacobi equation. This provides an exact correspondence between continuous and discrete Hamiltonian mechanics, which arise from the continuousand discrete-time H...
متن کاملMulti-Symplectic Runge-Kutta Collocation Methods for Hamiltonian Wave Equations
A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss-Legendre collocation in space and time leads to multi-symplectic integrators, i.e., to numerical methods that preserve a symplectic conservation law similar to the conservation of symplect...
متن کاملEccentricity content of binary black hole initial data
Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this pr...
متن کاملVariational integrators for constrained dynamical systems
A variational formulation of constrained dynamics is presented in the continuous and in the discrete setting. The existing theory on variational integration of constrained problems is extended by aspects on the initialization of simulations, the discrete Legendre transform and certain postprocessing steps. Furthermore, the discrete null space method which has been introduced in the framework of...
متن کامل